LHM - Level C - Teacher's Guide by lighthousecurriculum

Teacher's Guide

LEVEL C - TEACHER'S GUIDE

Lighthouse Math

Program Directors

Mrs. Zehava Kraitenberg M.S. Curriculum Advisor, Elementary School Principal

Jane Chamberlain Master of Education, Curriculum and Instruction

Credits

Curriculum Writers

Jane Chamberlain Middle School Math

Instructor M.Ed in Curriculum and Instruction

Susannah Maria Malarkey 4th Grade Instructor

M.A. in Teaching K-8

Karen Williams 5th Grade Instructor

PhD of Education in Curriculum and Instruction

Karen Legreid Math Interventionist K-5

M.A. in Curriculum and Instruction

Mizuho Shiomi 3rd Grade Instructor

M.A. of Arts in Education K-8

Joy Aragones 4th Grade Instructor

M.A. in Education Technology

Chelsea Ruocco 6th Grade Instructor

M.A. in Childhood Education 1-6

Kelly Boehme 1st Grade Instructor

M.Ed. in Elementary Education K-6

Jennifer Ramos-Martinez Curriculum Specialist

M.A. in Curriculum and Instruction

Rebecca Kay-Lewis 5th Grade Instructor

M.Ed. in Elementary Education K-6, 5-8 Math

Sarah Thorman 2nd/3rd Grade Instructor

B.S. Liberal Arts and Sciences (Psychology)

Post-Baccalaureate Teacher Certification (Grades K-6)

Francine S. Foote 5th and 6th Grade Instructor

M.A. in Instruction and Curriculum

Review Team

Zehava Kraitenberg M.S. Curriculum Advisor

Elementary School Principal

Layout & Design

Akiva Leitner Project Manager Kevanyc.com

Jane Chamberlain Middle School Math Instructor M.Ed. in Curriculum and Instruction

Elizabeth Szoc 4th Grade Instructor

B.A. in Elementary Education

Luke Bote K-12 Instructor

M.Ed. in Leadership

Molly Fernholz

K-6 Instructor

B.A. in Education

Joanna Bell 7th - 12th Grade Instructor

B.S. in Integrated Math Education

Yehuda Gartenhaus M.A. Elementary School Principal Mechi Weizer Curriculum Advisor Elementary School Principal

Mirko Zunic/Branko Pejovic Layout Directors

Distributed by Leren Curriculum Inc. T: 718-.834.1231 E: lerenec@gmail.com

Lighthouse Math Teacher's Guide level C • ISBN 978-1-955773-09-6

Issac Flores Illustration Director

No part of this publication may be reproduced, stored in a retrieval system, stored in a database and/or published in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher. To obtain permission to use portions of material from this publication, please contact Lighthouse curriculum.

Content developed in collaboration with The Reimagined Classroom

Contact Lighthouse curriculum: By calling: 718.285.7100, or emailing: info@lighthousecurriculum.com For more information visit www.lighthousecurriculum.com

Introduction and overview of skills at the beginning of each chapter

Vocabulary words with checkboxes for students to check off as they go through the lessons

Clearly coded lessons: blue for the lesson page, red for the exercise page

Let’s learn! helps introduce the concept

Try it together! provides guided practice as a class

Practice provides plenty of problems to practice the skill

Tabs on the top of each page allow you to find chapters and lessons easily

Teacher notes give tips and ideas to guide teachers during the lesson

Icons provide clear, visual instructions to help students understand the directions

About the Curriculum

The program builds in review and new concepts throughout each level as students step up through mastery of skills. By providing foundational skills and practice, students retain information. The stepwise approach is consistent as students work through 14 chapters comprising 8 lessons of review, new skills, guided practice and problem-solving. All lessons include step-by-step instructions for clarity, giving all teachers the tools for success.

Custom illustrations provide a vibrant learning experience. Illustrations complement math questions by including information directly tied to and used to solve the problem. The books are formatted in a way that each grade level can be completed successfully by the culmination of the school year. Lighthouse Math gives teachers the tools they need to teach and gives students everything they need to learn.

Name Date

Let’s learn!

Solving Two-Step Story Problems

Two-Step Story Problem: What do we know?

The teacher has 7 boxes of crayons. There are 8 crayons inside each box. Noah lost 17 crayons. How many crayons are left?

Visualize: There are 7 boxes of 8 crayons 17 crayons were lost What do we need to know and how can we ﬁnd out?

Step 1: How many total crayons are there?

Use T to represent Total crayons.

Step 2: How many crayons are left? Use L to represents crayons Left Noah had 56 crayons and lost 17 T - 17 = L L = 7 groups of 8 or 7 × 8 = T T =

Try it together!

Solve the 2-step problems. Write equations with a letter for the unknowns.

1. Mom put 30 fruit chews and 18 candy bars in a bowl. Then she made 8 goodie bags with the same number of candies per bag. How many pieces were in each bag?

C = total pieces of Candy

B = pieces of candy in each Bag

Step 1: 30 + 18 = C =

Step 2: C ÷ 8 = B =

Teacher Notes

2. Joe collects stu ed bears. He has 4 brown bears and 5 black bears. Each bear cost him $5, so how much did he spend on the bears?

= number of bears Joe has = total cost of the bears

Step 1:

Step 2:

Answer:

Walk students through the steps of solving the example problem. First, have students visualize what is happening in the problem. Remind students that they can always draw a picture to help them solve a story problem. Ask “What do we know?” Then tell them to think about what they need to ﬁnd out and which operations they need to perform on the numbers to solve the problem. Point out the underlined words “groups of” and “lost” that tell them they need to multiply and then subtract. Tell students that they can choose any letter to use in place of the unknown.

Lighthouse Math | Level C Chapter 8 Lesson 1

Table of Contents. A quick reference for skills and topics found in each chapter

How to use the student book

y The book is “all in one” and can easily be used without extra resources

y Easy to read numbers and spaces for student writing

y Custom images to assist in learning concepts

Each chapter has 8 lessons made up of 2 color-coded pages: (See page inserts for each left and right)

y Learning page (blue) provides daily review, guided lesson, and problems to complete together as a class

y Exercise page (red) provides practice problems for students to do independently or in groups, for class discussion, daily work or homework

Chapter 3

In Chapter 3, we will learn about understanding multiplication 0–5.

• Understand that multiplication is an extension of addition and is used to solve problems

• Add equal groups to help ﬁnd the total number of objects

• Use repeated addition to extend basic addition to counting larger quantities

• Use arrays to help us visualize how equal groups can be arranged to quickly calculate totals

• Skip counting increases mastery of “multiples”

• Knowing how factors relate to products helps build math understanding for division

• Multiplying by 1 results in a product identical to the other factor

• Multiplying by 0 results in a quantity of 0

• Knowing that the order of factors does not change the product helps us memorize math facts

• Using manipulatives and counting games makes multiplication a more concrete concept

• Noticing patterns through methods such as skip counting builds a knowledge of multiples

Intro to the chapter

y Provides an overview of skills covered in the chapter with images and easy to read bullet points

y Vocabulary

Listed with checkboxes on the chapter intro page

Students and teachers can check off the vocabulary as they learn and use it

Chapter Assessments

are provided after 8 lessons at the end of each chapter.

y 1 blackline page with problems that cover each lesson from the chapter.

Levels A & B have 4 problems.

Level C has 10 computation problems plus 2 problem-solving applications

Lesson 8 review lesson to prepare students for the chapter assessment

About the Program

Direct Instruction (Let’s learn)

y Custom made visuals and images directly linked to content

y Students are immediately engaged with a problem-solving task that promotes mathematical reasoning skills. These tasks allow for multiple points of entry, varied solution strategies, and provide opportunities for meaningful mathematical discussions

Guided Practice

(Try it together/ Learn and Connect)

y Provides for a gradual release of responsibility in solving the problems from the teacher onto the students.

Hands-on Partner and Group Activities

y Engages students in a productive struggle with the lesson concepts.

y Provides students with an opportunity to construct arguments and critique the reasoning of their peers.

Independent Practice (Daily review, Practice)

y Provides students with plenty of opportunities for repetition which builds fluency and helps them relate mathematical procedures to conceptual understanding. The teacher is able to differentiate to meet the needs of the class and of individual students.

Problem Solving Skills (Challenge, Word problems)

y Students apply skills to real-world problem-solving situations.

y Allows for extensions of learning and application opportunities

y Provides students opportunities to engage in mathematical discussion and sharing

Game-Based Learning

y Allows for students to learn and connect in a different way which leads to further retention

y Research shows that games provide an environment for learning and engaging with the concepts in multiple ways

y Games can provide a mind-body connection, reach students at all levels, open up conversations and communication about mathematics, and keep students motivated

Formative Assessment

y Quick assessments at the end of each lesson allow teachers to see evidence of student thinking, evaluate progress toward the learning goals, and adjust their instruction accordingly.

Summative Assessment

y Chapter assessments directly linked to the lessons to test mastery of skills

y Consistent in length and format that includes a variety of problems

y Teacher notes and sample problems to help guide students through instructions

Common Errors

y Notes and examples for teachers about common errors or what to look for when guiding students through a lesson

Differentiated Instruction

y Extra practice and support to help both struggling learners and early finishers

Spiral Review

y Daily review and warm-up activities provide a quick check of skills

y Important arithmetic skills are reinforced and reviewed throughout the levels

y All levels begin with a comprehensive review of foundational skills

Begin the lesson with direct instruction

Read the problem together and discuss the model or image provided

Use icons to assist with learning how to follow instructions independently

Interact with the visual model to find important information and apply it to the lesson or problem

Use Try it Together as a guided practice to help students try the problems on their own or with the class. Use this section to work together and discuss questions and answers. It provides gradual release to help guide teachers and students through the process in a stepwise fashion. Evaluate student understanding and add clarity before continuing with independent work

Name Date

Let’s learn!

Use skip counting and arrays to multiply by 4 s. Fill in the missing numbers.

Which #s are the factors?

Which # is the product?

Try it together!

Fill in the blanks.

3. Complete the multiplication table.

Fill in the blanks.

Find the product.

Teacher Notes

Direct instruction for teachers to read to assist with pre-readers or guided practice

Help Flash and figure out problems together

Use Step by Step guides to learn how to solve the problem

Refer to notes to find tips and lesson ideas for teacher guidance

Use sample problems to review steps and directions and complete answers by tracing along the dashed outline

Continue practice or assign problems for independent

A large number of problems to allow for differentiated instruction and practice. Choose odd number problems to complete first or choose some problems to assign

How to use the Teacher Guide

y Use the teacher guide to complement the student workbook.

y The exact version of student pages is shown with a green answer key

y Easy to use, consistent and color-coded sections

y Guide students through the workbook with extra activities, pre-requisite skills and game-based learning

y Differentiate with additional tips for both struggling learners and early finishers

Start off the class with review, mental math, or short activity so students can practice some math skills right away. A quick set of independent or class problems that include pre-requisite skills or warm-up activity

Use these questions to start the class, or ask them after the learning activity. Write the questions on the board to help guide the lesson for the day, so students can contemplate the answer and understand the big picture

Prepare your lesson

y Use objectives to guide you through the main idea.

y Quick reference and extra tips for vocabulary covered in the lesson.

y Materials list helps you be prepared to lead activities and be ready with resources

Pre-Lesson Warm-up

Guiding Questions

Use an activity or teacher prompts to get your students reading the book and answering questions together. Questions and dialogue for discussions are provided with answers to help guide the lesson. Prepare and lead group or partner activities to help reinforce the concepts

Copy of the student book pages with answers available for quick answer checks and corrections

Easy to find references to help differentiate your class.

Tips and ideas to assist learners who may need more support.

Struggling Learners

Students can make hops on a number line or hundreds chart to help them add the repeated addition equations. Explain that repeated addition is like skip counting. Also, provide counters or other objects for students to make groups and count up.

Early Finishers

For numbers 5 - 12, go back and write the equal groups

Challenge

with the 8 triangles. You can draw 4 circles and we will distribute the 8 triangles across the groups. First put 1 triangle in each circle, counting them as you go, 1, 2, 3, 4. Then put another triangle in each circle, counting them as you go, 5, 6, 7, 8. How many are in each group?” [2] “Write the equation 2 + 2 + 2 + 2 = 8.” If possible, have students do this with counters or other small objects. Give them 8 counters to distribute into 4 groups. Example:

Guide students to work in their student books Start with a problem together or help with another step-by-step guide. Find examples of work or tips for reading directions, showing work, and labeling answers correctly

Be on the lookout for common errors to help prevent mistakes or point out best practices

Do you have students who complete the work more quickly? Find activities or ideas to provide these students with useful work or sharing to reinforce concepts without just adding extra problems

Help guide students through problemsolving or challenge questions Extend the thought process by providing discussion points or writing about math so you can learn about how your students are thinking. Share and present ideas to hit upon performance learning and communication. This can also be used as a formative assessment for some of your advanced learners.

Find a game to help practice or learn the skill. Play and replay games to learn and review skills. Game-based learning has been shown to increase participation and communication. It increases problem-solving skills, provides students opportunities to explore concepts, fosters logic and decision making skills, and helps make learning more contextual and relevant

Every lesson comes with a quick assessment

This can be an exit ticket or quick check to see what your students learned that day. It can even be used as a short quiz and recorded to help you show progress and understanding. This allows you to determine whether your students are ready to move on or need more review. It can also help you determine homework or classwork assignments

Math Scope and Sequence

y Use the scope and sequence to see the main skills that are covered in each level

y Skills are organized through standards and grouped in an easy to read color-coded format

y The standards reference list is also included for details on standards and descriptions

y Both New York State Next Generation (NYS NG) and Common Core (CC) Standards are provided for each chapter

y The first chapters of the book cover arithmetic skills, practice and computation review to allow teachers to get a sense of student retention and skills at the beginning of each school year

Counting and Cardinality Number Sense

Number names

Count to tell the number of objects

Count in sequence

Compare numbers

Count within 1000; skip-count by 5s, 10s and 100s

Numbers and Operations in Base-Ten Place Value

Groups of ten, understand place value

Use place value to add and subtract within 100

Use place value for multi-digit operations - > than 1000

Explain patterns of 0 and powers of 10

Recognize that a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left

Round numbers to the nearest 10 or 100

Compare and order numbers

Round numbers to given place value

Read, write and compare decimals

Addition

Add within 100

10 more 10 less

Add more than 2 numbers

Math Scope and Sequence

Add within 1000 using models

Add multidigit numbers using standard algortithm with and without regrouping

Addition Properties

Understand and apply words used to describe addition, word problems

Add Money

Subtraction

Subtract within 100

Subtract within 1000 using models

Subtract multidigit numbers using standard algortithm with and without regrouping

Understand and apply words used to describe subtraction, word problems

Subtract Money

Multiplication

Multiply 1-digit whole numbers

Multiply 1 digit by multiples of 10

Multiply with strategies such as partial products, area models, arrays

Multipy by two 2-digit numbers

Estimate with multiplication

Multiply decimals

Multiplication Properties

Determine the unknown whole number in a multiplication or division equation relating three whole numbers

Multiply multi-digit numbers using the standard algorithm

Division

Division facts: Understand division as an unknown-factor problem.

Divide by 1 digit, no remainders

Find whole number quotients with dividends up to 4 digits and 1 digit divisors with and without remainders

Find whole number quotients with multi-digit dividends and 2 digit divisors with and without remainders

Divide decimals by whole numbers

Divide by a decimal

Divide and make the remainder a decimal or fraction

Interpret remainders

Whole numbers

Distinguish and use factors and multiples

Order of Operations

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12

Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor

Exponents

Math Scope and Sequence

Integers

Use positive and negative numbers to represent quantities in real-world contexts

Absolute value

Integers on a number line, compare and order

Addition of integers, understand and apply patterns

Subtraction of integers

Multipy and divide integers

Coordinate points

Number and Operations

Fractions

Partition circles and rectangles into two, three or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc.

Understand and represent a fraction as a number on the number line

Fractions of a shape, fractions of a group

Compare two fractions with the same numerator or the same denominator by reasoning about their size

Compare two fractions with different numerators and different denominators

Add and subtract mixed numbers with like denominators

Add and subtract with unlike denominators

Multiply a fraction or whole number by a fraction

Multiply and divide mixed numbers

Divide unit fractions by whole numbers and whole numbers by unit fractions

Divide fraction by fractions

Fluently add, subtract, multiply, divide fractions and mixed numbers

Decimals

Compare two decimals to hundredths by reasoning about their size

Read, write and compare decimals to thousandths

Add and subtract decimals

Add, subtract, multiply and divide decimals to thousandths

Divide to get decimals

Convert between fractions, decimals and percents

Use and apply decimals in all operations

Percents

Percent as out of 100

Compare and order percents, fractions and decimals

Percent Proportion

Percent equation

Simple Interest

Percent increase/decrease

Taxes, tips, commission, discounts

Math Scope and Sequence

Rational Numbers

Understand a rational number as a point on the number line

a/b where b ≠ 0

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers

Solve real-world and mathematical problems involving the four operations with rational numbers

Ratios and Proportional Relationships

Ratios and Rates

Identify, write and use ratios

Unit Rate, Unit Pricing

and rate

Proportional Relationships Set up and Solve proportions

proportion

drawings

with Tables and Graphs

Algebra and Functions

Algebraic Relationships

Generate a number or shape pattern that follows a given rule

Graph points on the coordinate plane

Write, read and evaluate expressions in which letters stand for numbers

Equations and Inequalitities

Reason about and solve one-variable equations and inequalities

Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams

Use properties of operations to generate equivalent expressions

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions and decimals), using tools strategically

Functions

Represent and analyze quantitative relationships between dependent and independent variables

Create graphs from tables and interpret graphs of linear equations

Slope, direct variation

Math Scope and Sequence

Measurement

Time

Tell and write time in hours and half-hours using analog and digital clocks

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m

Tell and write time to the nearest minute and measure time intervals in minutes

Elapsed Time

Calendar

Temperature

Money

Recognize and identify coins, their names, and their value

Count coins and make change

Operations with money, use the $ and .00

Linear Measurement

Measure and estimate the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks and measuring tapes

Convert like measurement units within a given measurement system

Liquid , mass and weight

Measure and estimate liquid volumes and masses of objects using standard units

Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units

Perimeter and Area

Measure areas by counting unit squares and square units

Relate area to the operations of multiplication and addition

Perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters

Apply, use and interpret formulas for perimeter and area of different shapes and figures

Geometry

2D and 3D shapes

Defining attributes (number of sides, angles) and non defining attributes (color, size, orientation)

Composite shapes

Describe and name shapes, color, relative position

Identify triangles, quadrilaterals, pentagons, hexagons and cubes

Identify line-symmetric figures and draw lines of symmetry

Congruency

Parts of a circle

Draw points, lines, line segments, rays, angles (right, acute, obtuse) and perpendicular and parallel lines. Identify these in two-dimensional figures

Math Scope and Sequence

Classify two-dimensional figures into categories based on their properties

Identify 3D figures

Angles

Measure angles in whole-number degrees using a protractor; sketch angles of specified measure

Transversals and properties

Angle sums and applications

Triangles, Circles, Quadrilaterals

Find area of triangles

Name and identify triangles by side lengths and angles

Area and circumference of circle

Area, perimeter, formulas of rectangle

Special triangles

Transformations

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points

Slides, Rotations, Reflections

Volume and Surface Area

Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures

Statistics and Probability

Data Sets

Represent Data: Organize, represent and interpret data with up to three categories

Measures of Center

and average

mode, range

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape

Probability

Investigate chance processes and develop, use and evaluate probability models

Likely and unlikely events

Probability model

Theoretical and experimental probability

In Review 1, we will review Level B. We will practice addition and subtraction facts to 18 and properties of addition.

• Addition facts to 10

• Addition facts to 18

• Add in any order

• Zero added to anything is that same number

• Subtraction facts to 10

• Subtraction facts to 18

• Check subtraction by adding

• Check addition by subtracting

• Dollars and coins values

• Counting money

Objective and Learning Goals

y Review and practice addition facts to 10

Vocabulary

y Addend - the numbers being added together in an addition equation

y Sum - the answer to an addition equation

Materials

y Paper

y Pencil

y Dry-erase marker

y Dry-erase board

y 6-sided dice

Pre-Lesson Warm-up

Guiding Questions

Tell students to draw 4 triangles on a piece of paper or dry-erase board. Then tell them to draw 2 rectangles next to their triangles. Ask,” How many total shapes did you draw?” [6] Have students write an addition equation to go with their drawing. [ 4 + 2 = 6]

Repeat this process with other shapes as you feel necessary.

Guiding Questions

1. How can we figure out an addition problem that we don’t know automatically? [strategies such as counting on, drawing pictures, making tally marks, etc.]

2. How can we become more automatic with addition facts? [practice through flash cards, games, writing facts, etc.]

Carol went to the store and bought 3 oranges and 5 apples. How many pieces of fruit did she buy? We want to know the total number of pieces of fruit that Carol bought.

She bought oranges.

She bought apples. To ﬁnd out the total we add and Carol bought pieces of fruit.

Introduce the Lesson (Try it Together)

Read through the example problem together and fill in the addends and sum. Define these terms for students. Point out that addition equations can be written horizontally or vertically, and that there is no difference in the sum. Discuss other strategies for figuring out the answer, such as counting on and making tally marks to count. For the first few problems ask students to share their strategies. Call on a student and ask, “What is 2 +3?” [5] “How do you know?” [possible answers: I started at 2 and counted up 3,4,5; I drew 2 circles and 3 circles and counted them all up; etc. Some students may say “I just knew it.” or “I have it memorized.”]

Discuss with students ways to practice and become more automatic with addition facts. Ask them, “Why is it important to know addition facts automatically?” [you will learn higher level math skills faster and more easily]

Activities

Students will practice addition facts to 10 with a partner. First, have a volunteer student come up and help demonstrate how partners should work together. Partner 1 will ask Partner 2 an addition problem, and Partner 2 will answer as quickly as possible. Partner 1 will then tell Partner 2 if they are correct or not. If the two partners disagree, they should use a strategy to try to prove to each other why they think they are correct. Model this by intentionally getting an answer wrong and pretending to disagree with the student who is modeling with you. Have your partner show the class a strategy they can use (counting on, drawing a picture, etc.) to prove to you why they are right. Put students into partnerships, and give them some time to “quiz” each other on addition facts to 10.

Using the numbers provided. Write as many ways as you can to get the sum of 10 . Each number can only be used once.

Make the sum of 9 using 3 addends. Each number can only be used once.

This machine is programmed to add 4 . Write missing sums on the “out” cards and the missing addends on the “in” cards.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Allow students to draw pictures or tallies. You can even provide small objects such as counters for students to model the problems with. Show students how to draw tallies next to the second addend, and then have them say the first addend out loud and count on from there using the tallies they drew.

Early Finishers

Students can draw their own adding machine like the one in number 36. Have them use a different addend (not 4) and write both the “in” and “out” numbers on their machine

Challenge and Explore

Have students look at the machine in problem number 36. The most challenging part is when the “in” number is unknown. Challenge students to write addition equations using a letter to represent the unknown part in each equation and then solve for the unknown part. Do the first one together. [5 + 4 =a, a = 9] [possible answers to the rest: 2 + 4 = b, b = 6; 4 + 4 = c, c = 8; 1 + 4 = d, d = 5; 6 +4 = e, e =10; f + 4 = 5, f = 1; g + 4 = 7, g = 3; h + 4 = 6, h = 2; i + 4 = 8, i = 4;

Read the directions for the first two sections to the class. Remind students that there is no difference in the answer whether a problem is written horizontally or vertically. Encourage students to work quickly but accurately on numbers 1-33. For numbers 34-35 encourage students to guess and check to find sums that work. Explain the machine in number 37. Tell students that when a number goes in at the top, 4 will be added to that number, and the answer will come out the bottom. Point out to students that in the last 5 problems, they have to figure out which number goes in, or the missing addend, not the sum. Do the first of these together. Say: “Something goes in, 4 is added to it, and 5 comes out. What plus 4 equals 5?” [1]

Common Errors

When students are using the “counting on” strategy, they may count the first addend as the first number they are counting on and come up short. For example, if the equation is 4 + 3, they may say “4,5,6, the answer is 6,” instead of “5,6,7, the answer is 7.” Some students will make careless errors such as drawing the wrong number of pictures or tally marks.

Students may think that they have the facts memorized and insist that they are correct when they are not. In this case, ask them to use a strategy to prove the answer to you, and they should find their own mistake.

Discuss the results by asking the following questions:

1. What strategies did you use to find the missing addends? [counting on fingers, using counters, a number line etc]

2. How can you use adding in the real world? [grocery shopping, counting money, etc.]

Games

Play 6s are Wild to practice addition facts to 10. p. 308

Assess

Create a brief assessment based on the machine concept. Tell students something goes in, 5 is added to it, and 7 comes out. What plus 5 equals 7? Repeat this a few times mixing up the numbers.

Objective and Learning Goals

y Review and practice addition facts to 18

Vocabulary

y Addend - the numbers being added together in an addition equation

y Sum - the answer to an addition equation

Materials

y Paper/pencil or dry-erase board/marker

Pre-Lesson Warm-up Guiding Questions

Have students hold up fingers to show their answers to the following addition facts through 10:

2 + 3 = [5]

3 + 4 = [7]

3 + 5 = [8]

2 + 4 = [6]

3 + 7 = [10]

1 + 8 = [9]

6 + 4 = [10]

Guiding Questions

1. How can we figure out an addition problem we don’t know automatically? [strategies such as counting on, drawing pictures, making tally marks, etc.]

2. How can we become more automatic with addition facts?

[practice through flash cards, games, writing facts, etc.]

James had 7 pieces of candy. His friend gave him 6 more. How many pieces of candy does James have now? We want to know the total number of pieces of candy that James has.

He started with pieces.

His friend gave him more.

To ﬁnd out the total we add and

James now has pieces of candy.

Introduce the Lesson (Try it Together)

Read the example problem aloud to the students. Remind them of the definition of addends and sum. Remind them that addition problems can be written horizontally or vertically. Fill in the addends for the example problem, and ask students to share their answers and the strategy they used to figure it out with the class. If students say that they just knew it or they have it memorized, ask them to prove that they are correct. After one student shares a strategy, ask for students to share a different way to solve the problem.

[Students may share a number of possible strategies: starting at 7 and counting on 6 more, drawing and counting a picture or tallies, using a close known fact like 6 + 6 = 12 and adding one more, etc.]

Activities

Students will practice addition facts to 18 with a partner. Remind students how they worked with partners in the last lesson to practice facts up through 10. Partner 1 will ask Partner 2 an addition problem, and Partner 2 will answer as quickly as possible. Partner 1 will then tell Partner 2 if they are correct or not. If the two partners disagree, they should use a strategy to try to prove to each other why they think they are correct. Remind students how you solved the disagreement with your partner in the last lesson. Put students into partnerships and give them some time to “quiz” each other on addition facts to 18. You can let them use facts from the book or from practice sheets.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Give students tools such as number lines or a hundreds chart to use to count on. Students could also use counters or other objects to add.

Early Finishers

Students can draw their own tables like the ones in numbers 36 and 37. Have them use a different addend (not 7 or 8) and be sure to write the answers.

Challenge and Explore

Solve the following word problem. Ben had 4 red marbles and 5 blue marbles in a jar. His dad gave him 3 yellow marbles and 5 green marbles to add to his jar.

1. How many marbles did Ben have to begin with? [9]

2. How many marbles did his dad give him? [8]

3. How many marbles does Ben have now? [17]

Discuss the results by asking the following questions:

1. What strategies did you use to solve the math sentences?

Tell students to work through the addition equations on this page quickly and accurately to help them develop automaticity with addition facts. Explain for #34-35 they are creating word problems, similar to the Let’s Learn section to match the math sentences. Answers may vary, be sure students are using correct wording such as “more” and “total/sum.” For #36-37, explain how to fill out the chart by taking the top number and adding 8 or 7.

Common Errors

When students are using the “counting on” strategy, they may count the first addend as the first number they are counting on and come up short. For example, if the equation is 9 + 3, they may say “9,10,11, the answer is 11,” instead of “10,11,12, the answer is 12.”

Some students will make careless errors such as drawing the wrong number of pictures or tally marks. Students may think that they have the facts memorized and insist that they are correct when they are not. In this case, ask them to use a strategy to prove the answer to you, and they should find their own mistake.

[counting on fingers, number lines, math facts, number chart, cubes, etc]

2. What types of objets did you use while creating the word problems?

[Used pencils, books, toys, other objects to say how much I have, and how many someone gave to me to find the sum]

Games

Play Brain vs. Hand to practice addition facts to 18. p. 308

Assess

Provide students with the following incorrect equation: 8 + 6 = 13. Tell students that another student solved this addition equation this way. Ask them to give the right answer and tell how they could prove or explain to the other student the correct answer. [8 + 6 = 14; students may prove it by counting on, drawing a picture, using a known fact or another strategy they have learned]

Level C Review 1-3

Objective and Learning Goals

y Understand the identity and commutative properties of addition

y Explain how the properties make adding easier

Vocabulary

y Addend - the numbers being added together in an addition equation

y Sum - the answer to an addition equation

Materials

y Two 0-20 number lines printed and laminated or in a sheet protector and dry-erase marker, or several printed 0-20 number lines in sets of 2

Pre-Lesson Warm-up Guiding Questions

Call out “easy” addition facts for your students to answer (these could include +1 facts, +2 facts, doubles facts or facts that equal 10). Then after, give them a number to add to their answer.

Say: “Add 3 + 3” [6] “Now add 5” [11]

“Add 6 + 1” [7] “Now add 7” [14]

“Add 4 + 0” [4] “Now add 6” [10]

“Add 4 + 4” [8] “Now add 5” [13]

Guiding Questions

1. How do the commutative and identity properties help us solve addition equations? [we know that adding zero will not change the number. We can use the commutative property to add numbers in a different order]

There are special properties that are true of every case in addition. 1 . When you add 0 to any number, the answer is that number. 1 + 0 = 1 128 + 0 = 128 124,963,021 + 0 = 124,963,021

If you start at 128 on the number line and add 0 , you will not move. This is called the Identity Property

2 . You can add numbers in any order and you will always get the same answer. 2 + 7 + 1 = 10

On a number line, no matter where you start, you will always end up at 10 when you add 1 , 2 and 7

Find the answer. Add in any order.

Read through the information at the top of the page to explain the identity and commutative properties to students. Emphasize that these properties will always be true.

Go through the example problems in the Try it Together section with the students. Point out that sometimes there is an arrow above the problem showing which two numbers to group and add first. Other times there are parentheses around part of the problem. This means that students should add that part first. Tell them that on problems that don’t have an arrow or parentheses, they can choose in which order to add. Encourage them to look for ways to group the numbers that will make adding easier. For example, in number 12, they may want to group 7 + 3 and 8 + 2 because those equations both equal 10, and adding 10 + 10 is easier than other combinations.

Activities

Students will practice representing problems with hops on a number line and determine which order would be easier to add numbers in.

Students can have two number lines 0-20 in a laminated sheet with a dry-erase marker, or a piece of paper with a few sets of two 0-20 number lines printed on it. Give students an addition equation that includes 3 or 4 addends (if you want to set this up as a center, you will need to have several equations printed on strips of paper or cards for students to use) and tell them to show 1 way to add the numbers with hops on the 1st number line. Then on the 2nd number line, have them show adding the numbers in a different order. After they are done, have them look at both number lines and decide which order would be easier to add mentally. They can circle that number line or put a star or other mark by it. For example, if the equation is 4 + 7 + 6, students may start at 0 and hop to 4, then add 7 and hop to 11, and then add 6 and hop to 17. On the 2nd number line they may start at 0 and hop to 4, then add 6 and hop to 10, then add 7 and hop to 17. They might circle the 2nd number line because finding a combination of 10 first and then adding on to 10 is easier.

91 20 15 18 32 21 17 25 20 14 16 13

16. Does the order in which you add numbers change the answer? Why or why not?

No, the order does not change the answer because you are adding the same numbers together

17. How can a number line help you when adding numbers?

Number lines can help you add because you start from the ﬁrst number and count the number being added by moving to the right

18. What is the rule when you add zero to a number? Why?

When you add zero to a number, the answer is that number because adding zero is neither adding more nor taking away

Story problems.

Add in any order. Group when possible.

19. Gregory, Drew and Blake combined all of their chocolate drops. Gregory had 6 . Drew had 11 Blake had 5 . How many chocolate drops did the boys have now?

20. Blake’s brother Damian came over to play with the boys. He had no candy to share. How many pieces of candy and chocolate drops did the boys have now?

22 chocolate drops 22 + 0 = 22

Apply and Develop Skills (Practice / Exercise page)

Read the directions on the page to the students. Remind them that when there are parentheses in a problem, they need to add those two numbers first, but if there are no parentheses, they can choose to add in any order. Encourage them to group and add in an order that will make it easier for them.

Struggling Learners

Show students which numbers to add first by putting arrows or parentheses in for them on problems that don’t already have them. Give students number lines to use when adding.

Early Finishers

Check your work by going back and adding the problems in a different order to see if you get the same answer.

Challenge and Explore

Read the word problems together. Discuss how these problems show the two properties they learned in this lesson. Ask which property is demonstrated by number 19 [commutative], and which property is demonstrated by number 20. [identity]

Ask students to share which order they added the numbers in problem 19, and why. [possible answer: (6 + 5) + 11 because 6 + 5 equals 11 and it’s easy for me to add 11 + 11 because it’s just adding 1 + 1 in the ones place and tens place]

Discuss the results by asking the following questions:

1. When you add the same numbers in different order, will you always get the same answer? Why or why not? [Yes, you will always get the same answer because of the commutative property]

Games

Play Brand to Hand to practice addition facts to 18 p. 308

Common Errors

Students may try to add mentally and lose track of which numbers they have already added. Encourage them to write the sum of the first two addends that they add over the arrow or parentheses to keep track of their work.

Assess

Have students solve the following equation and then write which order they added the number in, and why.

3 + 9 + 7 [19; possible explanation: I added 3 +7 = 10 and then 10 + 9 = 19 because I know my combinations of 10 and it’s easy to add a 1-digit number to 10 since you just change the 0 to the number you are adding]

Objective and Learning Goals

y Review and practice subtraction facts to 10

Vocabulary

y Minuend - the number that you start with in a subtraction equation

y Subtrahend - the number that is being taken away in a subtraction equation

y Difference - the answer to a subtraction equation

Materials

y Decks of playing cards or number cards

Pre-Lesson Warm-up

Guiding Questions

Practice counting backwards from 10 aloud with the class.

Then give students a number to start at and an amount to count back. Have students count back out loud together. Then tell them the corresponding subtraction fact. After a few examples, encourage them to say the subtraction fact with you.

y Say “Say 8, then count back 5.”

[8, 7, 6, 5, 4, 3] “8 minus 5 is 3.”

y “Say 9, then count back 4.”

[9, 8, 7, 6, 5] “9 minus 4 is 5.”

y “Say 10, then count back 3.”

[10, 9, 8, 7] “10 minus 3 is 7.”

Continue with more examples as you feel necessary.

Guiding Questions

1. How can we figure out a subtraction problem we don’t know automatically?

[strategies such as counting back, number lines, drawing pictures or tally marks and crossing out, etc.]

2. How can we become more automatic with subtraction facts?

[practice through flash cards, games, writing facts, etc.]

Hannah had a box of 10 pencils. She sharpened 4 of them. How many pencils still need to be sharpened? We want to know the number of pencils that are still not sharpened. Hannah started with pencils. She sharpened pencils. To ﬁnd how many pencils are not sharpened we subtract from Hannah still needs to sharpen pencils. minuend minuend subtrahend

Introduce

(Try

Read through the example problem in Let’s Learn together. Fill out the information, and teach students the definitions of minuend, subtrahend and difference. Remind students that the minuend must always be the largest number in the equation. Point out in the example problem that a picture was used as a strategy to help solve the problem. Ask students to share ideas for other strategies. Be sure to touch on strategies of counting back, drawing and crossing out objects or tallies and thinking about the related addition fact. For example, when trying to solve 10 - 4, students can think “What plus 4 equals 10?” If they know the addition fact 4 + 6 = 10, then they also know 10 - 4 = 6. Remind students that while using a strategy to figure out the answer is perfectly acceptable, the goal should be to have all of the facts memorized as soon as possible. Go through the examples in Try it Together quickly, stopping occasionally on a problem to have a student share a strategy for solving that problem if they don’t have it memorized yet.

Activities

Students will practice subtraction facts to 10 with a partner. First, have a student come up and model with you how partners should work together. Partner 1 will ask Partner 2 a subtraction problem, and Partner 2 will answer as quickly as possible. Partner 1 will then tell Partner 2 if they are correct or not. If the two partners disagree, they should use a strategy to try to prove to each other why they think they are correct. Model this by intentionally getting an answer wrong and pretending to disagree with the student who is modeling with you. Have your partner show the class a strategy they can use (counting back, drawing a picture and crossing out, etc.) to prove to you why they are right. Put students into partnerships, and give them some time to “quiz” each other on subtraction facts to 10.

the di erences.

Struggling Learners

Give students a 0-10 number line to use to count back, or give them counters or other objects to take away from. Encourage them to draw pictures or tallies. You might draw objects or tallies for the minuends in each problem for them and have them cross out the number they are subtracting.

Early Finishers

Circle the incorrect equations. Rewrite with the correct minuend and solve.

the tables.

Story problem.

30. In his backpack, Joe had 9 bouncy balls. Joe counted and found out that six bouncy balls were green. How many bouncy balls were not green? Identify the minuend, subtrahend, and di erence.

9 (minuend)-6 (subtrahend)=3 (di erence); 3 bouncy balls were not green

Apply and Develop Skills (Practice / Exercise page)

Students can draw their own tables like the ones in numbers 28 and 29. Have them use a different subtrahend (not 4 or 5), and be sure to write the answers.

Challenge and Explore

Show students the following table. Point out that this table is like the tables in problems 28 and 29 except in this table, the differences are already filled in, and they have to figure out the minuends. Discuss strategies for figuring these out. [think “what minus 3 equals the bottom number, add the bottom number to 3, count up on a number line, etc.]

Read the directions for the first two sections to the students. Remind them that there is no difference in the answer whether the problem is written horizontally or vertically. Explain how to solve the tables in numbers 28 and 29. Tell students that the numbers across the top are minuends, and they should start with this number and then subtract the amount that it says in the box on the right of the table. For number 28, look at the first box together. Say: “I see that the first minuend is 4, and this table says to subtract 4. So, I need to start with 4 and subtract 4. 4 minus 4 is 0, so I will write a zero in the box under 4.” Encourage students to work quickly and accurately through numbers 1-26, reminding them that the goal is to memorize these facts.

Common Errors

When students are counting back, they will count the minuend as one of the numbers they are counting back. For example, when counting back to solve 7 - 3, they may say “7, 6, 5” instead of “7… 6, 5, 4.” Remind students that they should say the number they are starting at and then count back the number they are subtracting.

[Answers to table from left to right: 10, 7, 3, 5, 9, 6]

Discuss the results by asking the following questions:

1. What is the minuend, subtrahend, and difference in a subtraction problem? [number you start with, number you take away, and the answer]

2. What happens when you take away 0? Why? [the number stays the same because taking away 0 is taking away nothing]

Games

Play Draw and Subtract to practice subtractions facts to 10. p. 309

Assess

Identify the error in the minuend in the following problems:

1. 5-1=3 [4-1=3]

2. 8-4=3 [7-4=3]

3. 10-8=1 [9-8=1]

Objective and Learning Goals

y Review and practice subtraction facts to 18

Vocabulary

y Minuend - the number that you start with in a subtraction equation

y Subtrahend - the number that is being taken away in a subtraction equation

y Difference - the answer to a subtraction equation

Materials

y Paper/pencil or dry-erase board/marker

Pre-Lesson Warm-up

Guiding Questions

Have students hold up fingers to show their answers to the following subtraction facts through 10:

5 - 3 = [2]

7 - 4 = [3]

8 - 5 = [3]

6 - 4 = [2]

10 - 3 = [7]

9 - 1 = [8]

10 - 4 = [6]

Guiding Questions

1. How can we figure out a subtraction problem we don’t know automatically? [strategies such as counting back, drawing pictures or tally marks and crossing out, etc.]

2. How can we become more automatic with subtraction facts? [practice through flash cards, games, writing facts, etc.]

David and Val are collecting cereal boxes for a school project. Val has 14 boxes and David has 9 boxes. How many more

Read the example problem aloud to the students. Remind them of the definition of minuend, subtrahend and difference. Fill in the blanks for the example problem, and ask students to share their answers and the strategy they used to figure it out with the class. If students say that they just knew it or they have it memorized, ask them to prove that they are correct. After one student shares a strategy, ask for students to share a different way to solve the problem. [Students may share a number of possible strategies: starting at 14 and counting back 9, drawing and crossing out pictures or tallies, using a known addition fact like 9 + 5 = 14, so 14 - 9 = 5]

Remind students that the goal is to memorize these facts. Work quickly through the rest of the example problems on the page, stopping occasionally to ask a student to share a strategy to use if they don’t have the problem memorized yet.

Activities

Students will practice subtraction facts to 18 with a partner. Remind students how they worked with partners in the last lesson to practice facts up through 10. Partner 1 will ask Partner 2 a subtraction problem, and Partner 2 will answer as quickly as possible. Partner 1 will then tell Partner 2 if they are correct or not. If the two partners disagree, they should use a strategy to try to prove to each other why they think they are correct. Remind students how you solved the disagreement with your partner in the last lesson. Put students into partnerships, and give them some time to “quiz” each other on subtraction facts to 18.

Story problem.

27. Jill and Kate are counting markers in the classroom. Jill counted 17 markers. Kate counted 13 markers. How many more markers did Jill count than Kate?

-13 =4 ; 4 more markers counted by Jill

Write a story problem that corresponds to the math sentence.

My friend and I are collecting pencils. I collected 16 pencils and my friend collected 9 . I have 7 more pencils than my friend. I had 13 toys in my room. I lost 10 toys. I now only have 3 toys in my room.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Give students tools such as number lines or a hundreds chart to use to count back. Students could also use counters or other objects to take away.

Early Finishers

Students can make their own wheels like the ones in numbers 30 and 31. Have them use a different subtrahend (not 7 or 9). Make sure the numbers in the middle of the wheel are greater than the subtrahend, and be sure to write the answers.

Challenge and Explore

Solve the following word problem:

Ben has some marbles in a jar. He has 6 blue marbles, 5 red marbles and 4 yellow marbles. If he takes out the blue marbles to play a game, how many marbles are left in his jar?

1. How many total marbles does Ben start with? [15]

2. How many does he take out? [6]

3. How many marbles are left in the jar? [9]

4. Write a subtraction equation to solve this problem. [15 - 6 = 9]

Tell students to work through the subtraction equations on this page quickly and accurately to help them develop automaticity with subtraction facts. Remind students that there is no difference in the answer whether the problem is written horizontally or vertically. Before students begin, explain for problems 28 and 29 they are to write a word problem that corresponds to the math sentence. Students can use the Let’s Learn problem as a reference. In problems 30 and 31 the green numbers in the center are the minuend. They should subtract the subtrahend in the center and write the difference in the outer circle in the box that corresponds to the minuend they started with.

Common Errors

When students are using the “counting back” strategy, they may count the minuend as the first number they are counting back and come up with a wrong answer. For example, if the equation is 12 - 3, they may say “12,11,10, the answer is 10” instead of “12 (start)… 11, 10, 9, the answer is 9.”

Some students will make careless errors such as drawing the wrong number of pictures or tally marks.

Discuss the results by asking the following questions:

1. What are some words/terms we can use when subtracting? [take away, how many left, subtract, minus etc]

2. When can we use subtracting in the real world? [counting down time, spending money etc]

Games

Play Brain vs Hand to practice subtraction facts up to 18. p. 308

Assess

Provide students with the following incorrect equation: 13 - 6 = 8. Tell students that another student solved this addition equation this way. Ask them to give the right answer and tell how they could prove to the other student that they are correct. [13 - 6 = 7; students may prove it by counting back, drawing a picture and crossing out, using a known addition fact, or another strategy they have learned]

Objective and Learning Goals

y Use inverse operations to check answers in addition and subtraction facts

Vocabulary

y Inverse Operations - the opposite operation that can be used to check your work

Materials

y Printed list of 10 problems, 5 addition facts, and 5 subtraction facts with answers, some correct and some incorrect

y Paper/pencil or dry-erase board/marker

Pre-Lesson Warm-up

Guiding Questions

Practice writing fact families. Give students an addition or subtraction fact, and ask them to write the other 3 facts in the family.

4 + 3 = 7 [3 + 4 = 7, 7 - 3 = 4, 7 - 4 = 3]

15 - 7 = 8 [15 - 8 = 7, 8 + 7 = 15, 7 + 8 = 15]

Guiding Questions

1. How can we use inverse operations to check our work?

[if we know fact families, we can use the addition facts in a family to check the subtraction facts and use the subtraction facts to check the addition facts]

Betty is doing her math practice. She has the problem

Subtract. Check by adding. Add. Check by subtracting.

Introduce the Lesson (Try it Together)

Read through the example problem in Let’s Learn with the students. Tell students to ask themselves, “What plus 8 equals 14?” [6] Remind them that if they know related facts in a fact family, they can figure out the answers to the other facts in the family.

Go through the example problems in Try it Together. For number 1 say, “I need to figure out 12 minus 7, so I’m going to think: what plus 7 equals 12? I know that 5 plus 7 equals 12, so 12 minus 7 equals 5.” Fill in the boxes as you go. Continue in this manner with problems 2 - 4. For number 5 say, “I need to figure out 7 plus 5, so I’m going to think: what minus 5 equals 7? I know that 12 minus 5 equals 7, so 7 plus 5 equals 12.” Fill in the boxes as you go, and continue through number 8. Consider having students write down the complete fact family for 1 or 2 of the problems.

Activities

Tell students that they get to be the teacher and grade another student’s work. Provide them with a sheet of 10 problems, 5 addition facts and 5 subtraction facts, all with answers written. Some of the answers should be correct and some incorrect. Tell students that as the teacher, they will use inverse operations to check this student’s work. They should write a related subtraction fact next to each addition fact, and write a related addition fact next to each subtraction fact. Then draw a star or smiley face next to each problem that was correct. After students have graded their papers, go over the answers, and discuss how they knew if the student was correct or incorrect.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Give students tools such as number lines or hundreds charts to help them figure out answers. You may want to help some students write out the fact families to help them solve the problems.

Early Finishers

Go back and write the 2 other facts in the fact family in the margin for problems 3, 6, 8, 12, 15 and 17.

Challenge and Explore

Present the following problem to students: Noah says that the answer to 17 - 9 is 9. Is he correct? [no]

1. How can you use inverse operations to check his work? [think “what plus 9 equals 17?” and use the related fact 8 + 9 = 17] 2. What is 17-9? [8]

Read the directions out loud to the students. Point out that in the first set of problems, they should subtract and check with addition. In the second set, they should add and check with subtraction. Remind them to pay attention to the plus and minus signs. Remind students to ask themselves questions like “What plus 9 equals 11? Or 9 plus what equals 11?”, and encourage them to write out the fact families if it helps them. Review the terms addend, sum, minuend, subtrahend, and difference. With a partner have students write a full fact family. Label each part with the correct term. Draw lines to matching numbers. Which parts have corresponding numbers? [minuend/sum, subtrahend/addend/difference]. Why do you think these parts match up? [minuend and sum represent the full amount. Subtrahend, addends and difference are all parts of the full amount]

Common Errors

Students may not know the answers to related facts automatically. Tell them to use a strategy to figure it out, and encourage them to practice to become more automatic with addition and subtraction facts.

Games

Play Brain vs. Hand to practice both addition and subtraction facts to 18. p. 308

Assess

Check work for problems 3, 6, 9, 12, 15 and 18.

Objective and Learning Goals

y Count money amounts with bills and coins

Vocabulary

y Dollars - one dollar is 100 cents, money amount represented by the sign $

y Cents - smallest unit of money, represented by the sign ¢

Materials

y Coins - play or real

Pre-Lesson Warm-up

Guiding Questions

Practice counting aloud by 5 cents, [5¢, 10¢, 15¢, 20¢, 25¢, etc.]

10 cents, [10¢, 20¢, 30¢, 40¢, 50¢, etc.] and 25 cents [25¢, 50¢, 75¢, 1 dollar, 1 dollar and 25¢, etc.]

Also practice counting by 10s starting at 25 [25, 35, 45, 55, 65, 75, etc.]

Guiding Questions

1. How can we count money in an efficient and accurate way?

[start by counting the bills, then count up the cents from the most valuable coins to the least valuable coins]

Introduce the Lesson (Try

Read the directions. Go over how to count money efficiently with students. For the first example in Let’s Learn, point out that the bills are all one dollar bills. Count them: “1, 2, 3. There are 3 dollars.” Fill in 3. Make sure students practice tracing the dollar sign when they fill in 3 dollars. Then, model how to count the coins beginning with the coin with the largest value. Ask students: “Which coin in this example has the largest value?” [quarter] “How much is it worth?” [25 cents] Write 25 underneath the quarter. Ask: “Which coin in this example has the next largest value?” [nickel] “How much is it worth?” [5 cents] “We can count up by 5s. We already know we have 25 cents, so we will count on from there. Count with me.” [30, 35] Write 30 under the first nickel and 35 under the 2nd nickel. Ask: “What is the last coin we have, and how much is each worth?” [penny, 1 cent] “Count up with me by ones.” [36, 37] Write 36 under the first penny and 37 under the 2nd penny. Write 37 on the line, and make sure students practice tracing the cent sign. Model counting up the bills and coins in this manner with the help of the students for the rest of the examples on this page. Make sure they write or trace the dollar and cent signs in each problem and write the amounts underneath the coins if they need to keep track of their counts.

Activities

Provide play or real coins in a container. Have each student (or pair or small group, if you don’t have enough coins) pull out a small handful of coins. First, they should sort the coins by type. Then arrange the coins in order from the highest value to the lowest value. Last, count up the amount. Give time for some students to share how they counted their money amount out loud.

Struggling Learners

Provide a poster or “cheat sheet” that has the values of each coin written on it for the students.

Early Finishers

Draw your own sets of bills and coins to count up. Write the counts under the bills and coins, and write the final amount of money for each.

Challenge and Explore

Apply and Develop Skills (Practice / Exercise page)

Read through and explain the directions for each set of problems on this page. For numbers 7 and 8, encourage students to write the counts below each bill and coin as they count up the money.

Present the following problem to the students: David has a jar full of coins. He pulls a handful of coins out of his jar to go buy some candy. He looks at the coins in his hand and sees that he has 4 pennies, 2 quarters, 3 nickels, and 3 dimes. How much money did David pull out of his jar? [99 cents]

Ask students to share their strategies for counting the money. [possible strategy: drawing the coins in order from largest to smallest value and writing the counts under each coin]

Common Errors

Students may lose track of their count when they move on to the next type of coin. They may confuse the value of each type of coin. Students often forget to write the dollar and cent signs.

Assess

Draw or display a picture of two 1-dollar bills and two 5-dollar bills, 3 pennies, 2 dimes, 1 nickel and 1 quarter. Have students redraw the bills and coins in order from largest value to smallest value and count up and write the amount of money. [they should draw the 5-dollar bills, then 1-dollar bills, then quarter, dimes, nickel and pennies. Amount = $12 and 53¢]

Level C Review 1-8

Objective and Learning Goals

y Review

y Addition and subtraction facts 0-18, inverse operations, counting money

Vocabulary

y Addend - the numbers being added together in an addition equation

y Sum - the answer to an addition equation

y Minuend - the number that you start with in a subtraction equation

y Subtrahend - the number that is being taken away in a subtraction equation

y Difference - the answer to a subtraction equation

y Inverse operations - the opposite operation that can be used to check your work

y Dollars - one dollar is 100 cents, money amount represented by the sign $

y Cents - smallest unit of money, represented by the sign ¢

Materials

y Blank white paper

Pre-Lesson Warm-up Guiding Questions

Practice writing fact families. Give students an addition or subtraction fact, have them solve the fact and ask them to write the other 3 facts in the family.

6 + 7 = ___ [13: 7 + 6 = 13, 13 - 7 = 6, 13 - 6 = 7]

14 - 8 = ___ [6: 14 - 6 = 8, 8 + 6 = 14, 6 + 8 = 14]

Guiding Questions

1. How can we use inverse operations to check our work?

[if we know fact families, we can use the addition facts in a family to check the subtraction facts and use the subtraction facts to check the addition facts]

2. How can we become more automatic with addition and subtraction facts? [practice through flash cards, games, writing facts, etc.]

3. How can we count money in an efficient and accurate way?

[start by counting the bills, then count up the cents from the most valuable coins to the least valuable coins]

Read through the information and example problems in Let’s Learn. Encourage students to keep practicing to become more automatic with addition and subtraction facts. Remind students that they can check their work by using the inverse operation. Ask a student to tell the class what 7 minus 4 is[3], then ask a student to tell you the related addition fact that you can use to check. [3 + 4 = 7] Then ask a student to tell you what 6 plus 3 is. [9] Ask another student to tell you the related subtraction fact that you can use to check. [9 - 3 = 6] Do Try it Together problems 1-4 in a similar manner. Work through numbers 5-10, reminding students to try and group numbers together to add first in a way that will make the problem easier when possible. In addition, you can change the order or make fact pairs to help reach the answer. Finish the page quickly by having students chorally answer the subtraction problems as you fill in the answers with the students.

Activities

Make “Fact Family Houses.” Each student should have a blank piece of white paper. Have them turn their paper to landscape

orientation and fold it right to left in half (hamburger style) and then in half again. Show students how to cut off the corners at the top, starting about an inch and a half or 2 inches down the paper, so that it comes to a point. Then, unfold the paper. They should have 4 rectangles with triangles at the top that look kind of like row houses. Tell the students to pick 4 addition or subtraction facts that they think they need to practice. They will make a fact triangle for each fact in the triangle at the top by writing the answer to the addition equation for that fact family at the top of the triangle and the two addends in bottom corners of the triangle. (It may help if students fold the triangle down first, so they can see the triangle more easily.) In the rectangle below each fact triangle, students should write all 4 facts in that fact family. They can use these to help them practice difficult facts. If there is extra time, 4 more fact families can be written on the back. Example: A student says they need to work on 17 - 9 = 8. They would write 17 at the top of the triangle and 8 and 9 in the bottom corners. They would then write 8 + 9 = 17,

8. 18. 9. 19. 10. Mike has 5 ﬁre trucks, 4 dump trucks, and 3 tow trucks. How many trucks does he have in all?

20. Simon and Tom go spider hunting. Simon finds 19 spiders and Tom finds 11 . How many more spiders did Simon find?

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Give students tools such as number lines, hundreds charts, counters and play money to help them add, subtract and count money. Allow students to use a poster or “cheat sheet” that has the coin values on it.

Early Finishers

Next to problem numbers 7 - 10, write a subtraction equation that can be used to check your answer. Next to numbers 11-16, write an addition equation that can be used to check your answer.

Challenge and Explore

Look at the following problem. Is it correct? If not, what is the correct answer? Explain one strategy to use to prove your answer. What is a subtraction problem you could use to check your work?

7 + 8 14

[no, the correct answer is 15. Possible strategy: start at 8 and count up 9, 10, 11, 12, 13, 14, 15. To check use 15 - 8 = 7]

Read through the directions on the page. Remind students to work quickly and accurately. Tell them that by now they hopefully have at least some of the addition and subtraction facts memorized, but if they need to, they should use a strategy that they have learned in this chapter. Remind students how to fill in tables in numbers 22 and 23. Say, “the left side of the table tells me to add 3. The first number at the top is 4, so I need to solve 4+3. That equals 7, so I will write 7 in the box underneath the 4.” For problem 24, tell students to come up with their own addition sentences that match the answer. Be sure to walk around and check their work.

Discuss the results by asking the following questions: What strategies did you use to solve the addition and subtraction sentences? [using a number line, imagine crossing out objects, etc]

Games

Choose a game to play and practice addition and/or subtractions facts.

Assess

Students may start with the wrong number when counting up or back as a strategy to add or subtract. Students rush and make careless errors.

Check work for numbers 10, 20, 22, and 24.

Review 2

In Review 2, we will learn about place value, rounding and how to compare and order numbers.

• Make numbers with base-10 blocks

• Round to the tens and hundreds places

• Round to the place indicated

• Match and write rounded numbers

• Understand why we estimate

• Order from greatest to least and least to greatest, up to ﬁve numbers

• Number lines can help us see which ten or hundred the target number is closest to

• We can use this rhyme to round: 5 or more, let it soar. 4 or less, let it rest.

• We can underline the target number to help us focus on the place to round

• Circling the number to the right of the target number helps us to decide what to do with the target number

• We can put numbers in order by looking at the largest place value ﬁrst

Vocabulary Words

Level C Review 2-1

Objective and Learning Goals

y Understanding place value - two-digit numbers are made up of tens and ones

Vocabulary

y Tens place - the 2nd digit from the right in a whole number, represents groups of 10 units

Materials

y Place value blocks - rods(tens) and small cubes(ones)

Pre-Lesson Warm-up Guiding Questions

Practice counting by 10s using base-ten rods. Have students count with you as you hold up rods. Hold up 1 rod, [10] 2 rods, [20] 3 rods, [30] etc.

Practice counting by 1s, starting at a multiple of 10. Say: “Start at 30,” show 3 rods and then count cubes. Show 1 cube, [31] 2 cubes, [ 32] 3 cubes, [33] etc.

Guiding Questions

1. How can we make 2-digit numbers with base-10 blocks?

[use rods for the number of tens the number has and cubes for the number of ones it has]

2. How can we read a number that is shown in base-10 blocks?

[count the rods by tens, and then count up by ones for the cubes]

Thomas and Martin were having a contest to see who could pull the biggest number out of the box of place value blocks.

Here is what Thomas pulled out: Here is what Martin pulled out:

Thomas has tens and ones or Martin has tens and ones or Who wins? wins!

Write each number.

Read the example problem to the students. Remind the students that rods are worth 10. Show them how you can line up 10 cubes (or ones) to make 1 rod (or ten). Ask the students to count the tens and ones out loud with you, and fill in the blanks together. First for Thomas [ten, twenty, thirty, thirty-one, thirty-two, thirty-three, thirty-four] and then for Martin. [ten, twenty, twenty-one, twentytwo, twenty-three, twenty-four, twenty-five, twenty-six, twenty-seven, twentyeight] Ask students who wins. [Thomas]

For the example problems in the Try it Together, make the numbers with base10 blocks (or possibly let students make them) for each example, and help the students to write the numbers.

Activities

Practice making 2-digit numbers with base-10 blocks. Give students some rods and cubes. Call out a number, such as 46. Have students make that number with blocks on their desk. [4 rods and 6 cubes]

Continue in this manner with other 2-digit numbers.

Draw base ten blocks and cubes to represent the following numbers.

Struggling Learners

Allow students to use base-10 blocks to complete the problems in the book.

Early Finishers

Students can draw base-10 blocks to represent the numbers in problems 10-15.

Challenge and Explore

each number.

Do you need to count every single block to know which number is greater?

Without counting, how do you know which number is greater?

The number with 8 ten rods is bigger than the one with 4 ten rods because 8 tens is bigger than 4 tens; 80 is bigger than 40

Write the two numbers and circle the greater number.

Apply and Develop Skills (Practice / Exercise page)

Show students 3 rods and 12 cubes. Ask: “What number is this?” [42] Say: “There are 3 rods, so why is this number not 30 something?” [you have to trade 10 cubes to make another rod because you have too many cubes]

Discuss the results by asking the following questions:

1. How can you identify bigger and smaller numbers without counting? [look at the tens place - the number with the bigger amount of tens is bigger]

2. How can you compare two numbers that have the same amount of tens? [look at the ones place, the number with the greater number of ones is bigger]

Read the directions with the students. Remind students to look at the place value chart of tens and ones to help them. Read through #16 with the students. Encourage them to find reasoning, before counting the base-10 rods and blocks. Tell them they are identifying the bigger number and must provide their reasoning. Then write both numbers, and circle the bigger number. This can be a reinforceable activity that you can do as a class using different numbers.

Common Errors

Students count the rods by ones instead of tens. Some students may lose track of which blocks they have already counted when counting base-10 blocks. Encourage them to cross out blocks as they count.

Assess

Games

Play The Biggest Handful to practice reading and making 2-digit numbers with base ten blocks. p. 310

Give students the following 2 problems:

1. (Draw or display 5 rods and 7 cubes.) This number has ____ tens and _____ ones. This number is _____. [5, 7, 57]

2. Draw the number 35 with base-10 blocks. [students should draw 3 rods and 5 cubes]

Objective and Learning Goals

y Understanding place value - three-digit numbers are made up of hundreds, tens and ones

Vocabulary

y Hundreds place - the 3rd digit from the right in a whole number, represents groups of 100 units

Materials

y Place value blocks/ Base-10 blocks : flats (hundreds), rods (tens) and small cubes (ones)

Pre-Lesson Warm-up

Guiding Questions

Practice counting by hundreds. [100, 200, 300, 400, etc.]

Practice counting by tens starting at a multiple of 100. For example, count by 10s starting at 300. [300, 310, 320, 330, etc.]

Practice counting by ones starting at a large number that is a multiple of 10. For example, count by ones starting at 460. [460, 461, 462, 463, etc.]

Guiding Questions

1. How can we make 3-digit numbers with base-10 blocks?

[use flats for the number of hundreds the number has, rods for the number of tens and cubes for the number of ones]

2. How can we read a number that is shown in base-10 blocks?

[count the flats by hundreds, then count up by tens for the rods and then count up by ones for the cubes]

Mrs. Moore asked students in her class to choose a number between 1 and 9 She recorded the numbers in the place value chart.

Judy chose 4 , so Mrs. Moore wrote 4 in the hundreds column. Kyle chose 7 , so Mrs. Moore wrote 7 in the tens column. Lisa chose 5 , so Mrs. Moore wrote 5 in the ones column. What number did the students make?

Their number has hundreds, tens, and ones. Their number is

Introduce the Lesson (Try it Together)

Read the example problem to the students. Make the number 475 with base10 blocks with the help of the students. Ask: “How many hundreds are in this number?” [4] Set out 4 flats, and ask: “How many tens are in this number?” [7] Set out 7 rods, and ask: “How many ones are in this number?” [5] Set out 5 small cubes. Remind the students that flats are worth 100. Show them how you can line up 10 rods (or tens) to make 1 flat (or hundred). Ask the students to count the rods by tens with you all the way to 100.

For the example problems in the Try it Together, make the numbers with base10 blocks (or possibly let students make them) for each example, and help the students to write the numbers.

Activities

Practice making 3-digit numbers with base-10 blocks. Give students some flats, rods and cubes. Call out a number, such as 346. Have students make that number with blocks on their desk. [3 flats, 4 rods and 6 cubes] Continue in this manner with other 3-digit numbers.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Remind students to look at the place value chart of hundreds, tens, and ones to help them. Encourage students to draw the blocks shorthand to help them if needed. They can draw a square for the flat, a line for the rod, and a dot for the cubes. Demonstrate such shorthand on the board. Sometimes students spend too much time trying to draw the base-ten blocks.

Struggling Learners

Allow students to use base-10 blocks or a place value chart to complete the problems.

Early Finishers

Students can draw base-10 blocks to represent the numbers in problems 7-10.

Challenge and Explore

Show students 2 flats, 13 rods and 2 cubes. Ask: “What number is this?” [332] Say: “There are 2 flats, so why is this number not 200 something?” [you have to trade 10 rods to make another flat because you have too many rods]

Discuss the results by asking the following questions:

1. How would you show or represent the number 612 with blocks? [6flats, 1 ten, 2 ones]

2. Why is it important to understand place value with larger numbers in the real world? [because confusing place value can change your number from $731 to $137 - which if that were money, is a big difference!]

Common Errors

Students may count the rods by ones instead of tens or count the flats by tens or ones instead of hundreds. Some students may lose track of which blocks they have already counted when counting base-10 blocks. Encourage them to cross out blocks as they count.

Assess

Play The Biggest Handful to practice reading and making 2 or 3-digit numbers with base ten blocks p. 310

Give students the following 2 problems:

1. (Draw or display 3 flats, 4 rods and 6 cubes.) This number has ____ hundreds, ____ tens and _____ ones. This number is _____. [3, 4, 6, 346]

2. Draw the number 251 with base-10 blocks. [students should draw 2 flats, 5 rods and 1 cube]

Objective and Learning Goals

y Round to the nearest ten Vocabulary

y Round - find a close but easier to work with number to a given number

y Tens place - the 2nd digit from the right in a whole number, represents groups of 10 units

Materials

y Number cards 0-9 or a deck of playing cards with the jacks, queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Count out loud by tens as a class. As you count, write the multiples of ten from 0-100 in order on the board for students to reference.

Give students a number between 1-100, and ask them to tell you which of the two multiples of ten your number comes in between.

33 [30 and 40]

67 [60 and 70]

45 [40 and 50]

28 [20 and 30]

Guiding Questions

1. How can we round a number to the nearest ten?

[Look at the ones place. If it is 5 or greater, round up to the next multiple of ten, if it is less than 5, leave the tens place the same, and change the ones to a 0]

On Sunday, Randy read 43 pages in his book. About how many pages did he read on Sunday?

Read through the example together. Ask students: “Which two multiples of ten is 43 in between?” [40 and 50] “Which one is it closer to on the number line?” [40] Show the students how to mark the halfway point (45) between 40 and 50 on the number line. Tell them that we traditionally will round that number up instead of down even though it is exactly halfway in between.

Go through the rest of the examples in Try it Together. On problems 1-12, encourage the students to first think, “Which two multiples of ten is this number in between?” and then, “Which one is it closest to?” When you get to the word problem, explain to students that when they see the word “about” it always means estimate. Work together with students to first estimate each distance and then add the estimates together.

Activities

Tell students that thinking about a hill can help them know which way to round numbers. Have students draw “rounding

hills” to round some numbers to the nearest 10. Give students a list of numbers to round: 36 87 41 29 93

Students should draw a small hill on their paper next to each number. They should decide which two multiples of ten the number is between, and write those numbers at the bottom of the hill. Write the smallest multiple of ten on the left and largest on the right. At the very top of the hill they should write the number that is halfway in-between the two multiples of ten. Lastly, they should write the number they are rounding on the hill. Write the number in a circle on the left side if it is smaller than the middle number and on the right side if it is larger than the middle number. Tell students that whichever multiple of ten the number would “roll down” the hill to is the number they should round it to.

Read each question. Solve. Show your work.

7. Sam says the number 55 rounds to 50 . His brother, Bill, says that 55 rounds to 60 . Who is correct Sam or Bill? Explain who is correct by using mathematical thinking.

Bill is correct. Using the hill method, 55 is at the top of the hill so it rounds up to the next multiple of 10 which is 60. Using a number line, since the ones place is a 5, the number rounds up to 60.

8. Jack bought a shirt for $16 , a pair of pants for $22 and shoes for $12 . About how much money did Jack spend?

Jack spent about $50.

$16 rounds to $20 $22 rounds to $20 $12 rounds to $10

$20 + $20 + $10= $50

Struggling Learners

Provide students with number lines or hundreds charts to find the closest multiple of ten on.

Early Finishers

Go back, and for problems 9-13, write the two multiples of ten that each number is between.

Challenge and Explore

14. John goes to the store and buys a notebook for $13 , pencils for $6 and erasers for $2 . About how much money did John spend at the store?

John spends about $20.

$13 rounds to $10, $6 rounds to $10, $2 rounds to $0. $10 + $10 + $0 = $20

Challenge

Isaac was asked to list all of the numbers that round to 50 . He lists the numbers 45 , 46 , 47 , 48 , 49

Do you agree with Isaac’s list? Explain why you agree or disagree. If Isaac is wrong, correct his work by listing other numbers that round to 50

Isaac is incorrect. The numbers 51, 52, 53 and 54 also round to 50.

Apply and Develop Skills (Practice / Exercise page)

Write the 3 digit number 134. Ask students how we could round this number to the nearest 10. If students don’t say it explain to students that we find the digit in the tens place. Then we look at the ones place. If the ones place is greater than 5, the tens place digit goes up by 1. If it’s less than 5, the tens place digit stays the same. The digit in the hundreds place remains the same. So 134 rounded to the nearest 10 would be 130. Have students try it with some other numbers such as 256 and 592.

Read the directions to the students. Point out that in numbers 1-6, the two multiples of ten that the number is between are given to them. In the rest of the problems, they will have to determine the multiples themselves. Work through the two word problems with students. Review with students what the word “about” means in a word problem. [estimate]. Have students try to solve the remaining problems on the page independently. Depending on the level of your class, you may need to give assistance for the Challenge problem.

Common Errors

Some students have a hard time telling which two multiples of ten a number is between. For example, they say that 42 is between 30 and 50 instead of 40 and 50 and round it down to 30. Using a hundreds chart is useful to help them see the multiples of 10.

Assess

Play Draw and Round to practice rounding to the nearest ten. p. 310

Check work for numbers 9-14.

Level C Review 2-4

Objective and Learning Goals

y Round to the nearest hundred

Vocabulary

y Round - find a close but easier to work with number to a given number

y Tens place - the 2nd digit from the right in a whole number, represents groups of 10 units

y Hundreds place - the 3rd digit from the right in a whole number, represents groups of 100 units

Materials

y Number cards 0-9 or a deck of playing cards with the jacks, queens, kings and jokers removed

y Dice and white board for Challenge and Explore

Pre-Lesson Warm-up

Guiding Questions

Count out loud by hundreds as a class. As you count, write the multiples of one hundred from 0-1,000 in order on the board for students to reference.

Give students a number between 1-1,000, and ask them to tell you which of the two multiples of one hundred your number comes in between.

343 [300 and 400]

678 [600 and 700]

455 [400 and 500]

218 [200 and 300]

Guiding Questions

1. How can we round a number to the nearest hundred?

[Look at the tens place. If it is 5 or greater, round up to the next multiple of one hundred, if it is less than 5, leave the hundreds place the same, and change the tens and ones to zeros]

Let’s learn!

We round when we want to ﬁnd a number

Try it together!

Round each number to the nearest hundred. Circle the tens place to help you. Circle the answer.

Write the hundreds place each number is between. Circle the nearest hundred.

Round each number to the nearest hundred.

Introduce the Lesson (Try it Together)

Read the Let’s Learn section to the students. Ask: “Which hundreds is 654 in between?” [600 and 700] “What is halfway between 600 and 700?” [650] Have students underline 650 on the number line. Ask: “Is 654 closer to 600 or 700?” [700] Guide students to draw an arrow pointing up to 700.

Read the directions and do the examples in the Try it Together section with the students. In number 5, remind students that since 750 is exactly halfway in between 700 and 800, we traditionally round up to 800. Emphasize that 5 and higher rounds up.

Activities

Tell students that they will be drawing “rounding hills” like they did yesterday, but this time, they will round to the nearest hundred. Give students a list of numbers to round: 436

187 741 829 593

Students should draw a small hill on their paper next to each number. They should decide which two multiples of one hundred the number is between and write those numbers at the bottom of the hill, the smallest on the left and largest on the right. Then at the very top of the hill, they should write the number that is halfway in-between the two multiples of one hundred. Lastly, they should write the number they are rounding on the hill. Place the number in a circle on the left side if it is smaller than the middle number or on the right side if it is larger than the middle number. Tell students that whichever multiple of one hundred the number would roll down the hill to is the number they should round it to.

Round each number to the nearest 100 .

Read each problem. Solve. Show your work. Round to the nearest hundred.

6. Elizabeth says 453 rounds to 400 . Do you agree with Elizabeth? Fill in the number line below and use words to explain if Elizabeth is correct.

Struggling Learners

Provide students with number lines to find the closest multiple of one hundred on. List the multiples of one hundred in order on a “cheat sheet” or on the board for students. Students may also benefit from drawing the rounding hill on their page as well.

Early Finishers

7. Joshua collected shells at the beach. He collected 123 shells on Monday and 354 shells on Tuesday. About how many shells did Joshua collect at the beach?

Answers will vary but should be similar to. Elizabeth is wrong. The number line shows that 453 is closer to 500 than 400. Since there is a 5 in the tens place, the 4 in the hundreds rounds up to a 5. 123 rounds to 100, 354 rounds to 400. 400 +

8. At the shoe sale, 264 people came the ﬁrst day and 189 people came the second day. About how many more people came the ﬁrst day than the second day? 9 . 568 children went to play at the park on Sunday. About how many children were at the park?

264 rounds to 300, 189 rounds to 200.

Challenge

267 children at the park were playing on the playground. About how many children were not playing on the playground?

Hint: Look at problem 9 to ﬁnd out how many children were at the park.

Apply and Develop Skills (Practice / Exercise page)

Go back and write the two multiples of one hundred that each number is between for numbers 2-5.

Also write your own word problems like the ones in numbers 8-9.

In question 1, have students write the multiple of 100 that is greater than and less than each of the numbers on the top row.

Challenge and Explore

Read the Challenge problem to the students. Have students circle the word “about”. Ask students what the word about means in a story problem. [it means you should round the numbers]. Remind students to look at the hint which tells them that they can find information they need to solve this problem in question 9. Ask students how many children were at the park. [568]. How many children were at the playground? [267]. Now, ask students to round the number of children at the park and the number of children at the playground. [600 at park, 300 at playground]

Review the directions for problem 1. Have students work with a partner to complete the problem. Review the answers. Have students complete problems 2-10 independently. Remind students to draw the rounding hill, if needed to help. Remind students that the word about in a word problem always means to round.

Common Errors

Ask students how they can find out how many children weren’t at the playground. Students should subtract the number of students on the playground [300] from the total number of children [600] [600-300=300 children weren’t on the playground.]

Games

Play Draw and Round to practice rounding to the nearest

Students may round to the tens place instead of the hundreds place. Some students have a hard time telling which two multiples of one hundred a number is between. For example, they say that 422 is between 300 and 500 instead of 400 and 500 and round it down to 300.

Students may round to the hundreds place but not put zeros in the tens place and ones place.

Students may also forget that “about” means to estimate or that “how many more” means to subtract.

Get 3 dice. Roll the dice. Make a three-digit number with the dice and write it on their dry-erase board. Then, round the number to the nearest hundred. For an added challenge, give students a fourth die and have them round the number they make to the nearest hundred or thousand.

Assess

Check work for numbers 2-9.

Level C Review 2-5

Objective and Learning Goals

y Round to the nearest ten

y Round to the nearest hundred Vocabulary

y Round - find a close but easier to work with number to a given number

y Tens place - the 2nd digit from the right in a whole number, represents groups of 10 units

y Hundreds place - the 3rd digit from the right in a whole number, represents groups of 100 units

y Target number - the number that is in the place value that is being rounded to

y Rhyme to round - rhyme used to help remember when to round up and when to round down

Materials

y Number cards 0-9 or a deck of playing cards with the jacks, queens, kings and jokers removed

y Base-10 blocks, if you’re doing the activity

Pre-Lesson Warm-up

Guiding Questions

Practice identifying place values. Write a number on the board, and have students read and copy the number. Then have them underline, circle, put a box around or otherwise mark the digit in whichever place value you tell them to.

Examples:

345 - Put an X through the digit in the tens place. [4]

267 - Circle the digit in the hundreds place. [2] 781 - Put a box around the digit in the ones place. [1]

Guiding Questions

Let’s learn!

The target place value can change. Underline the target place value. Circle the number to the right. Use this rhyme to help you: 5 or more, let it soar. 4 or less, let it rest.

Example: Round to the nearest ten. Round to the nearest hundred.

Try it together!

Look at the underlined digit. Circle the digit to the right. Round to the underlined place value.

Circle the correct rounded number. Look at the underlined digit. Write the rounded number. Look at the underlined digit.

1. How do we correctly round a number to the place value indicated? [underline the target number or place that you are rounding to, and circle the digit to the right. If the circled digit is 5 or more, round the target number up. If the circled digit is 4 or less, leave the target number as is. Change all digits to the right of the target number to zeros]

Introduce the Lesson (Try it Together)

Read the information in the Let’s Learn section to the students. Have students practice the Rhyme to Round out loud a couple of times with you. Throughout the lesson, you can ask students to recall this rhyme, and repeat it to help them remember whether to round up or down. Go through the example problems together. Stress to students that they need to underline the target number and circle the digit to the right to help them keep track of which place they are rounding to. In number 11, point out that this is a 3-digit number, but they are to round to the nearest ten since the tens place is underlined. The hundreds place will not change because it is greater than the place you are rounding to. After rounding 679 with students, show them what would happen if the number was 699, and they were asked again to round to the nearest ten. Tell students that the 9 in the tens place would round up to 10. However, 10 tens makes a hundred, so the 6 in the hundreds place becomes a 7, and the number rounds up to 700. You

can use base-10 blocks to show this if students still need clarification.

Activities

Explore rounding using base-10 blocks. Split the students into groups of 4. Give each group of 4 students a set of base-10 blocks, including small cubes, rods and flats. Give students a number to make with their blocks, then give them a place to round that number to. Start by doing an example together. Round the number 37 to the nearest 10. Have students get out 3 rods and 7 small cubes. Show students how to line the small cubes up next to a rod to show that they are closer to the next ten (40) than they are to the previous one (30). Tell students to trade the 7 cubes in for another rod. They have rounded 37 to 40. Now have them try with the number 32. Have them line the 2 small cubes up next to the rods to show that this number is closer to 30 than to the next ten of 40. Practice with several 2 and 3-digit numbers, rounding to the tens or hundreds place.

Prepare to round.

Draw a line under the place value indicated. Circle the digit to the right.

Write the place value of the underlined digit.

Struggling Learners

Provide students with tools such as number lines, hundreds charts or place value charts to help them. You might consider helping students by underlining the target number and circling the digit to the right with them.

Early Finishers

Round to the place value indicated.

Underline the target place value and circle the number to the right.

Round to the nearest ten.

Round to the nearest hundred.

Word problem.

21. Leo says that 57 rounded to the nearest ten is 50 . Do you agree with Leo? Use the number line and words to explain if Leo is correct.

Answers will vary but should include: Leo is incorrect. As you can see, I counted by ones on the number line, 57 is closer to 60 than it is to 50.

22. Rebecca doesn’t know how to round 145 to the nearest 100 . Use the number line and words to teach Rebecca how to round 145 to the nearest 100

Answers will vary but should include: Rebecca should underline the hundreds place, (1) and circle the tens place (4). Since the tens place is lower than 5, the one stays the same. 145 rounds to 100.

Apply and Develop Skills (Practice / Exercise page)

Read through the directions for each section with the students. For numbers 9-20, emphasize the importance of underlining and circling the correct digits to help them keep track of the place they should round to. For numbers 21-22 remind students to use math vocabulary in their explanations. Students should use words such as tens, or hundreds in their answers.

In numbers 1-8, round the number to the underlined place.

Challenge and Explore

Round numbers 15-20 again, but this time, round to the nearest ten [380, 830,660, 920, 280, 750]

Do you think it is more or less difficult to round 3-digit numbers to the tens place than the hundreds place? Why? [answers vary]

Common Errors

Students may round to the wrong place, especially when asked to round a 3-digit number to the tens place. Students may round to the correct place but forget to turn the lesser place value digits to zero. When the digit to the right of the target digit is a “5” students may forget if the target digit rounds up, since 5 is right in the middle.

Assess

Play Draw and Round to practice rounding to the nearest ten and hundred. p. 310

Check work for numbers 13, 14, 19-22.

Objective and Learning Goals

y Put 3 and 4-digit numbers in order from least to greatest

y Put 3 and 4-digit numbers in order from greatest to least

Vocabulary

y Order from least to greatest - to put numbers in sequence from smallest to largest

y Order from greatest to least - to put numbers in sequence from largest to smallest

Materials

y Index cards (possibly cut into smaller strips)

y Number cards 0-9 or decks of playing cards with jacks, queens, kings and jokers removed

Pre-Lesson Warm-up Guiding Questions

Practice reading large numbers and identifying place values. Write a 3 or 4-digit number on the board, and have students read and copy the number. Then have them underline, circle, put a box around or otherwise mark the digit in whichever place value you tell them to.

Examples:

381 - Put a box around the digit in the tens place. [8]

6,345 - Put an X through the digit in the thousands place. [6]

2,167 - Circle the digit in the hundreds place. [1]

Guiding Questions

1. How do we decide which numbers are greater or less than other numbers when ordering large numbers? [line up place values and compare, starting with the largest place value]

learn!

Matthew is keeping track of the distances he runs. We want to know which day he ran more steps. We need to compare. Monday he ran 4 ,353 steps. Tuesday he ran 4 ,567 steps. Look closely at the place values to compare.

Try it together!

Which is greater? Circle < or >. Write greater or less on the line.

Introduce the Lesson (Try it Together)

Read the problem in Let’s Learn together. Show the students how to compare each place value starting with the largest value, in this case thousands. Since both numbers have a 4 in the thousands place, tell students they should then look at the next largest place valuethe hundreds. The first number has 5 hundreds, and the second has 3 hundreds, so the first number is greater. It doesn’t matter what is in the tens and ones place since hundreds are greater than tens and ones.

Go through the examples in Try it Together with the class. Remind students that the greater than and less than symbols can be thought of as an open crocodile mouth, and the crocodile always opens his mouth toward the greatest number. When ordering groups of numbers, tell students that they can rewrite the numbers vertically, lining up the place values, and compare each place starting with the largest place.

Activities

Students will work in groups of 4 to write and put in order sets of 3 and 4-digit numbers. Give each student a small stack of index cards. You can cut the index cards into strips so that you don’t need as many cards. Make sure the strips are big enough for students to write a 4-digit number on. Start by telling students to write a 3-digit number on one of their strips without showing their group. Have all group members then put their numbers in the center of their table, read the numbers together and decide how to order the numbers from least to greatest. Do the same with a 4-digit number. Have students also order their numbers from greatest to least. You can repeat this as many times as you wish. You could also choose to give students some kind of criteria for the numbers, such as a 4-digit number that has a 2 in the thousands place. If you have the time, let some (or all) of the groups share some of their numbers and how they knew which order to put them in.

Compare numbers. Circle the greatest number in each group.

1. 765, 345, 890

4. 209, 211, 210

Circle the least number in each group.

10. 209, 211, 210 5. 910, 899, 909 11. 910, 899, 909

7. 765, 345, 890 2. 445, 440, 435 8. 445, 440, 435 3. 100, 400, 900 9. 100, 400, 900 6. 218, 318, 118 12. 218, 318, 118

Struggling Learners

Provide students with a place value chart to write the numbers in and compare.

Early Finishers

For numbers 1-6, rewrite the numbers in each problem in order from greatest to least. For numbers 7-12, rewrite the numbers in each problem in order from least to greatest.

Circle each set of numbers that are not in order from least to greatest 512, 521, 520 111, 211, 311 817, 878, 877

Put the numbers in order from greatest to least

Put the numbers in order from least to greatest. 13. 857, 858, 856 , , 16. 17. 345, 344, 346 , , 14. 321, 323, 322 , , 18. 123, 323, 222 , , 15. 888, 886, 880 , , 19. 102, 104, 100 , ,

I started with the greatest place value (hundreds) and compared the numbers. All had 1. Therefore, I compared the tens, and all had 0. Finally, I compared the ones and ordered them from greatest (4) to least (2 and 0).

1 st place

2 nd place

20. What strategies did you use to order the numbers in problem #19 ? 321 323 880 104 322 222 886 102 323 123 Sebastian Eric Brett 888 100

Challenge and Explore

Give the students the following list of numbers: 3,421; 3,212; 4,321; 4,214; 3,412; 3,214.

Ask students to write these numbers in order from least to greatest [3,212; 3,214; 3,412; 3,421; 4,214; 4,321] AND from greatest to least. [4,321; 4,214; 3,421; 3,412; 3,214; 3,212]

Make sure that students line up place values to compare. You may want to provide a place value chart for them, or encourage them to draw one.

21. Brett, Eric and Sebastian are having a contest to see who can create the longest chain. Brett made a chain with 867 links. Eric made a chain with 967 links. Sebastian made a chain with 976 links. Who won the contest?

3 rd place 856 857 858 346 345 344

Apply and Develop Skills (Practice / Exercise page)

Go over the directions and the first problem for each section on the page. The first problem has been done for the students, so ask them to explain how they know that it is correct. Remind students to write the sets of numbers vertically, and line up the place values to help them determine the correct order.

Discuss the results by asking the following questions:

1. When you compare three-digit numbers, do you start with the ones, tens, or hundreds place? Why? [You start with the hundreds place because that is the greatest value] 2. What happens when you compare numbers with the same value in the hundreds place? [you compare the amount of tens and/ or ones and then see which value is bigger and smaller]

Common Errors

Students may not line up and compare the correct place values. Some students may start by comparing the smallest place value (ones) instead of the largest (thousands or hundreds).

Assess

Games

Play Least or Greatest to practice ordering numbers. p. 310

Copy the two numbers, and write the correct sign < or > in between to compare. 546 [< ] 564 3,782 [>] 3,762

Write the following numbers in order from least to greatest: 296, 269, 279 [269, 279, 296]

Write the following numbers in order from greatest to least: 5,783; 5,738; 5,873 [5,873; 5,783; 5,738]

Level C Review 2-7

Objective and Learning Goals

y Put 3 and 4-digit numbers in order from least to greatest y Put 3 and 4-digit numbers in order from greatest to least

Vocabulary

y Order from least to greatest - to put numbers in sequence from smallest to largest

y Order from greatest to least - to put numbers in sequence from largest to smallest

Materials

y Index cards (possibly cut into smaller strips)

Pre-Lesson Warm-up Guiding Questions

Practice comparing two numbers. Write or display two numbers. Have students copy them and write a greater than or less than symbol in between.

56 ___ 65 [<]

38 ___ 35 [>]

145 ___ 45 [>]

339 ___ 393 [<]

722 ___ 277 [>]

Guiding Questions

1. How do we decide which numbers are greater or less than other numbers when ordering large numbers? [line up place values and compare, starting with the largest place value]

David loves to put together puzzles. Puzzles that have fewer pieces tend to be easier. Puzzles that have more pieces tend to be more challenging. Monday he put together a puzzle that had 1 ,500 pieces. Tuesday he put together a puzzle that had 1 ,200 pieces. Which puzzle was probably more di icult? Look closely at the place values to compare.

Start with the greatest place value. Both numbers have a 1 in the thousands place. Then look at the hundreds. The 5 in the hundreds place is greater than the 2 in the hundreds place. Since 1,500 is greater than 1, 200 the 1, 500 piece puzzle was more di icult.

Put these numbers in order from least to greatest. Use the place value chart above to help you.

5,823, 5,623, 5,723 , ,

435, 465, 445 ,

Circle the greatest number in each group. Put a rectangle around the least number in each group.

2. 578, 785, 857 , , 4. 56, 89, 43 , , 6. 302, 322, 332 , , 7. 789, 989, 589, 889, 1,089 9. 8,999, 9,004, 9,001, 9,000 11. 650, 630, 600, 620, 640 8. 3,465, 3,354, 3,645, 3,754 10. 587, 187, 346, 1,300, 465 12. 8,500, 8,512, 8,498, 8,450

Introduce the Lesson (Try it Together)

Read through and solve the example problem in Let’s Learn with the students. Emphasize the importance of starting with the greatest place value (in this case, thousands) when comparing numbers. Go through the examples in Try it Together with the students. Have students write the numbers in a place value chart and line the place values up vertically.

Activities

Tell students that they will be doing the same activity as in the last lesson, where they write numbers on index cards and put them in order with a group. However, in this lesson, they will have more numbers to order.

Put students in groups of 5 or 6, and pass out the index cards. Have students write numbers on their cards and put them in order as they did in the previous lesson. You can repeat this as many times as you wish. You could also choose to give students some kind of criteria for the numbers, such as a 4-digit number that has a 2 in the thousands place. If you have the time, let some (or all) of the groups share some of their numbers and how they knew which order to put them in.

Put these numbers in order from least to greatest. Use the place value chart on the learning page to help you.

1. 800, 80, 8,000 , ,

3. 780, 785, 790 , ,

5. 631, 623, 723 , ,

7. 625, 698, 676 , ,

9. 354, 445, 554 , ,

11. 139, 192, 178 , ,

2. 3,245, 3,268, 3,251 , ,

4. 6,789, 6,752, 6,711 , , 6. 1,824, 1,724, 1,224 , , 8. 8,675, 8,679, 8,665 , , 10. 4,843, 4,856, 4,897 , , 12. 5,021, 5,018, 5,025 , ,

Find the error in the following problem.

13. James ordered the following numbers from least to greatest: 6,241, 6,321, 6,317 James said his order is correct, but Kyle sees an error. Which numbers are out of order? Why do you think James made an error? Rearrange the numbers in the correct order.

The numbers 6,321 and 6,317 are out of order. James mixed up the tens place. The correct order is 6,241, 6,317, 6,321

Problem.

14. Central Park likes to keep track of how many visitors they have each day. They keep track in the data table below.

Day Number of visitors

Monday 5,873

Tuesday 2,890

Wednesday 4,678

Thursday 5,872

Friday 2,878

Write the numbers in order from greatest to least number of visitors.

15. On which day did the greatest number of people visit?

16. On which day did the least number of people visit?

Apply and Develop Skills (Practice / Exercise page)

Read the directions for numbers 1-12 to the students. Have students underline “least to greatest” in the directions. Ask: Will you be starting with the smallest number or the largest number? [smallest]

Struggling Learners

Provide students with a place value chart to write the numbers in and compare.

Early Finishers

For the odd-numbered problems in 1-12, write a number that is less than all of the other numbers in the set to the left of each problem. For the even-numbered problems, write a number that is greater than all of the other numbers in the set to the right of each problem.

Challenge and Explore

Give the students the following list of numbers: 54,821; 55,267; 45,832; 54,812

Ask students to write these numbers in order from least to greatest. [45,832; 54,812; 54,821; 55,267]

Make sure that students line up place values to compare. You may want to provide a place value chart through ten-thousands for them to use.

Discuss the results by asking the following questions:

1. What strategies help you order numbers? [using a number chart, lining up place values, moving through place value etc.]

Read the word problem in number 13. Explain that students have to find the error that James made and then rearrange the numbers in correct order from least to greatest.

Read the word problem in number 14 to the students, and have them underline “greatest to least” in the problem. Ask, for number 14, will you be starting with the smallest number or the largest number? [largest]

Common Errors

Students may not line up and compare the correct place values. Some students may start by comparing the smallest place value (ones) instead of the largest (thousands or hundreds).

Assess

2. What is the most challenging part while ordering numbers? Why? [answers may vary, could be keeping track of place value, lining up values, or when numbers are closer together]

Games

Play Least or Greatest to practice ordering numbers. p. 311

Arrange the following numbers from greatest to least: 7,142, 7,432, 7,812 [7812, 7432, 7142]

From least to greatest, which number is out of order in the following sequence? 3,452, 4,568, 4,332 [4568 and 4332 are switched]

Objective and Learning Goals

y Review

y Understanding place value, round to nearest ten and hundred, order 3 and 4-digit numbers from least to greatest and greatest to least

Vocabulary

y Round - find a close but easier to work with number to a given number

y Tens place - the 2nd digit from the right in a whole number, represents groups of 10 units

y Hundreds place - the 3rd digit from the right in a whole number, represents groups of 100 units

y Target number - the number that is in the place value that is being rounded to y Rhyme to round - rhyme used to help remember when to round up and when to round down

y Order from least to greatest - to put numbers in sequence from smallest to largest

y Order from greatest to least - to put numbers in sequence from largest to smallest

Materials

y Base-10 blocks - flats, rods and small cubes y Coins to flip

Pre-Lesson Warm-up

Guiding Questions

Practice place value with base-10 blocks. Set out, draw, or display pictures of base-10 blocks and have students write the number that is shown.

3 flats, 4 rods, 7 cubes [347]

1 flat, 8 rods and 2 cubes [182]

2 flats, 6 rods [260]

4 flats, 5 cubes [405]

Guiding Questions

Let’s review:

We round when we want to ﬁnd a number that is close to the given number. Remember this rhyme to help you: 5 or more, let it soar. 4 or less, let it rest.

Rounding can help us in real life. We estimate when we do not need an exact number, or when we want to know if our answer is reasonable.

Round each number to the nearest ten. Write each number.

1. How can we read a number that is shown in base-10 blocks?

[count the flats by hundreds, then count up by tens for the rods, and then count up by ones for the cubes]

2. How do we correctly round a number to the place value indicated?

[underline the target number or place you are rounding to, and circle the digit to the right. If the circled digit is 5 or more, round the target number up. If the circled digit is 4 or less, leave the target number as is. Change all digits to the right of the target number to zeros]

3. How do we decide which numbers are greater or less than other numbers when ordering large numbers?

[line up place values and compare, starting with the largest place value]

Put the numbers in order from least to greatest.

Put the numbers in order from greatest to least. Round each number to the nearest hundred.

Read through the Let’s Learn section with the students. Practice the rhyme: 5 or more, let it soar. 4 or less, let it rest. Have students recall and repeat it out loud a few times.

Go through the examples in Try it Together to review what the students learned in this chapter. Remind students to underline the target place value when rounding, and circle the digit to the right to help them. Encourage students to write numbers that they are trying to put in order vertically with the place values lined up.

Activities

Students work in pairs to practice rounding numbers. Student 1 writes down any 3-digit number they want. Student 2 flips a coin. If the coin lands heads up, Student 2 rounds that number to the nearest hundred. If the coin lands tails up, Student 2 rounds the number to the nearest ten. Student 1 and Student 2 must agree on the rounded number and help each other find any mistakes. Then they switch roles, and Student 2 writes down a number.

Round to the target number.

Round each number to the nearest ten.

Write the following numbers.

Round each number to the nearest hundred.

Struggling Learners

Provide tools like place value charts, number lines, rounding hills and base-10 blocks to help struggling students with the skills in this chapter.

Early Finishers

Write each number.

12. 6 hundreds, 5 tens, 0 ones

14. 7 hundreds, 1 ten, 2 ones

16. 8 hundreds, 5 tens, 4 ones

18. 3 hundreds, 0 tens, 8 ones

20. 1 hundred, 0 tens, 3 ones

13. 5 hundreds, 5 tens, 8 ones

15. 1 hundred, 0 tens, 5 ones

17. 2 hundreds, 1 ten, 0 ones

19. 4 hundreds, 3 tens, 8 ones

21. 5 hundred, 4 tens, 2 ones

Put the numbers in order from least to greatest.

22. 532, 527, 513 , ,

24. 121, 129, 136 , , 23. 359, 322, 354 , , 25. 925, 947, 913 , ,

Put the numbers in order from greatest to least.

26. 256, 238, 291 , ,

28. 625, 682, 623 , , 27. 247, 296, 293 , , 29. 576, 552, 584 , ,

Apply and Develop Skills (Practice / Exercise page)

Make a place value chart that goes up to the thousands place. Write numbers in your place value chart, and draw base-10 blocks in the chart to show the numbers.

Challenge and Explore

Look at your answers to numbers 12-21. Put those numbers in order from least to greatest. [103, 105, 210, 308, 438, 542, 558, 650, 712, 854] How did you decide on the order? [answers will vary]

Read the directions for the exercises on this page. Point out that the target number is underlined in numbers 1 and 5 but that students need to underline the target numbers in the rest of this section. For numbers 12-21, remind students that they can draw base-10 blocks to help them. Encourage students to write the sets of numbers in 22-29 vertically to compare the lined-up place values. Remind students to be careful about whether they are ordering from least to greatest or greatest to least.

Common Errors

Watch for students rounding to the wrong place instead of the target number. Some students may round to the correct place but forget to write zeros for the other digits. Make sure students pay attention to whether they are being asked to order numbers from least to greatest or greatest to least.

Students may not line up and compare the correct place values. Some students may start by comparing the smallest place value (ones) instead of the largest (thousands or hundreds).

Assess

Games

Choose a game to play to practice place value, rounding or ordering numbers.

Check work for numbers 3, 4, 7, 8, 23, 25, 27 and 29.

In Chapter 1 , we will learn about adding larger numbers with and without regrouping and using estimation to check an answer.

• Add without regrouping

• Add with regrouping

• Use rounding to estimate

• Estimate to check addition and subtraction of larger numbers

• We can add larger numbers by regrouping with groups of tens

• Place value blocks help us see how to regroup

• We round numbers to help us ﬁnd an estimate

• Estimating helps us check our work and gives us an idea of the ﬁnal answer

Vocabulary

Level C Chapter 1-1

Objective and Learning Goals

y Add two 2-digit numbers when no regrouping is required

Vocabulary

y Addition - the act of adding or putting numbers together

Materials

y Base-10 blocks

y Printable sheet of 2-digit addition problems

y 6-sided dice

How many did they

Jon and James used the leaves to make bookmarks for their family. How many bookmarks did they make in all?

Pre-Lesson Warm-up

Guiding Questions

Practice addition facts. Have students call out answers or write them on paper or a dry-erase board.

5 + 4 = [9]

6 + 2 = [8]

3 + 4 = [7]

8 + 1 = [9]

3 + 2 = [5]

Guiding Questions

1. How can we add two 2-digit numbers? [line the place values up vertically, start in the ones place, add the ones, then move left and add the tens]

(Try

Read the problems about Jon and James in Let’s Learn to the students. Show them how the first one was completed for them by adding the ones first and then adding the tens. Have students help you solve the second problem. Point out that Jon made 28 bookmarks, and James made 21. There are 8 ones in Jon’s number and 1 one in James’ number. Ask: “What is 8 ones plus 1 one?” [9 ones] Then point out that each number has two tens. Ask: “What is 2 tens plus 2 tens?”

[4 tens] They made 49 bookmarks in all.

Go through the examples in Try it Together in a similar manner.

Activities

Give students a sheet of 2-digit addition problems that do not require regrouping, with space to draw base-10 blocks next to each problem. Also provide a container of base-10 blocks. Students should make each number with base-10 blocks, then draw the blocks in, then add the two numbers together.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Provide students with grid paper or place value charts to help them line up the place values when they add. Students who do not have addition facts memorized could benefit from using a number line or base-10 blocks to count up.

Early Finishers

Go back and draw base-10 blocks for problems 5-8 in Try it Together.

Challenge and Explore

Read the word problems together, and help students set up the problems on the lines provided. Ask students: “Why is it important to line up the place values?” [if you don’t line them up, you will be adding the wrong numbers together. Only ones can be in the ones place, and only tens can be in the tens place]

Ask students: “What are the key words in these problems that tell us we need to add?” [in all] Have students come up with their own word problems using those key words, and give time for a few students to share. [answers vary]

Read the instructions on the practice page. For numbers 4 and 5 tell students the sum is correct, but the addends are incorrect. Students have to identify the error in the addends and rewrite the correct math equation using the correct addends to match the sum. One way to solve the error problems is provided in the answer key. If a student comes up with another way to fix the error, use that time to discuss how either addend may change. For number 6, students will find the missing number. Encourage students to look at place value. The ones place in 47 is seven. How many more to get to 9? [2] The ones place in the sum. Then repeat the process with the tens place.

Common Errors

Students may not line up place values correctly. Watch for students who add the tens first instead of the ones. It won’t make a difference to the answers in this lesson, but it will cause problems when they solve problems that require regrouping later on.

Assess

Discuss the results by asking the following questions:

1. What are the addends in an addition problem? [the numbers being added]

2. What strategies did you use in today’s lesson? [using place values, used subtraction, used cubes to add etc]

Games

Play 6s are Wild to practice addition facts to 10. p. 308

Give students the following problems. Have students write the problems vertically and solve. Tell them that they can draw base-10 blocks to help them.

56 + 33 = [89]

73 + 24 = [97]

45 + 42 = [87]

35 + 31 = [66]

Objective and Learning Goals

y Add 3 and 4-digit numbers when no regrouping is required

Vocabulary

y Addition - the act of adding or putting numbers together

Materials

y Plain white paper

y Scissors

y 6-sided dice

Pre-Lesson Warm-up

Guiding Questions

Practice addition facts. Have students call out answers or write them on paper or a dry-erase board.

2 + 4 = [6]

6 + 3 = [9]

3 + 5 = [8]

7 + 2 = [9]

4 + 3 = [7]

Guiding Questions

1. How can we add two 3 and 4-digit numbers? [line the place values up vertically, start in the ones place, add the ones, then move left and add the tens, then hundreds, then thousands]

Tell the students that in the last lesson, they added 2-digit numbers, and in this lesson, they will apply what they learned to add 3 and 4-digit numbers. Remind them of the importance of lining up the place values, and point out how a place value chart like the ones on this page can help them. Tell them that they can always draw a chart of their own. Point out the little green flags on the top of the ones column, and ask students why they think those are there. [to remind you to start adding the ones place and move left] Remind students that they can also break apart the addends into their place value places. Go through the example in Let’s Learn. Remind students that they should always start by adding the ones place first.

Activities

Have students make a place value chart for adding 3 to 4-digit numbers like the one below. Have them make number cards (four of each digit 0-9) to cut out and use to place inside the place value chart. thousands hundreds tens ones

Go through the example problems with the students. Emphasize that it is very important to start in the ones place. This will help them greatly when they begin regrouping in the next lesson. For the breaking apart problem, have students break apart the addends in problem 1. Make sure students break each addend apart into the correct values. Show students how to take a problem that is written horizontally and rewrite it vertically to solve.

They can use the tool they made to line up and add numbers starting with the ones. Give them a couple of practice problems, and then allow them to use this tool in their independent work.

1. Find the

Find the sum. Use a place value chart or breaking apart to solve.

Struggling Learners

Help students to line up their numbers in a place value chart. Base-10 blocks can be used to help students visualize adding larger numbers.

Early Finishers

Choose some problems on the practice page, and try to draw base-10 blocks to represent the problems.

Challenge and Explore

Give students the following problems to solve. Ask: “How can we add these even larger numbers?” [continue lining up the larger place values, and add the same way, beginning with the ones place]

23,469 + 32,110 = [55,579] 142,586 + 116,313 = [258,899]

12. Fill in the missing digits. 13. Read the problem. Solve. Show your work.

The ﬁrst grade class collected 2 ,345 cans in the food drive. The third grade class collected 3 ,524 cans. How many cans did the ﬁrst and third grade collect for the food drive in all?

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Remind students to always start with the ones place. Tell students that they can use their place value chart to help them. Remind students that they can use a place value chart or breaking apart to solve. Practice breaking apart numbers in expanded form.

Games

Play 6s are Wild to practice addition facts to 10. p. 308

Common Errors

Students may not line up place values correctly. Watch for students who start adding in the thousands place and move right. It will be very important in the next lesson to begin in the ones place. Students who use breaking apart may not fill in the correct place value places.

Assess

Check work for numbers 10 - 13.

Objective and Learning Goals

y Add 2 and 3-digit numbers with regrouping

Vocabulary

y Addition - the act of adding or putting numbers together

y Regroup - make groups of ten when carrying out operations such as addition and subtraction

Materials

y Base-10 blocks

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Practice adding without regrouping. Write the following problems on the board, have students copy them vertically and add.

26 + 22 = [48]

427 + 152 = [579]

2,345 + 1,412 = [3,757]

5,842 + 2,123 = [7,965]

Guiding Questions

1. What can we do if we have too many objects after adding the ones in 2 and 3-digit addition?

[make a group of ten, and carry it over to the tens place, then add the remaining ones. Add the tens, including the group that was carried over from the ones place]

Let’s learn!

Example: Henry and Charlie collected rocks on their walk. How many did they collect in all?

Sam gave all 34 of his rocks to John. John already had 28 rocks. How many rocks does John have in all?

You need to regroup when there are more than 10 objects in a place value. Add the new group to the next place value. How

Introduce the Lesson (Try it Together)

Read the example problem in Let’s Learn. Show and explain how to regroup by circling a group of 10 ones and then adding it to the tens column. Remind students to bring down whatever is left after they make a group of tens in the ones column. Then the students should add the ten they made with the tens already in the tens column. Show examples with actual base-10 blocks if possible, and model trading in 10 cubes for 1 rod.

Go over the examples in Try it Together, showing students to circle groups of ten blocks and trade them in. In the example problems, be sure to write +1 over the column where you need to add a group of 10. This will help students when they are no longer using base-10 blocks and instead are just using the standard algorithm.

Students will practice trading in groups of ten base-10 cubes to regroup when adding. Give students containers with base-10 blocks. Have students solve the following problems by making the numbers with base-10 blocks, trading groups of 10 cubes for rods when they can and then adding the numbers.

36 + 25 = [61] 48 + 27 = [75] 236 + 127 = [363] 519 + 245 = [764]

+ 148

14. Sarah solved the addition problem below. Did she solve it correctly? If not, correct her work and explain what she did wrong.

Answers will vary but should say that Sarah is wrong. When she had to regroup in the ones place, she carried the wrong digit to the tens place. The correct answer is 1 ,582

16. Jay had 125 blocks in

His older brother gave him 65 more. How many blocks does he have in his

now?

15. John isn’t sure how to

Answers will vary but should include John should start in the ones place. 5 +4 is 9 Then John should add the tens place 7 + 6 = 13 . John should put the 3 in the tens place and regroup the 1 to the hundreds place. Then, John should add 1 + 1 = 2 . The correct answer is 239

17. Hank and Jake were playing a math game. They were on the same team. Hank scored 345 points and Jake scored 270 points. How many points did they score in all?

Level C Chapter 1-3

Struggling Learners

Help students draw base-10 blocks to circle groups of 10, or allow them to use base-10 blocks to solve the problems. Give students grid paper or place value charts if they have trouble lining up the digits in the correct places.

Early Finishers

Draw base-10 blocks to represent problems, and circle groups of ten.

Challenge and Explore

Read the word problems 16-17 to the students. For each, ask: “What do we need to do to solve the problem?” [add the numbers together] “How do you know?” [key wordsgave him more and in all]

Help students to line up the place values and regroup as necessary.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Go over number 4 with them. Have them write +1 over the tens place. Explain that since 6 + 4 = 10, they need to add that ten to the tens column, and then there are no ones leftover. This is why there is a 0 on the answer line in the ones column. Do number 5 with the students as well. Ask: “What is 2 +9?” [11] Explain that they can make a group of 10 ones and add it to the tens column. Have students write +1 over the tens column. Now ask: “How many ones are left?” [1] Write 1 on the answer line in the ones column. Then have the students help you add the tens and then the hundreds columns. For problems 14-15, remind students to use math vocabulary (tens, ones, regrouping) in their explanations.

Common Errors

Students forget to carry over the ten they made with ones and add it to the tens column. Some students might write a 2-digit number when they should have regrouped. For example, when adding 28 + 23, they will add the ones, 8 + 3 = 11, and then add the tens, 2 + 2 = 4, and write 411 for their answer.

Assess

Games

Play Race to 500 to practice adding 2-digit numbers. p. 312

Check work for numbers 12-17.

Level C Chapter 1-4

Objective and Learning Goals

y Add 2 and 3-digit numbers with regrouping

Vocabulary

y Addition - the act of adding or putting numbers together

y Regroup - make groups of ten when carrying out operations such as addition and subtraction

Materials

y Base-10 blocks

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Practice addition facts. Have students call out answers or write them on paper or a dry-erase board.

5 + 9 = [14]

6 + 7 = [13]

3 + 8 = [11]

8 + 7 = [15]

3 + 9 = [12]

Guiding Questions

1. What can we do if we have too many cubes after adding the ones in 2 and 3-digit addition?

[make a group of ten cubes, and carry them over to the tens place, then add the remaining ones. Add the tens, including the one that was carried over, and add the hundreds]

2. What can we do if we have too many rods after adding the tens in 2 and 3-digit addition?

[make a group of ten rods, and carry them over to the hundreds place, then add the remaining tens and the hundreds, including one that was carried over]

Let’s learn!

= Circle groups of 10 . Write the equation with numbers to show your answer.

Did you regroup ones?

Did you regroup tens?

Equation + =

the Lesson (Try it Together)

Tell students that when adding, sometimes they will have to regroup a group of ten in more than one place. Read the example problem together. Ask: “How many ones are there all together?” [12] “What do we do?”

[circle a group of 10 ones, and add that to the tens. You have 2 ones left, so write that in the ones column] Write 2 in the ones column and +1 above the tens column. Ask: “How many tens are there all together? Don’t forget to add the one we just regrouped!” [10] Tell students that since 10 tens makes 100, we will add this to the hundreds column (write +1 above the hundreds column), and we have 0 left in the tens column (write 0 in the tens column). Now we add the hundreds. Don’t forget to add the one we just carried-4 + 2 + 1= 7. Write a 7 in the hundreds place. Do the Try it Together problems with the students. In number two, have students draw another rod and cross

out the group of 10 cubes that are circled to show that they traded those ones for a ten. Then have them circle the 10 rods to show that they need to regroup again. For the rest of the examples, draw or show base-10 blocks as needed.

Activities

Students will again practice trading in groups of ten base-10 cubes to regroup when adding. Give students containers with base-10 blocks. Have students solve the following problems by making the numbers with base-10 blocks, trading groups of 10 cubes for rods and groups of 10 rods for flats when they can and then adding the numbers.

346 + 265 = [611]

258 + 177 = [435]

286 + 127 = [413]

433 + 198 = [631] Introduce

579 + 245 = [824]

How many in all? Circle a group of 10 cubes. Check the box

Struggling Learners

Early Finishers

Choose some practice problems, and write word problems to go with the equations.

15. Did Max solve the addition problem below correctly? If not, correct his work and explain in words what he did incorrectly.

Answers will vary. Max is incorrect. When he added the ones place he regrouped the wrong digit. Max should have regrouped the 1 , not the zero. He did the same thing when he added the tens place. The correct answer is 930

16. Olivia can’t remember how to solve the problem below. Explain to Olivia, using words, how solve the problem. Then, solve the problem.

Answers will vary. Olivia needs to start in the ones place. 5 +7 is 12 She should put the 2 down in her answer and regroup the 1. Then, Olivia should add the tens place. 8 + 9=17 +1 she regrouped = 18 She should put down the 8 and regroup the . Then Olivia adds the hundreds place. 2 +0 = 2 + that was regrouped = 3 Put the 3 down in her answer. The correct answer is 382

17. Trevor did 135 jumping jacks on Monday and 87 jumping jacks on Tuesday. How many jumping jacks did he do in all? 18. Dad carried 186 apples. Mike carried 148 pears. How many fruits did they carry all together?

Challenge and Explore

Read the word problems to the students. Have students underline the words “in all” and “together” as key words that show they will need to add. Then have students circle the two addends in each problem. Remind students of the importance of lining up the correct place values when they copy the problems. Extend number 17 by posing the following problem: If Trevor did 88 more jumping jacks on Wednesday, what is his new total for the week? [310 jumping jacks]

Apply and Develop Skills (Practice / Exercise page)

Read the directions, and do the first 3 problems with the students. Point out in number 3 that it requires regrouping twice. Draw base-10 blocks, and show students how they will need to make a group of 10 ones first and add that to the tens. Then they will need to make a group of 10 tens, and add it to the hundreds. Remind students how important it is to remember to write +1 over the place they have regrouped, and encourage them to draw base-10 blocks to help them visualize regrouping. As students work through the remaining problems on the page, walk around to ensure students are regrouping the correct digit and are adding the regrouping. In question 16, remind students to use mathematical vocabulary in their response- ones, tens, hundreds, regrouping.

Common Errors

Students may forget to add the group of ten they carried over to the tens or hundreds place. Some students may try to write a 2-digit sum in one place value. Some students may regroup the wrong digit.

Assess

Games

Play Race to 1,000 to practice adding 3-digit numbers. p. 312

Look at the following two addition problems. Solve the problems to find the correct answers, and explain what mistakes the students who solved these made.

[71, the student wrote a 2-digit number in the ones instead of regrouping]

[322, the student didn’t add the carried over tens and hundreds after regrouping]

In addition to these problems, use number 11-18 to assess students’ understanding of addition with two regroupings.

Level C Chapter 1-5

Objective and Learning Goals

y Round to the nearest hundred to estimate

y Add 3-digit numbers

Vocabulary

y Round - find a close but easier to work with number to a given number

y Estimate - to find a close enough answer when the exact answer is not needed

Materials

y Base-10 blocks

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Practice rounding to the nearest hundred. Give students a number and have them round it to the nearest hundred. All students should write answers on a piece of paper or dry-erase board.

124 [100]

678 [700]

532 [500]

871 [900]

356 [400]

812 [800]

Guiding Questions

1. What can we do when we don’t need an exact answer to an addition problem? [round the numbers and add to find an estimate]

An estimate is a number that is close to the answer. It helps us see if our answer makes sense.

Zookeepers want to know how much food the bears need weekly at the zoo. Green bear eats 120 pounds of food a week. Blue bear eats 156 pounds of food. About how much food do they eat all together per week?

We do not need an exact number for the food. We can round to estimate the amount of food.

Read the example problem together with the class. Have students underline the word “about” in the problem. Tell them that this is a key word that tells us we do not need an exact answer and can estimate. Tell students that they will be rounding to the nearest hundreds to estimate in this lesson. Have students underline the target number in the hundreds place, and then look to the right. Remind students of the rhyme to round (5 or more, let it soar, 4 or less, let it rest). Go through the examples on the page. Tell students that they will find the exact answer and then an estimate. The estimate can tell them if their exact answer makes sense or if they might have made a mistake.

Activities

Students work with partners to make 3-digit numbers, round and add. Give partners base-10 blocks. Have each partner make a 3-digit number that is less than 500 with base-10 blocks. Now have students line up the rods and cubes next to a flat to see if they are closer to the next hundred or not. They should round their number up or down to the nearest hundred, and then add their two numbers together. They can also practice adding and regrouping with base-10 blocks to find the exact answer. Have students write down their exact equation and their rounded equation with answers to both. Then each partner should make new numbers and repeat the process as time allows.

it together!

13. Ducks migrated 125 miles on Monday and they ﬂew another 216 miles on Tuesday. About how many miles did they ﬂy on both days?

Struggling Learners

Post the rhyme to round somewhere visible to the students for them to reference. Have students underline the target number in the hundreds place and circle the tens place to help them round to the correct place. Allow students to use number lines to help them round, or have them draw “rounding hills.” Encourage students to draw base-10 blocks or use actual base-10 blocks if they are struggling to regroup and find exact answers.

Early Finishers

Make a list of situations where an exact answer is not needed and you can estimate.

14. Jim picked 267 apples. Alan picked 106 apples. About how many apples did they pick in all?

Challenge and Explore

Look at problems 3, 6, 9 and 12 again. Make another estimate. This time, round the numbers to the nearest ten and add. Which estimate is closer to the exact answer, and why? [rounding to the nearest ten is closer because those numbers are closer to the original numbers]

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Tell them that they will be rounding to the nearest hundred in all of these problems. Do number 1 with the students. Remind students that they will be finding an estimate for all of the problems. Read the word problems to the students, and have them underline key words in the problems. [on both days, in all]

Common Errors

Assess

Games

Play Draw and Round to practice rounding to the nearest hundred. p. 310

Check work for numbers 10, 11 and 12.

Level C Chapter 1-6

Objective and Learning Goals

y Round to the nearest hundred to estimate

y Add 3-digit numbers

Vocabulary

y Round - find a close but easier to work with number to a given number

y Estimate - to find a close enough answer when the exact answer is not needed

Materials

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Practice rounding to the nearest hundred. Give students a number, and have them round it to the nearest hundred. All students should write answers on a piece of paper or dry-erase board.

264 [300]

518 [500]

782 [800]

621 [600]

336 [300]

942 [900]

Guiding Questions

1. How can we check that an answer to an addition equation makes sense? [round the numbers and add to find an estimate. Compare the estimate to the exact answer. If they are close, the answer makes sense]

About how many toppings are there? Do we need an actual answer or an estimate? Rounding can help us in real life. We can estimate:

• How much milk to pour in a cereal bowl

• How many pages you can read in 15 minutes

• How many raspberries on a bush We estimate when we do not need an exact number, or when we want to know if our answer is reasonable.

Daniel has 25 red marbles and Michael has 32 blue marbles. About how many marbles do they have all together? We do not need an exact number. So:

amount

Sometimes we want to know if our answer makes sense. For example, I wrote that: Does that answer seem reasonable? Let’s check! Yes! The actual answer is reasonable.

Read through the information and examples at the top of the page. Focus on using an estimate to check whether an exact answer is reasonable. Tell students that if the exact answer is close to the estimate, it is reasonable and likely to be correct. Tell students that in this lesson, they will focus on using estimates to check their work to see if their answers are reasonable. Do the rest of the examples in Try it Together. For each one, have a student tell you if the answer is reasonable or not, and ask them to explain why or why not.

Activities

Students work in pairs to practice adding 3-digit numbers and estimating to check that their answers are reasonable. Each partner should write down a 3-digit number that is less than 500. Then one partner should add to find the exact answer while the other partner rounds the numbers to the nearest hundred and adds them to find an estimate. The partners use the estimate to decide whether the exact answer makes sense. If it does not, then they must try to find the mistake. If it does, they write down new numbers and switch roles. The partner who estimated finds the exact answer, and the partner who found the exact answer estimates.

Struggling Learners

Post the rhyme to round somewhere visible to the students for them to reference. Allow students to use number lines to help them round, or have them draw “rounding hills.” Encourage students to draw base-10 blocks or use actual base-10 blocks if they are struggling to regroup and find exact answers.

Early Finishers

Choose some of the equations on the practice page. Write a word problem to go with each equation where an exact answer is not needed, only an estimate.

687 people rode the Main Street bus on Monday. 934 people rode the same bus on Tuesday. Would 1 ,600 people be a reasonable estimate for how many people rode the bus in all for both days?

people waited at the Cherry Street bus stop this morning. 285 people waited there this afternoon. Would 500 be a reasonable estimate for how many people waited there in all today?

Challenge and Explore

Look at problems 9-12 again. Make another estimate. This time, round the numbers to the nearest ten, and add. Which estimate (rounding to nearest hundred, or rounding to nearest ten) is easier to find, and why? [rounding to the nearest hundred is easier because when you add, you have more 0s to add]

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Remind them that they are to find the exact answer and then find an estimate to see if their answer makes sense. Tell them that this is a way to check their work. If their exact answer and estimate are not close, they should solve for the exact answer again to see if they get closer. Read the word problems to the students. Remind students that we use estimation to see if an answer is reasonable.

Common Errors

Some students may just change the tens and ones place to zeros and leave the hundreds place the same every time when rounding. When finding the exact answers, students may forget to add the carried over tens and hundreds when they regroup. Watch for students who get the correct exact answer when using the algorithm but do not round and estimate correctly. These students may think that their exact answer is not reasonable.

Assess

Games Play Draw and Round to practice rounding to the nearest hundred.

Have students answer the following question: How do you know if your answer is reasonable or not? [round the numbers and estimate. If your exact answer and estimate are close, then your answer is reasonable]

Objective and Learning Goals

y Solve 2-step word problems by adding and subtracting centimeters and meters

Vocabulary

y Centimeters - a unit of measuring length; 100 centimeters make a meter

y Meters - a unit of measuring length; a meter is 100 centimeters long

Materials

y Dry-erase boards and markers

y Centimeter rulers

y Strips of precut paper of varying lengths

Pre-Lesson Warm-up

Guiding Questions

Tell students to add 3 + 4 and write the answer on their white board. Say “Now take away 2 from your answer. How much is left?” [5] Have the students record the equations with a ? for the unknown as you write them on the board. 3 + 4 = ?

7 - 2 = ?

Tell students that today they will be solving word problems that have 2 steps. They will need to add and subtract and record their equations in this way.

Guiding Questions

1. How can we solve a 2-step word problem? [draw a picture to help you and write out the equations needed to find both parts of the answer]

The school has a fence at the back and on one side of the school. The fence in the back is 134 meters. The fence on the side is 63 meters. A storm knocked down 26 meters of the fence. How much fence was left? Then write equations. Use a ? to represent the

Try it together!

Solve the story problems. Draw a picture if it helps you. Write equations to represent the problems.

1. In art class, Daniel drew a line that was 15 centimeters long. He then erased 4 centimeters. After that he drew 22 more centimeters onto his line. How long was his line in the end?

2. The teacher made a banner for the hallway that was 154 centimeters long. The students added 62 centimeters. Then the teacher taped 68 more centimeters on. How long is the banner now?

Notes

(Try

Read the problems in Let’s Learn and Try it Together to the class. Encourage students to sketch out what is happening in the story problems to help them visualize and decide what they need to do to solve the problem. Show them how the Let’s Learn problem has a picture showing the fence and walk them through the steps in solving the problem. Have them try to come up with their own sketches and methods for solving the Try it Together problems and then go over the answers. Students may think to solve the problems in different ways, but make sure they record their ideas using equations. For example, in number 1, students may realize that if 4 centimeters was taken away and Daniel added 22 back on, that the line is 18 centimeters longer than it was originally. Have them record 2 steps by writing equations like 22 - 4 = ? and 15 + 18 = ?

Activities

Give students each a strip of paper of different lengths. Have them measure their paper strip to the nearest centimeter. Then have them line up their paper strip with a partners strip and tape them together end to end. Have them add to find the total length, then measure to check their work. Next tell students to cut some off of their combined paper strips and measure the piece they cut off. Then subtract that amount from the length of their combined strips. After they solve for what is left, tell them to measure the strip that is left to see if they subtracted correctly. Introduce the Lesson

Solve the story problems. Draw a picture if it helps you. Write equations to represent the problems.

1. The music teacher set up chairs for the class. The row was 12 meters long. Parents added 5 meters worth of chairs to one end. Then the teacher took 3 meters of chairs o the other end. How many meters long is the row now?

2. One class made a paper chain 218 cm long and another made one 213 cm long. They put their chains together and then another class added 142 cm. How long is the paper chain now?

3. The man was planting ﬂowers in the park. First he dug a hole 10 cm deep. Then he dug down 8 more cm. He realized that was too deep, so he put 9 cm of dirt back in the hole. How deep is the hole now?

4. The hiker hiked 402 m. Then he rested and hiked another 316 m. He then hiked 79 m to get to a waterfall. How far was the waterfall from where he started?

5. The students laid their crayons end to end. The crayons were 32 cm long. They added more crayons and it was 13 cm longer. Then the teacher added a crayon which was 6 cm long. How long is it now?

Sketches will vary.

Sketches will vary. Sketches will vary.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Read problems aloud to students or partner struggling readers with strong readers to read the problems together. Have students underline key words in the problem that tell them whether to add or subtract (add, put together, more, take away, fell off, etc.)

Early Finishers

Students can write their own 2-step word problems for classmates to solve.

Challenge and Explore

Present the following problem to students to solve:

Dad had 3 pieces of wood that were 3 meters long each. He laid them end to end and then sawed off 2 meters. How many meters long was the wood after that? [7 meters]

Students may draw a picture or use multiple different strategies and equations to solve this problem. Have them share their strategies if time.

Read the directions to the students. Read the first problem and have students sketch out what is happening in the problem and suggest equations to use to solve the problem. Have students complete the page independently. When students finish have them share the equations they used to solve the problems. Point out that some students solved the problems in different ways, but still got the same answer. Try having students listen to how a classmate solved the problem and then explain it in their own words to the class.

Common Errors

Some students may struggle to read word problems or may not read carefully. Students may struggle to know when to add and when to subtract.

Assess

Games

Play The Biggest Difference to practice subtracting larger numbers p. 313

Check work for number 5.

Level C Chapter 1-8

Objective and Learning Goals

y Add 2, 3, and 4-digit numbers with regrouping

y Use estimation to check that sums are reasonable

Vocabulary

y Addition - the act of adding or putting numbers together

y Regroup - make groups of ten when carrying out operations such as addition and subtraction

y Round - find a close but easier to work with number to a given number

y Estimate - to find a close enough answer when the exact answer is not needed

Materials

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Practice addition facts. Have students call out answers or write them on paper or a dry-erase board.

6 + 9 = [15]

8 + 7 = [15]

5 + 8 = [13]

9 + 7 = [16]

4 + 9 = [13]

Guiding Questions

1. What can we do if we have too many objects after adding the ones, tens or hundreds in 2, 3 and 4-digit addition?

[make a group of ten, and carry it over to the tens, hundreds or thousands place, then add the remaining ones. Add the tens, hundreds and thousands, including any groups that were carried over from the ones, tens or hundreds place]

2. How can we check that an answer to an addition equation makes sense? [round the numbers, and add to find an estimate. Compare the estimate to the exact answer. If they are close, the answer makes sense]

Read the information at the top of the page to the students, and do the example together. Go over the rest of the examples on the page to review adding with regrouping and estimating. Draw base-10 blocks on some problems so students can visualize regrouping. Emphasize how important it is to remember to write +1 when carrying regrouped tens, hundreds and thousands.

Activities

To review, students will practice the same activity from lesson 1-6. Students work in pairs to practice adding 4-digit numbers and estimating to check that their answers are reasonable. Each partner should write down a 4-digit number that is less than 5,000. Then one partner should add to find the exact answer while the other partner rounds the numbers to the nearest thousand and adds them to find an estimate. The partners use the estimate to decide whether the exact answer makes sense. If it does not, then they must try to find the mistake. If it does, they write down new numbers and switch roles - the partner who estimated finds the exact answer, and the partner who found the exact answer estimates.

Apply and Develop Skills (Practice / Exercise page)

Read through all the directions, and answer any questions students have about the review problems on this page. Give plenty of time for students to work and ask questions.

Struggling Learners

Help students line up place values by writing the numbers on grid paper or in place value charts. To help with rounding, have students draw number lines or “rounding hills.”

Early Finishers

Estimate to check that your answers to numbers 1-15 are reasonable.

Challenge and Explore

Try the following multi-digit addition problem. Can you make an estimate to check that your answer is reasonable?

128,457 + 134,675 [263,132]

[Estimates may vary depending on which place students choose to round to, but many may choose to do 100,000 + 100,000 = 200,000]

Common Errors

Students may not line up place values correctly when adding. Some students may forget to add what they carried over to a place value.

Assess

Games

Play Race to 1,000 to practice adding 3-digit numbers. p. 312

Check work for numbers 14, 15, 16, 17 and 18.

Chapter 2

In Chapter 2, we will learn to subtract larger numbers with and without regrouping. We will also learn to use addition to check subtraction and estimate to check the answers.

• Subtraction without regrouping

• Subtraction with regrouping

• Subtracting numbers through the thousands place

• We can subtract large numbers by regrouping groups of 10

• Place value blocks can help us see how to regroup

• Using addition to check the answer to a subtraction problem

• Rounding numbers to hundreds or thousands to estimate

• Estimating to check to see if our answer makes sense

• Using metric units of length

Level C Chapter 2-1

Objective and Learning Goals

y Subtract 1 and 2-digit numbers from 3-digit numbers without regrouping.

Vocabulary

y Subtraction - the act of subtracting or taking a number away from another number

Materials

y Base-10 blocks

y Printable sheet of subtraction problems

y Deck of playing cards or number cards

Pre-Lesson Warm-up

Guiding Questions

Practice subtraction facts. Have students call out answers or write them on paper or a dryerase board.

5 - 4 = [1]

9 - 2 = [7]

8 - 4 = [4]

8 - 2 = [6]

7 - 3 = [4]

Guiding Questions

1. How can we subtract 1 and 2-digit numbers from 3-digit numbers?

[line the place values up vertically, start in the ones place, subtract the ones, then move left and subtract the tens and then the hundreds]

Sam has 126 buttons. He uses 5 of them to repair his coat. How many buttons are left over?

Sam’s brother, Ted, also needs to use one button to ﬁx his pants. How many buttons are left over?

Read through the example problems, and model how to subtract using base10 blocks. Remind students that when adding, they always started in the ones place. Tell them that it will be just as important when subtracting. They should always start in the ones place, and move to the left. Go through the examples on this page. Use or draw base-10 blocks to model at least some of the problems. Cross out or remove the cubes, rods and flats according to the problem. Look at the answer key for the Try it Together problems to see an example of how the students should cross out base-10 blocks.

Activities

Give students a sheet of subtraction problems that do not require regrouping. Make sure there is space to draw base-10 blocks next to each problem. Also provide a container of base-10 blocks. Students should make each number with base-10 blocks, then draw the blocks in, then cross out blocks and subtract.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Early Finishers

Go back and draw base-10 blocks for the starting number in the problems, then cross out blocks to show how many you subtracted.

Challenge and Explore

Read the word problems to the students. Ask them to underline keywords in the problem that tell them to subtract. [left over] Extend problem 16 further: The next day at school, Carl gave a piece of gum to each of his 21 classmates, then he chewed a piece himself. How many pieces does he have left over now? How many did he start with when he went to school? [144] How many pieces does he have now? [122- he gave away 21 and chewed 1 so 144-22=122.]

Read the directions to the students. Tell students to cross out place value blocks in the pictures on numbers 1-3. Encourage them to draw their own place value blocks to cross out if they need help with the rest of the page. Remind students to always start at the ones place, and move to the left. For numbers 12-15, you may need to guide students to help them fill in the missing digits. Question 17 could be a challenge for some students because it is a two-step problem. Guide students, if necessary.

Common Errors

Watch for students who subtract starting with the hundreds place instead of the ones place. It won’t change their answers in this lesson, but will cause problems later on when they have to regroup.

Assess

Games

Play Draw and Subtract to practice subtraction facts to 10. p. 313

Give students the following problems. Have students write the problems vertically and solve. Tell them that they can draw base-10 blocks and cross out to help them.

156 - 33 = [123]

738 - 4 = [734]

485 - 42 = [443]

235 - 31 = [204]

You can also use problems 10-16 to assess students’ understanding.

Level C Chapter 2-2

Objective and Learning Goals

y Subtract 3 and 4-digit numbers without regrouping

y Solve word problems involving multi-digit addition and subtraction

Vocabulary

y Subtraction - the act of subtracting or taking a number away from another number

Materials

y Deck of playing cards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice subtraction facts. Have students call out answers or write them on paper or a dryerase board.

6 - 4 = [2]

9 - 3 = [6]

9 - 4 = [5]

7 - 5 = [2]

8 - 3 = [5]

Guiding Questions

1. How can we subtract 3 and 4-digit numbers? [line the place values up vertically, start in the ones place, subtract the ones, then move left and subtract the tens, then hundreds and then the thousands]

2. What are the steps in solving word problems involving addition and subtraction? [define what problem you need to solve, make a plan and decide whether to add or subtract, solve the equation, check to be sure your answer makes sense]

Start in the ones place when subtracting numbers. Move from right to left. Solve one place value at a time.

Read the problem. Show your work. Solve.

(Try

Tell students that today they will build on what they learned in the last lesson by subtracting larger numbers. Read the example problem, and remind students that the green flag shows them to start with the ones place and then move left to subtract. Emphasize the importance of lining the place values up vertically. Have the students help you complete all of the problems on this page. Make sure they understand that they must always start in the ones place and move left. When you get to the word problem, introduce the problem solving strategies that you’ll practice on the next page. Read the problem with students. Ask students to underline the question that you’re being asked to answer. Then, work with students to underline the key words in the problem that will help you solve. Now, with the help of students, determine the correct operation and solve the problem. After getting the answer, model how to go back into the problem and make sure the answer makes sense.

Activities

Have students work in pairs or small groups to write word problems to go with the following two equations. Have the students underline the keywords in the problems they wrote that tell them whether to add or subtract. Students should also solve the problems.

Follow these rules to help you solve a story problem. Read the problem. What’s the question I need to answer?

Clues - What do I need to do to solve the problem?

1. Jason did 1 ,342 jumping jacks this week. He did 1 ,498 jumping jacks last week. How many more jumping jacks did he do last week?

Strategy - What operation should I use and why?

2. Jason walked 4 ,980 steps today. He walked 5 ,001 steps yesterday. How many steps did he walk in all?

What question do I need to answer? What question do I need to answer?

How many more jumping jacks did he do last week?

Underline how many more, 1,342 jumping jacks, 1,498 jumping jacks

Underline the clues to help me solve. Underline the clues to help me solve. What operation will you use? Solve. What operation will you use? Solve.

Underline in all, 4,980 steps, 5,001 steps

Struggling Learners

Subtraction

1,498-1,342= 156 more jumping jacks 4,980 + 5,001 = 9,981 steps

Look at your answer. Does it make sense? Look at your answer. Does it make sense?

Yes, I reread the question. I found the di erence between the number of jumping jacks.

Yes, I reread the question. I found the total number of steps.

Find the di erence. Fill in the missing digits.

4. 5. 6523 — 312

3. Jason skipped rope 1 ,286 times last week. He skipped rope 1 ,145 times this week. How many more skips did he do last week? 4 6 8 2 5 5 1

1,286-1,145= 141 more skips 6,211

How many steps did Jason walk in all? Addition 4 4 6 3

Jason wants to work for 9 ,890 minutes total for this month and next month. He already worked for 5 ,450 minutes this month. How many minutes will he need to work next month to reach his goal?

9,890 - 5,450 = 4,440 more minutes

Apply and Develop Skills (Practice / Exercise page)

Provide students with grid paper or place value charts to help them line up the place values when they subtract. Students who do not have subtraction facts memorized could benefit from using a number line or hundreds chart to count back. Student may also benefit from a chart listing key words that signal addition or subtraction. For example- how many more would mean subtract and how many in all would mean to add.

Early Finishers

Go back and write word problems to match the equations in the Try it Together section.

Challenge and Explore

Read the Challenge problem to the students:

Jason wants to work 9,890 minutes for this month and next month. He already worked for 5,450 minutes this month. How many minutes will he need to work next month to reach his goal? [4,440 minutes]

Help students to understand what the problem is asking and that they need to subtract. Remind students to line the places up carefully before they solve.

Tell students that they will use the skills they have learned to add and subtract large numbers and apply those skills to word problems. Go over the steps at the top of the page for solving problems. Read problem number 1 to the students, and go through the steps with them. Depending on the level of your students, you can have students work with a partner or work independently to complete questions 2 and 3. As students work, remind them of the problem solving steps.

Common Errors

Watch for students lining up place values incorrectly. When solving word problems, some students may not choose the correct operation. Help them to identify keywords in the problem that will help them decide which operation to use.

Assess

Extend this problem: The month after next, Jason works for 5,275 minutes. If he reached his goal exactly, how many total minutes does he work next month and the month after?

[9,715]

Games

Play Draw and Subtract to practice subtraction facts to 10. p. 313

Have students copy the following problem, underline the keywords [how many more] in the problem that help them decide which operation to use, set up the problem vertically and solve.

Jason walked 6,322 steps on Tuesday. He walked 9,487 steps on Wednesday. How many more steps did he walk on Wednesday? [3,165 steps]

Level C Chapter 2-3

Objective and Learning Goals

y Subtract 2 and 3-digit numbers with one regrouping.

Vocabulary

y Subtraction - the act of subtracting or taking a number away from another number y Regroup - make groups of ten when carrying out operations such as addition and subtraction

Materials

y Base-10 blocks

Let’s learn!

You need to regroup when there are not enough objects in a place value. To regroup, take a group of 10 away from the next place value. Add it to the place value where you are working.

Liam and Owen are playing with 150 bricks. Liam uses 25 bricks to build a house. How many bricks are left over?

Pre-Lesson Warm-up

Guiding Questions

Practice subtracting without regrouping. Write the following problems on the board, have students copy them vertically and subtract.

126 - 22 = [104]

427 - 215 = [212]

5,365 - 2,132 = [3,233]

3,842 - 2,120 = [1,722]

Guiding Questions

1. What can we do if there are not enough objects to subtract from in the tens or ones place when subtracting 2 and 3-digit numbers?

[If there are not enough ones to subtract from, borrow from the tens place by breaking a ten into 10 ones and moving it to the ones place. If there are not enough tens to subtract from, borrow from the hundreds place by breaking a hundred into 10 tens and moving it to the tens place]

How many are left over? Regroup rods to subtract in the ones place or regroup ﬂats to subtract in the

Introduce the Lesson (Try it Together)

Read the example problem at the top of the page. Make the numbers with base-10 blocks, and show students how to “borrow” a rod from the tens place and exchange it for 10 cubes so that you have enough in the ones place to subtract from. Go through the problems in Try it Together with the students, showing them how to “borrow” tens or hundreds as needed with base-10 blocks. As you do the problems with base-10 blocks, make sure students are crossing out and changing the numbers they have borrowed from and adding them to the smaller place value. It is important that students record these steps in the algorithm to prepare for doing the problems without base-10 blocks.

For number 1 in Try it Together say: “I’m starting in the ones place. Can I take 7 away from 5?” [no] “What should I do?” [borrow a ten, and make 10 ones] “If I borrow a ten, how many tens will I have left?” [3] (Cross out the 4, and write 3). “I’m going to draw the 10 ones

I just borrowed next to the 5 I already have. How many ones do I have now?” [15] “Can I take 7 away from 15?” [yes!] “How many will I have left?” [8] “I had 3 tens left after I borrowed 1, and there are no tens to take away, so I will bring the 3 down. What is 45 minus 7?” [38]

Activities

Students will practice borrowing and regrouping rods or flats to get enough to subtract in each place value. Give students containers with base-10 blocks. Have students solve the following problems by making the numbers with base-10 blocks, borrowing from the next higher place value when needed and taking away what they need to subtract.

36 - 28 = [8]

43 - 27

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Do the first 4 problems with the students and more if you feel they need it. Emphasize the importance of always starting in the ones place. Have them start by thinking, “Are there enough ones on top to take away the bottom number?” If not, they will need to regroup. Encourage students to draw out the base-10 blocks if it helps them.

Struggling Learners

Give students base-10 blocks to use, or help them draw the base-10 blocks to represent the numbers.

Early Finishers

Choose some of the subtraction problems on this page. Write your own word problems to match the equations.

Challenge and Explore

Read the word problems to the students. Have them underline the key words that tell them to subtract. [left over, left] Have students write the problems vertically, making sure to line up place values. Extend the problem by telling students that Liam used 38 bricks for the garage on his house. Ask how many bricks will be left in Liam’s house if he decides to take the garage off. [56]

Common Errors

Some students will subtract the top number from the bottom number when there isn’t enough to subtract the bottom number from the top. For example, in the problem 75 - 28, some students will subtract 7 - 2 and 8 - 5 and say the answer is 53 instead of borrowing a ten like they need to. Some students may borrow but then forget to change the 7 in the tens place to a 6, or they may forget to add the ones that were already there to the ten they borrowed and subtract 8 from 10 instead of from 15.

Assess

Play Brain vs. Hand to practice subtraction facts to 18. p. 308

Check work for numbers 16, 17, 18 and 19.

Objective and Learning Goals

y Subtract up to 4-digits with two regroupings

Vocabulary

y Subtraction - the act of subtracting or taking a number away from another number

y Regroup - make groups of ten when carrying out operations such as addition and subtraction

Materials

y Base-10 blocks

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed (for game)

Pre-Lesson Warm-up Guiding Questions

Practice subtraction facts to 18. Have students call out answers or write them on paper or a dry-erase board.

12 - 4 = [8]

16 - 8 = [8]

13 - 4 = [9]

12 - 5 = [7]

11 - 8 = [3]

Guiding Questions

1. What can we do if there are not enough objects to subtract from in both the tens and ones place when subtracting 2 and 3-digit numbers?

[borrow from the hundreds by breaking a hundred into 10 tens and moving it to the tens place; then borrow from the tens by breaking a ten into 10 ones and moving it to the ones place. Subtract, starting with the ones place]

Read the example problem together with the class. Explain that some problems require regrouping in more than one place. Emphasize the importance of beginning in the ones place and moving to the left to solve each problem. Go through the examples together, drawing base-10 blocks as needed to help students visualize. Remind students to first think “Are there enough ones on top to take away the bottom number of ones?” If not, regroup. Then they should think “Are there enough tens on top to take away the bottom number of tens?” If not, regroup again.

Activities

Students will practice borrowing and regrouping rods or flats to get enough to subtract in each place value as they did in the last lesson. In this lesson, they will need to regroup across more than one place value. Give students containers with base-10 blocks. Have students solve the following problems by making the numbers with base-10 blocks, borrowing from the next higher place value when needed and taking away what they need to subtract. Have students also write the problems vertically and solve using the algorithm to record what they did with the base-10 blocks.

436 - 158 = [278]

-167 = [76]

- 187 = [59] 513 - 245 = [268]

- 149 = [284]

- 166 = [198]

How many are left over? Regroup a tens rod or hundreds ﬂat when needed.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Encourage students to draw base-10 blocks to help them if needed. Remind students to start in the ones place and clearly show their work to keep track of what they borrow and what is left in each place after they borrow.

Struggling Learners

Give students base-10 blocks to use, or help them draw the base-10 blocks to represent the numbers.

Early Finishers

Make up your own subtraction problems that require regrouping. Make the number you are starting with using base-10 blocks, or draw the blocks to show the number. Think of a number to subtract from your blocks. Challenge yourself to come up with a number that will require regrouping. Then write your problem vertically, cross out or take away blocks and record the algorithm on your paper.

Challenge and Explore

Present the following problem, which requires regrouping 3 times, to students: 6,432 - 3,847 = [2,585]

Discuss what makes this problem more challenging [you must regroup or “borrow” 3 times] and how students solved it [answers will vary. Some students may draw or use base10 blocks and borrow a group of 10 from the next higher place value. Other students may know how to use the algorithm to borrow from the thousands place the same way they have for other places]

Common Errors

Some students will subtract the top number from the bottom number when there isn’t enough to subtract the bottom number from the top. For example, in 34 - 7 , they may subtract 4 from 7 in the ones place and say the answer is 33 instead of borrowing a ten and subtracting 7 from 14. Watch for students who borrow tens or hundreds and then forget to cross out and record the new number of tens or hundreds that are left.

Look at the following two addition problems. Solve the problems to find the correct answers, and explain what mistakes the students who solved these made.

[179, the student subtracted the top number from the bottom number in the ones and tens place instead of regrouping]

[164, the student borrowed a hundred and added it to the tens to subtract but then still subtracted from the original amount of hundreds instead of one less]

Level C Chapter 2-5

Objective and Learning Goals

y Use inverse operations to check 2 and 3-digit addition and subtraction Vocabulary

y Inverse operations - the opposite operation that can be used to check your work Materials

y Printable sheet of subtraction problems with correct and incorrect answers for students to check

Pre-Lesson Warm-up

Guiding Questions

Give students an addition or subtraction fact, and have them write that fact with the answer and also write the rest of the fact family.

8 + 7 = [8 + 7 = 15, 7 + 8 = 15, 15 - 7 = 8, 15 - 8 = 7]

4 + 5 = [4 + 5 = 9, 5 + 4 = 9, 9 - 4 = 5, 9 - 5 = 4]

12 - 9 = [12 - 9 = 3, 12 - 3 = 9, 3 + 9 = 12, 9 + 3 = 12]

14 - 6 = [14 - 6 = 8, 14 - 8 = 6, 6 + 8 = 14, 8 + 6 = 14]

Guiding Questions

1. How can we use inverse operations to check our work on addition and subtraction equations?

[after adding, subtract one of the addends from your answer, and you should get the other addend. After subtracting, add your answer to the subtrahend (the number you took away), and you should get the minuend (the number you started with)]

Let’s learn!

Addition and subtraction are opposites. We can use addition to check our answer to subtraction. We can also use subtraction to check addition. They are inverse operations.

There were 86 candies in the jar. Je ate 35 candies. How many candies are in the jar now? Check your answer by adding.

Start with a subtraction problem. Then use addition to check it.

Always start with your answer, then work backwards and add the smaller number.

Games

Choose a game to practice addition or subtraction.

Introduce the Lesson (Try it Together)

Read the information at the top of the page in Let’s Learn with the students. Tell the students that just like addition and subtraction facts are related in “fact families,” multi-digit addition and subtraction are related as well. Go through the example problem saying, “When we take 35 away from 86, we are left with 51. So if we add 51 and 35 together, we should get 86. Let’s check!” Do the Try it Together problems in a similar manner. Number 1 is done for you. Say: “Do you agree that 86 minus 45 is 41?” [yes] “So 41 plus 45 should equal 86. Does it? Do the addition to see.” [yes; 41+45 = 86] Do number two together. Ask: “What is 3 minus 2?” [1]Write a 1 in the ones place. Ask: “What is 6 tens minus 5 tens?” [1 ten] Write a 1 in the tens place. Ask: “What is 7 hundreds minus no hundreds?” [7 hundreds] Write a 7 in the hundreds place. “We think 763 minus 52 is 711. If that’s true, then 711 plus 52 should equal 763. Add to see if

we are correct.” Give students a minute to add, and ask “Are we correct?” [yes] Go through the other examples this way.

Activities

Tell students that they will be the teacher and “grade” another student’s work. Give students the printable sheet of subtraction problems that have been solved. Some of the answers are correct, and others are incorrect. Tell the students to use addition to check whether this student is correct or incorrect, and then fix any incorrect answers. Explain that you are looking at the inverse operation to see how they checked each problem. Encourage students to show this work and not just redo the original problem. Let students write a star or a check next to the correct answers and circle the problems that are incorrect. If there is time, students can do the correct work for those problems and check again.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Help students set up the addition problem they need to do to check subtraction. Draw a down arrow next to the addition problem and then an up arrow next to the subtraction problem to show that they need to start from the answer and do the opposite or “turn the problem upside down.”

Early Finishers

Write your own subtraction problems. Solve them, and write an addition equation to check your work. Challenge yourself to write problems that require regrouping and use 4-digit numbers.

Challenge and Explore

Solve the following problems. Check your work by using inverse operations.

6,531 - 3,356 = [3,175; 3,175 + 3,356 = 6,531] 3,425 + 2,378 = [5,803; 5,803 - 2,378 = 3,425]

How does using inverse operations work to check our answers to addition and subtraction problems? [answers will vary. Possible answer: Addition and subtraction are opposite operations. When you add, you are putting together two parts(addends) to come up with a total (sum). If you take one of those parts away (subtract it) from the total, you should end up with the other part]

Read the directions on the page to the students. Help students choose or set up the correct addition problem to check their work by reminding them to simply turn the problem upside down and put the numbers in the opposite order. Help them understand how this works by explaining to them that the answer to the subtraction problem plus the number they took away are the two parts they need to add together to get the total. The total is the number they start with in a subtraction problem. Draw a diagram like the one below, and encourage students to draw or think about this diagram when solving the problems.

Total (the number you start with in subtraction and the answer in addition)

Part

(addition: one of the addends subtraction: the number you take away or the answer)

Students may not add the correct numbers to check subtraction. For example, in 45 - 22 = 23, they may add 23 + 45 instead of adding 23 + 22.

Assess

Part

(addition: one of the addends subtraction: the number you take away or the answer)

Check work for numbers 7, 8 and 9.

Level C Chapter 2-6

Objective and Learning Goals

y Estimate to check that an answer to a subtraction problem makes sense

Vocabulary

y Round - find a close but easier to work with number to a given number

y Estimate - to find a close enough answer when the exact answer is not needed

Materials

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Practice rounding.

Round to the nearest ten:

67 [70]

42 [40]

81 [80]

36 [40]

128 [130]

Round to the nearest hundred:

813 [800]

575 [600]

491 [500]

358 [400]

243 [200]

Guiding Questions

1. How can we use estimation to check that an answer to a subtraction equation makes sense?

[round the numbers, and subtract the rounded numbers to find an estimate. Compare the estimate to the exact answer. If they are close, the answer makes sense]

Let’s learn!

In the last chapter we learned that we estimate when we do not need an exact number, or when we want to know if our answer is reasonable. You can estimate with subtraction too.

Pierce has 68 red marbles and Nolan has 24 blue marbles. About how many more marbles does Pierce have? We do not need an exact number. So:

Sometimes we want to know if our answer makes sense. For example, I wrote that:

Does that answer seem reasonable? Let’s check!

There's a mistake. Looks like I added instead of subtracted. No! Let’s see where I made a mistake.

Subtract. Estimate to check. Is your answer reasonable? Circle yes or no.

Introduce the Lesson (Try it Together)

Read the information and example problem at the top of the page to the students. Have students underline the word “about” in the problem, and remind them that this is a key word that tells us we do not need an exact answer and can estimate instead. Explain that an estimate is a number that is close to the answer, but it is not the exact answer. Tell students that they will round to the highest place value, which in this case is the tens place. Remind students to start by underlining the target place value. Underline the 6 in 68. Then circle the digit to the right, the 8. Ask students to repeat the rhyme to round: 5 or more, let it soar, 4 or less, let it rest. Ask students: “Is the number we circled 5 or more?” [yes] “What do we do?” [round the number up to 70] Go through this process to round 24 to 20. Point out to students that the rounded numbers are now much easier to work with: 70 - 20. If they know 7-2, they know 70 - 20!

Read through the second example in the Let’s Learn section, and point out that the estimate and the exact answer are VERY different. Ask: “What does that mean if the answer and the estimate are not close?” Tell students that this is their cue to try the problem again, and figure out what went wrong. There may be

a calculation error. Solve the problem with students for the correct answer, and compare it to the estimate. [679 - 598 = 81; compare to 100] “Now is our answer reasonable?” [yes]

Do the Try it Together problems with the students.

Activities

Students work in pairs to practice subtracting 3-digit numbers and estimating to check that their answers are reasonable. Each partner should write down a 3-digit number. Choose roles. One partner should subtract the smaller number from the bigger number to find the exact answer. At the same time, the other partner should round the numbers to the nearest hundred and subtract them to find an estimate. The partners use the estimate to decide whether the exact answer makes sense. If it does not, then they must try to find the mistake. If it does, they write down new numbers and switch roles. The partner who estimated finds the exact answer, and the partner who found the exact answer estimates.

Subtract. Estimate. Is your answer reasonable?

George walked halfway up the Empire State building, 788 stairs. His brother only walked half of that, 394 stairs. How many more stairs did George walk?

Jake walked 354 steps to the top of the Statue of Liberty. Then he walked half of the Chrysler Building stairs, 616 . How many more stairs did he climb in the Chrysler Building?

Struggling Learners

Post the rhyme to round somewhere visible to the students for them to reference (5 or more, let it soar, 4 or less, let it rest). Allow students to use number lines to help them round or have them draw “rounding hills.” Encourage students to draw base-10 blocks or use actual base-10 blocks if they are struggling to regroup and find exact answers.

Early Finishers

Billy and Colin went on a walk in Central Park. Billy walked 967 steps around the lake. Colin walked 236 steps to the top of Belvedere Castle. How many more steps did Billy walk?

There were 462 people on the observation deck at Rockefeller Center. 132 people are biking across The Brooklyn Bridge. Which attraction had more people? How many more people?

Subtract. Estimate. Is your answer reasonable?

852 people are waiting for their train at Grand Central Station. 257 of them are taking the train to Times Square. How many people are not going to Times Square?

Apply and Develop Skills (Practice / Exercise page)

Go back through the problems on the exercise page. Round the numbers to the nearest ten instead of hundred to get a closer estimate, and compare to your original estimate and exact answer.

Challenge and Explore

Read the word problem to the students. Help them to determine that they need to subtract because they are looking for the difference between people waiting for the train who are going to Times Square and people who are not going to Times Square. Discuss what the word difference means and how it tells us to subtract.

Extend the problem: Of the people not going to Times Square, 238 of them are going to Central Park. How many people are going someplace other than Times Square or Central park? [357, Estimate: 600 - 200 = 400]

Read the directions to the students. Do the examples that have already been solved with the students. In number 1, show students how to find the exact answer using the algorithm. Make sure they cross out the tens and ones and record what’s left after they borrow. Ask: “Is the estimate close to the exact answer? Is the answer reasonable?” [yes, yes] Read number 5 to the students and ask: “Which words let us know that we need to find a difference, or subtract?” [how many more] Have students underline these key words. Again, be sure that students record their steps in the algorithm and compare the estimate to the exact answer.

Common Errors

Some students may just change the tens and ones place to zeros and leave the hundreds place the same every time when rounding. Watch for students who get the correct exact answer when using the algorithm, but do not round and estimate correctly. These students may think that their exact answer is not reasonable.

Assess

Games

Play The Biggest Difference to practice subtracting 3 and 4-digit numbers. p. 313

Present the following problem to the students: A student solved 533 - 292 = ____ and wrote down the answer 361. Then the same student estimated by subtracting 500 - 200 = 300. This student says that his answer is reasonable.

What did he do wrong? [he did not borrow when he needed to in the exact answer, and he rounded wrong when finding the estimate] Is his exact answer correct? [no] If not, what is the exact answer? [241] Is his estimate correct? [no] If not, what is the correct estimate? [500 - 300 = 200]

Objective and Learning Goals

y Students will measure objects in centimeters and meters

y Students will subtract multi-digit numbers

Vocabulary

y Centimeter- metric unit of length.

y Meter- metric unit of length, equal to 100 cm

Materials

y Centimeter ruler for each student

y Meter stick for teacher to display

y Objects for groups of students to measure in the activity.

y Suggestions of objects include: paperclips, base 10 rods, marker, pencil, eraser cap and a plastic coin

Pre-Lesson Warm-up Guiding Questions

Teacher should hold up a piece of paper. Teacher asks “I want to measure the length of this paper. What tool should I use?” [a ruler]. Teacher holds up a ruler. “What unit of measure would I use?” [students should mention inches and/or centimeters] Teacher explains that today we will be using centimeters to measure the length of objects.

Guiding Questions

1. Which unit of measure, centimeters or meters, would be better to measure the length of your thumb? Why? [ centimeters because my thumb is smaller than a meter.]

2. Which unit of measure, centimeters or meters would be better to measure your height? Why? [meters. Answers will vary for why but could include that centimeters are small and we are a lot larger so we need to use a larger unit]

Before measuring any objects hand each student a centimeter ruler. Have students look closely at the ruler and share their noticitings. [Noticitings will vary but may include that centimeters are smaller than inches, there are lots of little lines]. Explain to students that the little lines are millimeters. Today we are going to focus on centimeters. Show students the centimeter markings on the ruler. Explain to students that 100 centimeters equals a meter. Hold up a meter stick for students to see.

Now, look at Let’s Learn with students. Go through each of the examples with students. Ask the Guiding Questions. Encourage students to use their ruler to help answer the questions In Try it Together work with students to measure the objects correctly and then to use their measurements to solve the problems.

Activity

Have students use their rulers to measure classroom objects. Give groups of students 5-10 objects. Example of objects are paperclips, base-10 rods, marker, pencil, eraser cap and a plastic coin. Each student should measure each object. Teacher needs to remind students to measure to the nearest centimeter. Groups should discuss their measurements. Then, the class should discuss measurements of objects.

Joshua did a science experiment. He measured the height of his plant for 3 weeks. Use his experiment to answer questions.

Struggling Learners

When using a regular ruler students may become confused about what lines to look at. Struggling students may benefit from rulers where the inch side has been covered.

Early Finishers

Students can make a list of classroom objects that would be measured using centimeters and meters. Students can compare their list with a classmate.

1 4 8

6. About how many centimeters did Joshua’s plant grow between week 1 and 2 ?

7. About how many centimeters did Joshua’s plant grow between week 1 and 3 ?

4 - 1 = 3 cm 8 - 1 = 7 cm

Read each problem. Solve and include units of measurement.

8. Joshua decided to continue his experiment for 3 more weeks. At the end of Week 6 his plant was 29 cm. How many centimeters did his plant grow between Week 3 and 6?

9. Joshua’s sister grew a plant too. Her plant measured 15 cm at Week 2 . How much taller was her plant than Joshua’s that week?

29 - 8 = 21 cm taller 15 - 4 = 11 cm taller

10. Joshua’s plant measures 46 cm at the end of the experiment. His sister’s measures 53 cm. Whose plant is taller? How much taller?

53- 46 = 7 cm taller Joshua's sister's plant is taller

11. Joshua is 132 centimeters tall. His sister is 107 centimeters tall. How much taller is Joshua than his sister?

= 25 cm

Apply and Develop Skills (Practice / Exercise page)

Read the directions with students and have them work through the problems on this page. Depending on the level of your students, you can have students work independently or in pairs. Circulate while students are working to make sure students are on the right track.

Challenge and Explore

Students take their rulers and measure objects in the classroom. Teacher can assign students objects (height of a desk, workbook, pencil, dry-erase board) or teacher could have students choose objects to measure. Teacher will have to show students how to use their rulers to measure objects that are larger than their ruler.

Questions

1. What was the longest object you measured? [answers will vary]

2. What was the shortest object you measured? [answers will vary]

3. What is the difference between the longest object you measured and the shortest object? [answers will vary]

Games

Play The Measurement is Right but have students measure to the nearest centimeter.

Common Errors

Students may need to be reminded to look at the ruler closely when determining the length of the object. Some students may get confused by all of the lines on the ruler.

Use problems 3-11 to assess understanding Assess

Level C Chapter 2-8

Objective and Learning Goals

y Review

y Subtract multi-digit numbers with and without regrouping, check subtraction with addition, round to estimate and check

Vocabulary

y Subtraction - the act of subtracting or taking a number away from another number

y Regroup - make groups of ten when carrying out operations such as addition and subtraction

y Inverse operations - the opposite operation that can be used to check your work

y Round - find a close but easier to work with number to a given number

y Estimate - to find a close enough answer when the exact answer is not needed

Materials

y None needed except for whichever game you choose to play

Pre-Lesson Warm-up Guiding Questions

Practice subtraction facts to 18. Have students call out answers or write them on paper or a dry-erase board.

13 - 6 = [7]

15 - 7 = [8]

14 - 9 = [5]

12 - 7 = [5]

17 - 8 = [9]

Guiding Questions

1. How can we use inverse operations to check our work on addition and subtraction equations?

2. How can we use estimation to check that an answer to a subtraction equation makes sense?

[round the numbers to the highest place value, and subtract the rounded numbers to find an estimate. Compare the estimate to the exact answer. If they are close, the answer makes sense]

Let’s review. Sometimes

the Lesson (Try it Together)

Read the information and problem in Let’s Learn to the students. Relate the picture of the base-10 blocks to the algorithm in the place value chart. Point out that there are not enough ones in the top number to subtract from. Show students that 1 tens rod has been borrowed and circled with the 6 ones cubes in the picture. Then in the algorithm, the 6 in the ones place has been changed to 16, since 10 plus 6 is 16. Ask students: “After we borrow 1 ten, how many tens are left?” [5] “Is that enough to subtract from, or do we need to borrow from the hundreds?” [we need to borrow]

Point out that in the picture, 1 hundreds flat has been borrowed and circled with the 5 tens rods that were left. Then in the algorithm, the 6 in the tens place has been changed to 15 because there were 5 left, and then we borrowed 1 hundred, which is the same as 10 tens. 10 plus 5 is 15, so there are 15 tens now. Ask students, “How many hundreds are left after we borrow 1?” [1] “Now we can subtract. What is the answer?” [88] Have a student explain how the numbers were rounded to find the estimate. [underline the target number,

circle the digit to the right and use the rhyme to decide whether to round up or down] Go through the problems in Try it Together with the students to review what they’ve learned in this chapter. Answer any questions students may still have about these skills.

Activities

To review, students will practice the same activity they did in a previous lesson. Students will work in pairs to practice subtracting 4-digit numbers and estimating to check that their answers are reasonable. Each partner should write down a 4-digit number. Then one partner should subtract the smaller number from the bigger number to find the exact answer while the other partner rounds the numbers to the nearest hundred and subtracts them to find an estimate. The partners use the estimate to decide whether the exact answer makes sense. If it does not, then they must try to find the mistake. If it does, they write down new numbers and switch roles. The partner who estimated finds the exact answer, and the partner who found the exact answer estimates.

Apply and Develop Skills (Practice / Exercise page)

Read the directions for each set of problems to the students. Consider doing the first problem in each section with them as an example.

Struggling Learners

Give students base-10 blocks to use, or help them draw the base-10 blocks to represent the numbers. Post the rhyme to round somewhere visible to the students for them to reference (5 or more, let it soar, 4 or less, let it rest). Allow students to use number lines to help them round, or have them draw “rounding hills.”

Early Finishers

In numbers 17-22, you estimated to check your work. Now check it a different way. Use inverse operations. Add to check your answers to numbers 17-22.

Challenge and Explore

Look at number 21.

What is the difference between the exact answer and the estimate?

[666; 2,666 - 2,000 = 666]

Round the numbers to the nearest ten, and subtract for a closer estimate.

[7,490 - 4,830 = 2,660]

What is the difference between the exact answer and this closer estimate?

[6; 2,666 - 2,660 = 6]

Which estimate is closer?

[rounding to the nearest ten]

How much closer? [660; 666 - 6 = 660]

Games

Choose and play a game from this chapter to practice subtraction or rounding.

Common Errors

Students may not add the correct numbers to check subtraction. For example, in 45 - 22 = 23, they may add 23 + 45 instead of adding 23 + 22. Watch for students who make careless errors like forgetting to record what is left in a place value after they borrow.

Assess

Check work for numbers 13, 16, 19 and 22.

Let’s learn!

Chapter 3 In Chapter 3, we will learn about understanding multiplication 0–5.

• Understand that multiplication is an extension of addition and is used to solve problems

• Add equal groups to help ﬁnd the total number of objects

• Use repeated addition to extend basic addition to counting larger quantities

• Use arrays to help us visualize how equal groups can be arranged to quickly calculate totals

• Skip counting increases mastery of “multiples”

• Knowing how factors relate to products helps build math understanding for division

• Multiplying by 1 results in a product identical to the other factor

• Multiplying by 0 results in a quantity of 0

• Knowing that the order of factors does not change the product helps us memorize math facts

• Using manipulatives and counting games makes multiplication a more concrete concept

• Noticing patterns through methods such as skip counting builds a knowledge of multiples

Vocabulary Words

Level C Chapter 3-1

Objective and Learning Goals

y Use equal groups to multiply

y Use repeated addition to multiply Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Repeated addition - a multiplication strategy in which groups are added

Materials

y Counters, beans or other small objects

y Dice (for game)

y Number cards 1-9 or a deck of cards with the jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up Guiding Questions

Practice doubles addition facts. Have students call out answers or write them on paper or a dry-erase board.

5 + 5 = [10]

3 + 3 = [6]

2 + 2 = [4]

4 + 4 = [8]

Guiding Questions

1. How can we find out how many objects are in a certain number of equal groups? [use repeated addition. Add the number in each group as many times as there are groups]

groups of

There are 3 groups of 2 ducks. There are 5 groups of 3 ducks. 2 +

Games

Play Go Fishing to practice multiplying by making equal groups. p. 314

Introduce the Lesson (Try it Together)

4 groups of 4 3 groups of 2 2 groups of 6

groups of 3 4 groups of 3 3 groups of 5 6 groups of 2

Begin by asking students: “What does it mean if two things are equal?” [they are the same] Tell students that today they will be making equal groups, which means that each group must have the same number of objects in it. Read through the examples in Let’s Learn. Emphasize the words “groups of” as you explain: “There are 3 groups of 2 ducks, so we can add the number 2 three times, 2 + 2 + 2 = 6, so 3 groups of 2 equals 6.”

In the second example ask students to circle groups of 3. Ask: “How many groups of 3 are there?” [5] “We can add 3 five times. 3 + 3 + 3 + 3 +3 = 15 so 5 groups of 3 equals 15.”

Go through the first two examples in Try it Together the same way, and then have the students help you match the repeated addition with equal groups in number 3. Say: “2 + 2 + 2, how many 2s are there?” [3] “So there are 3 groups of 2.” Have students trace the line. Ask:

“3 + 3 + 3 + 3, how many groups of 3 are there?” [4] “4 groups of 3.” Draw the line to match, and have students do the same. Continue for the rest of the examples.

Activities

Students will make equal groups and write repeated addition equations to match. Give students counters, beans or other small objects. Have them make equal groups, draw them on their paper and then write a repeated addition equation to match the equal groups. Make 2 groups of 3 [3 + 3 = 6]

Make 5 groups of 2 [2 + 2 + 2 + 2 + 2 = 10]

Make 4 groups of 5 [5 + 5 + 5 +5 = 20]

Make 7 groups of 2 [2 +

Then let students make up their own equal groups and write the repeated addition equations to match.

Circle equal groups. Show how to add the groups up.

1. Circle groups of 4 2. Circle groups of 5 3. Circle groups of 3

Struggling Learners

There are groups of 4 baseballs. There are groups of 5 acorns. There are groups of a 3 leaves.

4. Draw a line to Match.

4 + 4 + 4

5 + 5 + 5 + 5

6 + 6 + 6 + 6

4 groups of 5

3 groups of 4

2 groups of 9

6 groups of 2

4 groups of 6

3 groups of 5

6 groups of 7

Break the number into equal groups. Show the equation using repeated addition. 15 5 5 5 15

Early Finishers

For numbers 5 - 12, go back and write the equal groups shown in each problem. For example, next to number 5, you would write: “3 groups of 5.”

Challenge and Explore

In number 4, solve the repeated addition equations to find the total number of objects. Draw pictures of the matching equal groups to help you.

4 + 4 + 4 [12]

5 + 5 + 5 + 5 [20]

6 + 6 + 6 + 6 [24]

7 + 7 + 7+ 7+ 7+ 7 [42]

5 + 5 + 5 [15]

9 + 9 [18]

2 + 2 + 2 + 2 + 2 + 2 [12]

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. The first two sections of problems are just like the examples they did in Try it Together. For the last section, do the first two problems with the students. For number 5, point out that since there were 3 lines for addends, they split 15 into 3 equal groups. Tell students to count and make sure there are the same number of triangles in each group. Have them trace 5 + 5 + 5 = 15. For number 6, ask “How many lines are there before the equal sign?” [4] “We need to make 4 equal groups with the 8 triangles. You can draw 4 circles and we will distribute the 8 triangles across the groups. First put 1 triangle in each circle, counting them as you go, 1, 2, 3, 4. Then put another triangle in each

Common Errors

Students may have trouble adding repeatedly and keeping track of how many they have added. Watch for students who circle groups of objects that are not equal. They may circle objects that they think look like they are grouped together without counting to make sure the groups are equal.

circle, counting them as you go, 5, 6, 7, 8. How many are in each group?” [2] “Write the equation 2 + 2 + 2 + 2 = 8.” If possible, have students do this with counters or other small objects. Give them 8 counters to distribute into 4 groups. Example:

Assess

Have students draw 3 groups of 6, write a repeated addition equation to match their groups and solve for the total. [pictures will vary. Accept any picture that shows 3 groups with 6 objects in each group. 6 + 6 + 6 = 18]

Objective and Learning Goals

y Use arrays to multiply

Vocabulary

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

Materials

y Grid paper

y Square tiles or counters

Pre-Lesson Warm-up

Guiding Questions

Solve the repeated addition equations:

2 + 2 + 2 + 2 = [8]

4 + 4 + 4 = [12]

3 + 3 + 3 = [9]

5 + 5 + 5 = [15]

Guiding Questions

1. How many groups of 2 are we adding together? [4]

2. How many groups of 3? 4? 5? [3]

3. Arrange objects of the groups we are adding into rows and columns. This is called an array. How does an array make it easy to find the total? [it is easy to count up the total. We can multiply the rows by the columns]

(Try

Tell students that an array is another way of drawing equal groups. The groups are arranged in nice neat rows and columns. Tell students that rows go across like the rows of seats in an auditorium, and columns go up and down like the columns on a building (show students a picture of a building with columns, if possible). Have students look at the array of hay bales in Let’s Learn. Ask: “How many rows are there?” [3] “How many are in each row?” [4] Tell the students that this array shows us 3 rows of 4 or 3 groups of 4, so we can use repeated addition like in the last lesson to add three 4s : 4 + 4 + 4 = 12. This is a 3 by 4 array. Next, point out the array of balls and ask: “How many rows are there?” [4] “How many are in each row?” [4] “This array has 4 rows of 4 or 4 groups of 4. It is a 4 by 4 array.”

Tell the students that when we find how many total items are in equal groups, we are multiplying. When they see the multiplication symbol, they can think

“groups of.” 4 times 4 means 4 groups of 4.

Go through the examples in Try it Together with the students. Emphasize that the meaning of multiplication is “groups of.” You can ask: “What is 3 x 5, or 3 groups of 5?” [15] Have them look at the array. Say “It has 3 rows of 5 or 5… 3 times, 5 + 5 + 5.”

Activities

Students practice making multiplication arrays by shading in squares on grid paper and writing the multiplication equation underneath. Give students grid paper. Have them shade equal rows for each of the following multiplication equations and count the squares to find the answer.

2 x 7 = [14; shade in 2 rows of 7] 6 x 3 = [18; shade in 6 rows of 3]

4 x 5 = [20; shade in 4 rows of 5]

6. Jay is baking cookies. His cookie sheet has 5 rows of cookies with 4 cookies in each row. How many cookies are on the cookie sheet? Draw an array to solve.

5 x 4 = 20 cookies

8. There are 24 desks in the classroom. Make 3 di erent arrays to show how the desks could be arranged. Word problems.

7. Tim is planting a garden. He plants 3 rows of bell peppers and puts 6 plants in each row. How many pepper plants does he plant? Draw an array to solve.

3 x 6 = 18 plants

[answers will vary. Arrays may be drawn in the other orientation than shown here]

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Provide grid paper for students to shade in arrays. Provide counters or other small objects for students to make arrays with.

Early Finishers

Write the answers next to each equation in number 1.

Challenge and Explore

Pass out 20 square tiles or counters and grid paper to each student. Have them count to make sure they have exactly 20. Tell them to make an array using all 20 tiles. Shade in the array and write the repeated addition and the multiplication equation that shows the array. Now, using the same 20 tiles, make a different array. Do the same with this array as with the first one. Have students share out the different arrays they find.

1. What arrays did you come up with? [ 5 x 4, 4 x 5, 2 x 10, 10 x 2, 1 x 20, 20 x 1]

2. Are a 5 x 4 and a 4 x 5 array the same? [yes, they are just oriented differently]

3. Which other arrays are the same? [20 x 1 and 1 x 20, 10 x 2 and 2 x 10]

Read the directions for each section to the students, and do the first problem together. For number 1 say: “I see 3 x 2. I’m thinking 3 rows of 2. The ears of corn are arranged in 3 rows with 2 in each row, so I draw a line to the ears of corn. Look at the next equation. We see 3 x 4, and we can think 3 rows of 4.” Guide students to make arrays in number 2 by saying: “For 3 x 4, shade in 3 rows of 4. Count the squares that are shaded. There are 3 rows with 4 squares in each row. There are 12 total squares shaded in.” Look at the word problems. Read carefully to find the information you need to solve. Use counters or tiles to make the array before you draw it out. For number 8, give students 24 square tiles or counters. Tell them to make as many different arrays as they can using all the tiles. Be sure that each row has the same amount of tiles.

Common Errors

Games

Play Go Fishing to practice multiplying by making equal groups. p. 314

Students have trouble keeping track when they are counting small squares or small objects. Have them cross out boxes or objects as they count them. If students are making their own arrays without grid paper, they may not make equal rows. Encourage them to make the rows and columns as straight and neat as possible. Also encourage students to find “shortcuts” to counting the objects. For example, in a 3 by 5 array, they can count by fives 3 times because they know that there are the same number of objects (5) in each row.

Assess

Check work for numbers 4-8.

Objective and Learning Goals

y Multiply by 2s using skip counting

Vocabulary

y Skip counting - counting by multiples of a certain number

Materials

y Grid paper

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Have the students practice counting by twos out loud.

Count by twos 5 times [2, 4, 6, 8, 10]

Count by twos 7 times [2, 4, 6, 8, 10, 12, 14]

Count by twos 3 times [2, 4, 6]

Count by twos 6 times [2, 4, 6, 8, 10, 12]

Count by twos 10 times [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

Guiding Questions

1. How can we solve a times 2 multiplication fact?

[skip count by 2s the number of times you are multiplying 2 by. You can also double the number that you are multiplying by 2]

Introduce the Lesson (Try

Have students look at the problems in Let’s Learn. Tell them that the red brackets underneath the fruit show them groups of objects. Ask: “How many groups of oranges are there?” [5] “How many oranges are in each group?” [2] Say: “Since there are 2 in each group, we can count by 2s. Count with me: 2, 4, 6, 8, 10. How many oranges are there in all?” [10] So 5 groups of 2, or 5 x 2, equals 10. Have students fill in the blanks as you go over the problem. Do the second example with bananas in the same way.

Tell students whenever we are multiplying by 2, we are working with groups of 2, so we can count by 2s to find the answer. Do the example in Try it Together the same way you did the first two examples. Then have students look at number 1. Say: “We can make arrays with groups of 2 also. Here are two groups of 2. 2 plus 2 equals 4. 2 times 2 means 2 groups of 2, so 2 x 2 also equals 4.” Have students count the groups of 2 in the arrays by 2s to help you find the answers to the rest of the Try it Together problems.

Activities

Give students grid paper. Have them shade in arrays for each x2 fact and write the fact underneath their array. Have students count their rows of 2 by twos to find the products.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Give students who still need help skip counting a number line or hundreds chart to count on. Provide counters or other small objects for students to make groups of two with.

Early Finishers

Think of things that come in pairs (socks, shoes, gloves, etc.). Draw pictures of groups of these items, and write a multiplication equation under your picture. For example: Draw 3 pairs of socks. Write 3 x 2 = 6 socks.

Challenge and Explore

Have students draw arrays or equal groups and count them by twos to solve the following problem.

2 x 15 = [30]

Read the directions to the students. Do the example problems with the students. For number 1, say: “This problem is 2 x 2, which means 2 groups of 2. The line has been drawn to the picture that shows 2 groups of 2 squares. Count them by 2s, 2, 4. 2 times 2 is 4.” Do number 9 with the students. Point out that the picture shows groups of 2 squares and have the students count the squares by twos out loud with you. [2, 4, 6, 8, 10, 12]

Common Errors

Some students will not count by twos the correct number of times. Encourage them to keep track by drawing equal groups, making arrays or counting on their fingers.

Assess

Games

Play Times Table War to practice multiplying by 2s. p. 315

Draw an array or equal groups for each equation and write the product: [drawings will vary, make sure they include the correct number of groups of 2]

y 4 x 2 = [8]

Objective and Learning Goals

y Multiply by 5s using skip counting

Vocabulary

y Skip counting - counting by multiples of a certain number

Materials

y Grid paper

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Have the students practice counting by fives out loud.

Count by fives 5 times [5, 10, 15, 20, 25]

Count by fives 7 times [5, 10, 15, 20, 25, 30, 35]

Count by fives 3 times [5, 10, 15]

Count by fives 6 times [5, 10, 15, 20, 25, 30]

Count by fives 10 times [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]

Guiding Questions

1. How can we solve a “times 5” multiplication fact?

[skip count by 5s the number of times you are multiplying 5 by]

Tell students that in this lesson, they will learn to multiply by 5 by skip counting by 5. Remind students that a nickel is worth 5 cents, so they can think about nickels when multiplying by 5. Count the groups of nickels in the Let’s Learn section by 5s with the students. Say: “5 groups of 5 cents is 25 cents. So 5 times 5 is 25.” Do the Try it Together problems with the students. For number 1 say: “8 x 5 means 8 groups of 5. We can count by 5s 8 times. Count with me: 5, 10, 15, 20, 25, 30, 35, 40. 8 times 5 is 40.” Do the rest of the problems with the students. Have the students count the number of lines in each problem to be sure it is the right number of groups of 5. Have them write the skip counts on the lines.

Activities

Just like the activity in the last lesson, give the students grid paper. Have them shade in arrays for each x5 fact and write the fact underneath their array. Have students count their rows of 5 by fives to find the products.

Games

Play Times Table War to practice multiplying by 5s. p. 315

Fill in the missing numbers.

Struggling Learners

Give students who still need help skip counting a number line or hundreds chart to count on. Provide counters or other small objects for students to make groups of five with.

Early Finishers

Pick some of the equations in the problems on this page. Draw pictures representing groups of 5 objects to go with the equations.

Use the train above to help you multiply.

Use the clock to help you multiply.

Challenge and Explore

Have students look at the Challenge problems. Ask: “How many groups are there?” and “How many are in each group?” Have students write an equation for each. Prompt them by writing “___ groups of ___ or ___ x ___,” and have them fill in the blanks. Encourage students to skip count to find the products.

Write 2 equations using the following information:

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. For number 3, you may need to make sure they understand that the pattern is counting by 5s and they should start with 0. Do number 4 with the students. Tell them to start with their finger on the 0 in the train and then hop “cars” 3 times. Count 5, 10, 15, as you point to each of the 3 cars. Guide them to do number 5 the same way. Emphasize that they should start on 0 and then hop 5 times. Ask: “What number did you hop to? What is 5 times 5?”[25]

Show students the clock for numbers 14 - 21. Remind them that when they tell time, they can find the minutes by starting at the 12 and then counting by 5 for each number on the clock. The 1 on the clock is 5 minutes after the hour, the 2 is 10 minutes, the 3 is 15 minutes, etc. Do number 14 with them. Say: “We are going to use the clock to find 6 times 5. Put your finger on the 12, and count by fives as you move to each number until you get to 6. Count with me: 5, 10, 15, 20, 25, 30. 6 times 5 is 30.”

Assess

Some students will not count by fives the correct number of times. Encourage them to keep track by drawing equal groups, making arrays or counting on their fingers.

Draw an array or equal groups for each equation and write the product:

[drawings will vary, make sure they include the correct number of groups of 5]

y 4 x 5 = [20]

y 7 x 5 = [35]

Objective and Learning Goals

y Multiply by 3s

Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Skip counting - counting by multiples of a certain number

y Repeated addition - a multiplication strategy in which groups are added

Materials

y Counters, beans or other small objects

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up Guiding Questions

Practice skip counting by 3s. Say to the students: “I’m going to count by 3s. When I stop and point at you, say the number that comes next in my count.” Count by 3s, and periodically stop and point at the class, having them chorally count the next number. Count slowly “3, 6, 9.” Point at students [12] “15, 18.” Point at students. [21] “24, 27.” Point at students. [30]

Try again. “3, 6.” Point at students. [9] “12, 15.” Point at students. [18] “21, 24.” Point at students. [27] “30.”

One more time “3.” Point at students. [6] “9, 12.” Point at students. [15] “18, 21.” Point at students. [24] “27, 30.” Point at students. [33] Point at students again. [36]

Guiding Questions

1. How can we solve a times 3 multiplication fact?

[skip count by 3s the number of times you are multiplying 3 by, draw equal groups of 3 objects, make arrays with 3 in each row]

Introduce the Lesson (Try it Together)

Tell students that in this lesson, they will multiply by 3s. They can use many different strategies to multiply. Show them the example in the Let’s Learn section, and tell them that 3 x 3 can be solved in many different ways. Here are three: First, skip counting by 3s three times - 3, 6, 9. Next, by making an array that has 3 rows with 3 in each row. There are 9 objects in the array. And last, by using repeated addition to add 3 three times. 3 + 3 + 3 = 9. Do the problems in the Try it Together section with the students. For numbers 1 and 2, point out that the brackets show groups of 3. Have the students count out loud by 3s with you.

Activities

Students will use strategies to practice multiplying by 3s. Give pairs of students a container of counters, beans or other small objects. Students take turns calling out a factor between 2 and 9 for the other students to multiply by 3. The other students should draw that many circles and put 3 counters in each circle to make equal groups of 3, then they should make an array. Underneath their groups, they should write the skip counts and the repeated addition equation. Then they should write the multiplication equation with the product.

For example, if the partner calls out 5, they might make something like this:

Find the product.

7. 3 × 4 =

8. 9 × 3 = 9. 3 × 8 = 10. 0 × 3 = 11. 3 × 6 =

10 × 3 =

Struggling Learners

Provide students with a number line or hundred grid and help them to skip count by 3s and circle the counts. Provide grid paper to help students make arrays, or give them counters or small objects to make equal groups.

Early Finishers

Choose one of the problems from 7-18. Students will write their own word problem from one of the equations in problems 7-18. Have students then draw a picture to show how to solve the problem. They can make equal groups, an array, or another representation of problem.

1 × 3 =

3 × 3 =

5 × 3 =

19. Rob has 3 cupcakes with 3 candles on each cupcake. How many candles does he have?

20. Marybeth made an array with her star stickers. She made 3 rows of 8 stars. How many stickers did she have?

Challenge and Explore

Solve the riddle. I am an odd number. My factors are 3 and 5 . Who am I?

Apply and Develop Skills (Practice / Exercise page)

Go over the directions for the table at the top of the page. Tell students that they will be writing a multiplication equation to go with the array in the middle column, and then they should write a repeated addition equation in the last column. Do the example with the students. Say: “How many 3s are in this array?” [6] “So the multiplication equation is 6 x 3. Since there are six 3s, we add 3 six times. The repeated addition equation is 3 + 3 + 3 + 3 + 3 + 3. “

Look at the word problems 19-20. Remind students to look for the important information in each problem and circle it. Encourage students to draw a picture of the problem to help them solve.

Common Errors

Students may not know how to skip count by 3s. This is not as familiar a task as skip counting by 2s or 5s. They may try to skip count but accidentally leave too few or too many in between each count.

Assess

Read the riddle to the students. Have a student remind the class how to tell whether a number is odd or even. [Even numbers can be split into two equal groups. Odd numbers cannot be evenly split in two. Even numbers are the numbers we say when we count by 2s.] Remind students that factors are the numbers that are multiplied together in a multiplication equation. Games

Play Times Table War to practice multiplying by 3. p. 315

Show two different strategies (equal groups, arrays, skip counting, repeated addition) for solving the following multiplication facts.

4 x 3 = [answers will vary. Students could draw 4 groups of 3 objects, draw a 4 x 3 array, write the skip counts 3, 6, 9, 12 or the repeated addition equation 3 + 3 + 3 + 3 = 12]

7 x 3 = [answers will vary. Students could draw 7 groups of 3 objects, draw a 7 x 3 array, write the skip counts 3, 6, 9, 12, 15, 18, 21 or the repeated addition equation 3 + 3 + 3 + 3 + 3 + 3 + 3= 21]

Objective and Learning Goals

y Multiply by 4s

Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Skip counting - counting by multiples of a certain number

y Repeated addition - a multiplication strategy in which groups are added

Materials

y Counters, beans or other small objects

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up Guiding Questions

Play “Buzz” to start thinking about multiples of 4. Begin by having one student count out loud with “1”, the next student should say, “2,” and the next “3,” etc. On “4,” the next student says, “Buzz,” instead of “4.” After that, the next student says, “5”, “6”, etc. For every multiple of 4, the student who it “lands” on says, “Buzz!”

See how high students can go before someone messes up by saying the multiple of 4 or by saying “Buzz” at the wrong time. Practice a few times.

[1,2,3,buzz,5,6,7,buzz,9,10,11,buzz…]

Guiding Questions

1. How can we solve a “times 4” multiplication fact?

[skip count by 4s the number of times you are multiplying 4 by, draw equal groups of 4 objects, make arrays with 4 in each row]

Try it together!

Read through the example in Let’s Learn with the students. Have the students help you fill in the missing numbers on the skip counts. If they get stuck, remind them to add 4 to the previous number. Show them that there are 4 squares in each row, so these are equal groups of 4. We are multiplying by 4 today. Review the meaning of “factors” and “product” with the students. Do the Try it Together problems with the students. For number 1 ask: “How many groups of 4 are there?” [6] “So we are doing 6 x 4. We can add six 4s together to get the answer.” Give students time to figure out the total. Encourage them to skip count if they can. Go through the rest of the times 4 facts on the page and in the table with the students. Encourage students to use any of the strategies they have learned (skip counting,

equal groups, arrays, repeated addition), and periodically have a student share the strategy that they used. For numbers 4, 5 and 6, point out that the product is there, but one factor is missing. Show them how they can use the same strategies to figure out the missing factor. For number 4 say: “We need to know how many 4s are in 16. We can skip count until we get to 16, we can add 4 until we get to 16 or we can draw equal groups or rows of 4 until we have a total of 16.” Have the students try whichever strategy they want to solve the problem, and then have a few students share their strategy.

Activities

Have students work in pairs to make tables like the one below showing all of the strategies to solve a x4 fact.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Provide students with a number line or hundred grid and help them to skip count by 4s and circle the counts. Provide grid paper to help students make arrays, or give them counters or small objects to make equal groups.

Early Finishers

Make your own multiplication wheel like in numbers 19 and 20 but for times 4 facts.

Challenge and Explore

Read the riddle to the students. Ask: “What does “identical” mean?”[exactly the same] Remind students that factors are the numbers that are multiplied together in a multiplication equation. Tell them that they need to find a number that if you multiply it by itself, you will get 16. Encourage them to draw equal groups or arrays, or use skip counting or repeated addition to figure it out. Have some students share their strategies.

Go over the directions for the table at the top of the page. Tell students that they will be writing a multiplication equation to go with the array in the middle column, and then they should write a repeated addition equation in the last column. Do the example with the students. Say: “How many 4s are in this array?” [6] “So the multiplication equation is 6 x 4. Since there are six 4s, we add 4 six times. The repeated addition equation is 4 + 4 + 4 + 4 + 4 + 4. “

Remind students how the multiplication wheels in numbers 19 and 20 work.

Common Errors

Students may not know how to skip count by 4s. This is not as familiar a task as skip counting by 2s or 5s. They may try to skip count but accidentally leave too few or too many in between each count.

Assess

Games

Play Times Table War to practice multiplying by 4. p. 315

Show two different strategies (equal groups, arrays, skip counting, repeated addition) for solving the following multiplication facts.

3 x 4 = [answers will vary. Students could draw 3 groups of 4 objects, draw a 3 x 4 array, write the skip counts 4, 8, 12 or the repeated addition equation 4 + 4 + 4 = 12]

7 x 4 = [answers will vary. Students could draw 7 groups of 4 objects, draw a 7 x 4 array, write the skip counts 4, 8, 12, 16, 20, 24, 28 or the repeated addition equation 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28]

Objective and Learning Goals

y Multiply by 0 and 1

Vocabulary

y Identity property - when multiplied by one, a number keeps its identity

y Zero property - multiplying by zero always results in zero

Materials

y Paper/pencil or dry-erase board/marker (for game)

Pre-Lesson Warm-up

Guiding Questions

Ask students “groups of” questions to get them thinking about equal groups in multiplication. If I have 3 groups of 2 socks, how many socks do I have? [6]

If I have 2 groups of 6 eggs, how many eggs do I have?[12]

If I have 4 groups of 3 bananas, how many bananas do I have? [12]

If I have 8 groups of 1 block, how many blocks do I have?[8]

If I have 5 groups of zero pencils, how many pencils do I have? [0]

Guiding Questions

1. How can we use the identity and zero properties to help us multiply? [we know that if one factor is 0, the answer is always 0, and if one factor is 1, the answer is always the other factor]

Point to the first set of fish bowls at the top of the page. Ask: “How many fish are in each bowl?” [0] “How many fish bowls are there?” [3] “How many fish are there?” [0] Explain to the students that this is called the zero property. Anything times 0 is always 0. It doesn’t matter how many groups you have, if there are 0 items in each group, there are 0 items in all. Then have students look at the second set of fish bowls and ask: “How many fish are in each bowl?” [1] “How many fish bowls are there?” [3] “How many fish are there in all?” [3] Explain to students that this shows the identity property. When a number is multiplied by 1, its identity stays the same. Any number times 1 is that same number because if you have one object in each group, the product is always the same as the number of groups. Go through the birdcage examples the same way, and then have students help you fill in the charts. Ask students to describe the patterns they see in the charts.

Activities

Have students work in pairs to come up with word problems to match the following equations:

Write the equation.

Fill in the product.

Level C Chapter 3-7

Struggling Learners

Have students who are struggling to visualize multiplying by 0 and 1 draw pictures of the scenarios to help them.

Early Finishers

Go back to numbers 4-7. Change the 1 or 0 in the equation to a 2, 3, 4 or 5. Draw a picture of the new equation and solve to find the product.

Challenge and Explore

Read the Challenge problem to the students. Ask them to recall the identity property and the zero property. Tell them to use these properties to explain which option they choose. [Answers will vary. Possible response: I would choose $36 x 1 because then I would have $36. Anything times one is that same number. If you multiply 1 million times 0, you have nothing because anything times 0 is 0]

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Review how the multiplication wheels in numbers 1-3 work. Remind students to draw a picture to help them solve each problem if it helps them.

Games

Play Brain vs. Hand to practice multiplying by 0 and 1. p. 308

Common Errors

Some students will confuse the properties and say that a number times 0 is the same number. Give them an equal groups word problem to help them visualize how this is impossible. For example, if a student says that 4 x 0 is 4, ask them to draw 4 bags, put 0 pieces of candy in each bag and tell you how many pieces of candy there are in all.

Assess

Write an equation that demonstrates each property of multiplication. Also, write the product.

Identity property: [answers will vary. Accept anything times 1 with a product of the factor that is not 1]

Zero property: [answers will vary. Accept anything times 0 with a product of 0]

Level C Chapter 3-8

Objective and Learning Goals

y Review

y Use equal groups, repeated addition, arrays and skip counting to multiply by 0-5

Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Repeated addition - a multiplication strategy in which groups are added

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Skip counting - counting by multiples of a certain number

y Identity property - when multiplied by one, a number keeps its identity

y Zero property - multiplying by zero always results in zero

Materials

y Grid paper

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up Guiding Questions

Practice skip counting. Have students count aloud together by:

2s to 20 [2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

3s to 30 [3, 6, 9, 12, 15, 18, 21, 24, 27, 30]

4s to 40 [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]

5s to 50 [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]

Guiding Questions

1. How can we solve a multiplication fact we don’t know?

[skip count, draw equal groups, make arrays or use repeated addition]

Let’s

We can also arrange the ducks in an array:

The array shows the ducks arranged in 3 rows of 2 3 x 2 = 6

Introduce the Lesson (Try it Together)

Read through the example problem in Let’s Learn. Review all of the strategies that the students have used to multiply in this chapter (repeated addition, skip counting, equal groups and arrays). Ask students to talk about which is their favorite strategy and why with a partner. Then have some students share with the class. Have students solve the problems in Try it Together and then go over the answers, asking students to share the strategy they used on some of the problems.

Activities

Have students choose some multiplication facts 1-5 that they need to practice. Give students grid paper and have them color arrays for the problems they chose and write the fact underneath with the product.

Use the train above to help you solve these problems.

Struggling Learners

Provide number lines and hundreds charts for students to skip count on. Provide counters or small objects for students to make equal groups or arrays with.

Early Finishers

Use the clock to help you solve these problems.

Find the products.

Make your own multiplication wheels for x3 and x4.

Challenge and Explore

Present the following problem to students:

At the grocery store, Mr. Jones bought 5 cartons of a dozen eggs. How many eggs did he buy? Show the problem using one of these strategies - repeated addition, equal groups, array or skip counting.

How many is a dozen? [12] Which strategy did you use and how did you show your strategy? [Answers will vary] How many eggs did Mr. Jones buy? [60 eggs]

Apply and Develop Skills (Practice / Exercise page)

Read and explain the directions for the page. For numbers 10 - 17, remind students that each number on the clock is 5 minutes, so they count by 5s. Remind students how the multiplication wheels work. Have students work as independently as possible on this page. Tell students that it’s great if they already have some of the products memorized but to be sure to use a strategy when they aren’t sure of the answer.

Games

Play Times Table War to practice multiplying by 2s, 3s, 4s or 5s. p. 315

Common Errors

Watch for students who get confused when multiplying by 0 and 1. Remind them to think of a scenario of groups of objects with 0 or 1 in each group. Some students may try to skip count or use repeated addition but make mistakes in their counts or adding.

Assess

Check work for numbers 20 - 26.

Chapter 4

For factors 6 -9 , we will understand how to:

• Use equal groups, arrays and repeated addition to multiply.

• Relate products for the factors 4 and 8

• Use patterns and strategies to recognize and memorize the multiples of 8 and 9

• Read story problems to solve multiplication problems

• Use the “factor, factor, product” relationship to ﬁnd missing parts

Practice multiplication facts using di erent formats including:

• traditional horizontal and vertical problems

• wheel multiplication circles

• input/output function tables

• number bonds and fact triangles

Vocabulary Words

Level C Chapter 4-1

Objective and Learning Goals

y Use equal groups and arrays to multiply

y Multiply by 2 and 3

Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

Materials

y Index cards

y Coins to flip

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice skip counting. Have students count aloud together by 2s. Have students count aloud together by 3s. Repeat as needed.

Guiding Questions

1. How can we use equal groups to multiply? [Draw a picture; one factor tells you the number of groups to draw, and the other factor tells you how many objects are in each group.]

2. How can we use an array to help us solve a multiplication equation?

[Arrays are another way of drawing equal groups. The objects are drawn in neat rows and columns, making them easy to count up.]

Read the examples at the top of the page to the students. Remind them that multiplication means equal groups. Say: “3 times 2 means 3 groups of two.” Draw their attention to the 3 groups of two balls on the page. Then point out the array underneath. It also shows 3 groups of 2, but an array is always arranged in nice straight rows and columns. Do the Try it Together problems with the students. In some of the problems, have a student explain how the picture of equal groups or the array represents the equation.

Activities

Students will practice drawing equal groups and arrays to multiply by 2 and 3. Take 4 index cards, and cut them each into 3rds so that they have 12 cards. On each card, write a number 1-12. Students should shuffle the cards and lay them face down. Draw a card. Then flip a coin. If it lands on heads, they multiply the number on the card by 2. If it lands on tails, they multiply by 3. Students should draw equal groups or arrays to match the equation.

Games

Play Times Table War to practice multiplying by 2s or 3s. p. 315

Struggling Learners

Provide grid paper for students to shade in arrays. Provide counters or other small objects for students to make equal groups with.

Early Finishers

Draw or model arrays or equal groups for numbers 11- 16.

Challenge and Explore

Read the word problem to the students. Point out that this problem is talking about equal groups.

How many equal groups of fish are there? [3]

How many are in each group? [3]

What is the equation? [3 x 3 = 9]

Jacob has 3 fish bowls. Each fish bowl has 3 goldfish. How many goldfish does Jacob have altogether? Use the blanks for help.

Apply and Develop Skills (Practice / Exercise page)

Read the directions, and do number 1 with the students. Say: “3 times 3. That means 3 groups of 3. So let’s draw 3 groups of 3 triangles.” Have the students draw what you draw. Read the directions for numbers 6-10. Say: “7 times 2. That means 7 groups of 2. So, let’s draw 7 groups of 2 squares in a nice neat array.” Have the students draw what you draw. Tell students to be careful on numbers 11 - 16 since they will be filling

Common Errors

Students have trouble keeping track when they are counting small squares or small objects. Have them cross out boxes or objects as they count them. If students are making their own arrays without grid paper, they may not make equal rows. Encourage them to make the rows and columns as straight and neat as possible. Also, encourage students to find “shortcuts” to counting the objects. For example, in a 3 by 5 array, they can count by fives 3 times because they know that there are the same number of objects(5) in each row.

in a missing factor instead of the product on some of the problems. Have them look at number 12. Tell them to ask themselves “What times 8 equals 16?” or “How many 8s are in 16?” Remind them that they can draw equal groups or arrays to help them. Review how the multiplication wheels in numbers 17-19 work. Take the middle number, multiply it by the outside number and put the product in the outside of the wheel.

Assess

Solve the following problems. For each problem, draw a picture of equal groups or an array to match the equation.

2 x 7 = [14, pictures will vary. Make sure it has the correct number of equal groups]

3 x 8 = [24, pictures will vary. Make sure it has the correct number of equal groups]

Level C Chapter 4-2

Objective and Learning Goals

y Multiply by 6 using strategies such as skip counting, arrays and equal groups. Look for patterns in multiples of 6.

Vocabulary

y Multiples - the product of multiplying one whole number by another

y Factors - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

Materials

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplication facts from earlier lessons.

2 x 8 = [16]

3 x 3 = [9]

5 x 7 = [35]

4 x 5 = [20]

2 x 3 = [6]

3 x 5 = [15]

4 x 3 = [12]

Guiding Questions

1. How can we solve a times 6 multiplication equation?

[skip count by 6s the number of times you are multiplying 6 by, draw equal groups of 6 objects, make arrays with 6 in each row]

Let’s learn!

Multiplying with 6 s! Color each multiple of 6 Use the multiples to solve these problems. How many legs? How many crayons?

How many eggs? Write the equation to

Use the multiples of 6 chart. Write the product.

Introduce the Lesson (Try it Together)

Have the students color in the multiples of 6 on the chart with you. [6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72] Then solve the problems below the chart with the students. For 5 x 6 count the multiples of 6 five times until you get to 30. Then for 7 x 6 count the multiples of 6 seven times until you get to 42. Do the Try it Together problems with the students. Point out that we can draw groups of 6 like in the first two problems to help us solve them. For the first problem ask: How many groups of 6 eggs are there? [4] The equation for 4 groups of 6 is 4 x 6. How many eggs are there in all? [24] “4 x 6 is 24.” Do number 2 - 9 groups of 6 petals- the same way. Then go through the multiples of 6 chart problems the same way you did the first two example problems.

Activities

Play “Buzz” to practice multiples of 6. Remind students of the “Buzz” game played with earlier lessons. Explain that the game is patterned after finding “multiples.” A multiple is the product result of one number multiplied by another number. Play “Buzz” - go around the room. Whoever has a multiple of 6 says “Buzz” instead. For example: 1, 2 ,3, 4, 5, Buzz, 7, 8, 9, 10, 11, Buzz and so on. If the person says the multiple of six instead of buzz, they are out. Continue playing until there are only a few players left.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Give students counters or small objects to make equal groups or allow them to use the multiples of 6 chart or graph paper to make arrays. Since the numbers are getting larger, consider reducing the number of problems for students who are still needing to count by ones to figure out the products. Have them do only the even-numbered problems.

Early Finishers

Create your own multiplication wheel like the ones in numbers 13, 14, and 15. Make yours a x6 multiplication wheel.

Challenge and Explore

Present the following problem: Oranges come in bags of 6. The coach bought 8 bags of oranges for the team. How many oranges did the coach buy in all? What strategy will you use? [students could draw the 8 groups of 6 oranges or an array. They could count by 6s or add 6 eight times] How many oranges did the coach buy? [48]

Read the directions to the students. For number 1 tell the students to use the number line to help them count by 6s and write each count, or multiple, on the line. Explain how the table in number two works. They should multiply the number across the top row by 6 and write the product below. For numbers 3 - 12 explain to students that the two circles on the bottom are the factors, or numbers that are multiplied together. The circle on the top is the product, or the answer to the multiplication fact. Point out how in number 3, the two bottom circles are 2 and 6, and the answer to 2 x 6 has been written in the top circle for them. Point out number 5, and say: “Sometimes one of the factors is missing. In this problem, we know that something times 6 equals 36. What times 6 equals 36? Or how many 6s are in 36?” [6] Review how the multiplication wheels in numbers 13, 14 and 15 work.

Common Errors

Students may not know how to skip count by 6s. This is not as familiar a task as skip counting by 2s or 5s. They may try to skip count but accidentally leave too few or too many in between each count. Watch for students who count by 1s when counting the number of objects in equal groups or arrays and make careless mistakes in their counting.

Assess

Level C Chapter 4-3

Objective and Learning Goals

y Multiply by 7 using strategies such as skip counting, equal groups and arrays. Look for patterns to help remember multiplication facts.

Vocabulary

y Multiples - the product of multiplying one whole number by another

y Factors - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

Materials

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplication facts from earlier lessons.

6 x 8 = [48]

3 x 7 = [21]

6 x 3 = [18]

4 x 4 = [16]

2 x 5 = [10]

6 x 5 = [30]

4 x 2 = [8]

Guiding Questions

1. How can we solve a times 7 multiplication equation?

[skip count by 7s the number of times you are multiplying 7 by, draw equal groups of 7 objects, make arrays with 7 in each row]

Use

Have the students color in the multiples of 7 on the chart with you. [7, 14, 21, 28, 35, 42, 49, 56, 63, 70] Then solve the problems below the chart with the students. For 5 x 7, count the multiples of 7 five times until you get to 35. Then for 3 x 7, count the multiples of 7 three times until you get to 21. Do the Try it Together problems with the students. Point out that we can draw groups of 7 like in the first four problems to help us solve them. For the first problem, ask: “How many groups of 7 ice cream scoops are there?” [4] “The equation for 4 groups of 7 is 4 x 7. How many ice cream scoops are there in all?” [28] “4 x 7 is 28.” Do numbers 2-4 in the same manner. Then go through the multiples of 7 chart problems the same way you did the first two example problems.

Activities

Play “Buzz” to practice multiples of 7. Remind students of the “Buzz” game played with earlier lessons. Remind them that the game is patterned after finding “multiples.” A multiple is the product result of one number multiplied by another number. Play “Buzz” going around the room. Whoever has a multiple of 7 says “Buzz” instead. 1, 2 ,3, 4, 5, 6, “Buzz”, 8, 9, 10, 11, 12, 13, “Buzz” and so on. You can start over when someone forgets to say “Buzz” or says the “Buzz” on the wrong multiple, or have students sit down or move to a new place.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Review how the chart in number 2 works. Point out that number 3 is done for the students, and review how to fill in the circles. Remind them that sometimes the factor will be missing instead of the product as in number 7 and that they should ask themselves, “What times 7 equals 63?” Or ,“How many 7s are in 63?”

Level C Chapter 4-3

Struggling Learners

Give students counters or small objects to make equal groups or allow them to use the multiples of 7 chart or graph paper to make arrays. Since the numbers are getting larger, consider reducing the number of problems for students who are still needing to count by ones to figure out the products. Have them do only the odd-numbered problems.

Early Finishers

Write the x7 multiplication facts, and draw pictures of equal groups for each fact.

Challenge and Explore

Present the following problem: Markers come in boxes of 7. The teacher bought 8 boxes of markers for the class. How many markers did the teacher buy in all? What strategy will you use? [students could draw the 8 groups of 7 markers or an array. They could count by 7s, or add 7 eight times] How many markers did the teacher buy? [56]

Common Errors

Students may not know how to skip count by 7s. This is not as familiar a task as skip counting by 2s or 5s. They may try to skip count but accidentally leave too few or too many in between each count. Watch for students who count by 1s when counting the number of objects in equal groups or arrays and make careless mistakes in their counting.

Assess

Check work for the chart in number 2.

Objective and Learning Goals

y Multiply by 8, find patterns, and relate facts to various strategies of multiplication

Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Factor - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

Materials

y Graph paper

y Colored pencils, markers or crayons

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice x4 facts

2 x 4 = [8]

5 x 4 = [20]

8 x 4 = [32]

6 x 4 = [24]

3 x 4 = [12]

9 x 4 = [36]

4 x 4 = [16]

7 x 4 = [28]

10 x 4 = [40]

Guiding Questions

1. How can we solve a times 8 multiplication equation?

[use a x4 fact and double it, draw equal groups of 8 objects, make arrays with 8 in each row]

Ask students to study the x4 and x8 facts to discover how they are related. Guide them to realize that the products of the x8 facts are double that of the x4 facts. Show them in the example how 2 groups of 8 is double that of 2 groups of 4. Circle 2 groups of 4 in the picture of 2 groups of 8 to show that it is doubled. Do the problems in Try it Together with the students. In each problem 1- 8 help students to use the x4 fact to find the x8 fact by doubling the product of the x4 fact. Draw groups of 4 to show the x4 fact and then draw another set to show that groups of 8 are just two groups of 4. For example in number 3 draw 3 groups of 4 on the board. Then next to each group of 4, draw another group of 4. Tell students: “Now it is 3 groups of 8. When we double 4, we get 8, so we can double 3 groups of 4 and get 3 groups of 8.” Ask: “What is 3 groups of 4, or 3 x 4?” [12] “What do we get if we double 12?” [24] “So, 3 x 8 is 24!” On numbers 9-15 encourage students to think of the x4 they can double to find the x8 fact. For number 9, say: “If we don’t know 8 x 9, maybe we can use the x4 fact and double it. What is 4 x 9?” [36] “What is double that, or 8 x 9?” [72]

Hand out graph paper. Have students choose a color and color in arrays for all of the x4 facts. Have them start at the top of the page and color in 1 row of 4 squares. Underneath that, have them write the fact 1 x 4 = 4. Then have them go down the page, and do the same for 2 x 4, 3 x 4, etc., all the way to 9 x 4. If they run out of room, have them fold the paper in half to make two columns, and make some of their arrays in the second column. When they are done coloring arrays for x4 facts, have them choose a different color and double the array so it now shows rows of 8 instead of rows of 4. Have them write the x8 fact underneath the new part of the array. Example for 3 x 4 and 3 x 8: Introduce the Lesson (Try

Activities

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Consider leaving the x4 facts with products displayed on the board, or allow students to make and use a “cheat sheet” that has the x4 facts on it. For students who still struggle to add with regrouping, have them use base-10 blocks or count up on a hundred grid to help make the doubling easier.

Early Finishers

Go back and write the x4 facts that you can use to help you solve the x8 facts in numbers 1-8.

Challenge and Explore

Have students look at the Challenge problem. After they have had some time to look for and write down patterns they see, point out that the products are all even. Also, with products, the numbers in the ones’ place keep decreasing by 2 from 8 to 0, and then the pattern repeats. Tell students that this can help them remember x8 multiplication facts. Have the students cover up the problem and practice the facts out loud keeping the pattern in mind. You might even write the pattern 8, 6, 4, 2, 0, 8, 6, 4, 2, 0 on the board, and point to each number as you go through the facts. Remind students that the number you are pointing to will be in the ones place of the product.

Point out to students that all of the creatures in problems 1-4 have 8 legs. Tell them to find how many groups of 8, and write the x8 facts on the lines. Encourage them to use x4 facts that they already know to help them with x8. In number 9, do a few examples with the students to show them how the chart works. For most students, it will be helpful if they go straight across and do all of the x4 facts first, then move down to the next row and multiply by 5, then 6, 7 and 8.

Common Errors

Watch out for students who think they know the x4 fact but have the wrong product. They may double correctly, but they are doubling the wrong number. Also watch for students who have trouble doubling, especially when it requires regrouping. For example, a student may know that 4 x 7 is 28 but have a hard time doubling 28.

Assess

Check work for the last row of the chart in number 9, the x8 facts.

Objective and Learning Goals

y Multiply by 9 using equal groups and arrays Also use patterns in the products to learn these facts

Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Factors - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

Materials

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Ask students to list all of the addition facts that equal 9.

[0 + 9, 1 + 8, 2 + 7, 3 + 6, 4 + 5, 5 + 4, 6 + 3, 7 + 2, 8 + 1, 9 + 0]

Write these on the board vertically in this order so that the students see the pattern. Ask students to describe the pattern they see. [the first addend increases by one, and the second addend decreases by 1]

Guiding Questions

1. How can we solve a times 9 multiplication equation?

Take another look. What other pattern do you see?

Use the strategies above to multiply by 9 . Write

[use the patterns in the products to help you remember, draw equal groups of 9 objects, make arrays with 9 in each row, use the hands strategy]

Games

Play Heads Up to practice finding missing factors. p. 316

Introduce the Lesson (Try it Together)

Ask students to look at the x9 facts, and discuss patterns that they see in the products. Have them add the digits in each product to confirm that they always add up to 9. Then discuss other patterns that they see. Make sure that they recognize that the tens place increases by 1, and the ones place decreases by one. Also, help the students to see that the digit in the tens place is always 1 less than the factor they are multiplying by 9. For example, 9 x 4 is 36. 3 is one less than 4. If they know that and the fact that the digits in the product always add up to 9, they can figure out any x9 fact by thinking “What is one less than the factor I’m multiplying by 9?” And then “What do I add to that number to get 9?” For example, when figuring out 9 x 8, they would think “What is one less than 8?” [7] and “What plus 7 equals 9?” [2] So the answer is 72.

Go through the Try it Together problems with the students. Help them to see that they have a few “tricks” they can use to multiply by 9, but they can also use the same strategies they use for any other multiplication fact: drawing equal groups or arrays, skip counting and repeated addition.

Activities

Play “Buzz” to practice multiples of 9.

Remind students of the “Buzz” game played with earlier lessons. Remind them that the game is patterned after finding “multiples.” A multiple is the product result of one number multiplied by another number. Play “Buzz”, going around the room. Whoever has a multiple of 9 says “Buzz” instead. 1, 2 ,3, 4, 5, 6, 7, 8, “Buzz”, 10, 11, 12, 13, 14, 15, 16, 17, “Buzz” and so on.

the 9 s equation these hands can help solve.

Struggling Learners

Leave the addition facts that equal 9 visible to students. Provide counters or graph paper for students to make equal groups and arrays. Make an anchor chart to show students how the hands trick works, and leave it visible to students as they work.

Early Finishers

Go back and fill in the products for numbers 1 - 10. Also, draw what the hands would look like if you used the hands trick to solve each of these problems.

Challenge and Explore

Read the Challenge problem to the students. Have them draw the pizzas to help them solve the problem. After they have found the product, have them check to make sure the product fits the patterns they learned about earlier in the lesson. For example, if they said that 7 x 9 = 62, that can’t be right because 6 plus 2 does not equal 9. Also, the product of 6 x 9 is 54, so the tens digit has to increase by one to 6, and the ones digit has to decrease by one to 3.

Riley’s dad baked 7 pizzas. He cut each pizza into 9 slices. How many slices were there altogether?

Apply and Develop Skills (Practice / Exercise page)

Read the directions for each section to the students. Do the first problems in each set with the students. Have the students use a second strategy or trick to check each problem. For example, in number 1, have them count to see that the array has 27 dots. Then ask them to use the hands trick or patterns in the product, and see if they get the same answer. When they put their 3rd finger down,

Common Errors

When using the hands trick, some students might start on the right instead of the left. Remind them that we read words and numbers left to right, so they need to start on the left. Also, when “reading” their hands after they put a finger down, some students say the numbers that are up on the left hand and then the right hand, instead of looking at all of the fingers that are up to the left and right of the finger that they put down.

Assess

they should have 2 fingers up on the left side and 7 fingers up on the right side. If they think about the patterns in the products, they will see that they are multiplying 9 by 3, so the tens digit is one less than 3 or 2. Then, they add 7 to 2 to get 9, so the ones digit has to be 7. Therefore, 27 is the correct product.

Solve the following two multiplication facts. For each fact, draw or describe two strategies for solving the fact.

9 x 5 = [45, strategies will vary. Accept any drawing or strategy that correctly solves the problem, such as an array, picture of equal groups, skip counting, repeated addition, the hands trick or using the patterns in the products of 9]

9 x 6 = [54, strategies will vary. Accept any drawing or strategy that correctly solves the problem, such as an array, picture of equal groups, skip counting, repeated addition, the hands trick or using the patterns in the products of 9]

Objective and Learning Goals

y Multiply by 10s using skip counting

y Multiply by 10s using patterns

Vocabulary

y Skip counting–counting by multiples of a certain number.

y Product–the answer to a multiplication equation.

y Factors–the numbers being multiplied in a multiplication equation

Materials

y Base-10 rods

y Number cards 1-9 or a deck of cards with J, Q, and K removed (for game)

y Bean counters

Pre-Lesson Warm-up Guiding Questions

Review the identity property, and practice multiplying by 1. What is the identity property? [any number multiplied by 1 is that same number]

4 x 1 = [4]

1 x 7 = [7]

9 x 1 = [9]

3 x 1 = [3]

1 x 35 = [35]

250 x 1 = [250]

1 x 1,234 = [1,234]

Guiding Questions

1. What patterns do you notice when we use the identity property? [ the factor that isn’t 1 is the same as the product]

2. How might this pattern help us when we multiply by ten? [ten has a 1 and 0, we can multiply by 1 and then add a zero to the end of the product]

Start the lesson by skip counting by 10. Have students fill in the top row of boxes as they count. The boxes go to 110, but it is okay to keep counting. Ask students what patterns they notice about the numbers they count. Pass out base-10 rods to students. Hold up one base-10 rod. How many ones are in this rod? [10]. If I have 1 group of 10, how many do I have? [10]. If I have two groups of 10, how many do I have? [20]. 3 groups of 10? [30]. Keep following this pattern and fill in the multiplication table. Do the Try it together problems with students. Encourage them to model with the base-10 rods. After you’ve done the problems, discuss what patterns they see. Students should realize that when multiplying by 10, they can multiply the number by 1, and then put a 0 at the end. Help them to realize that works since we are multiplying by 1 ten. Show the base-10 rods again, and say “each rod represents 1 ten. When we multiply 10 by 8, we have 8 rods.”

Activities

Have students grab a big handful of counting beans and put them on their desk. Tell students they must count the beans as fast as they can. Give students a few minutes to count their beans. Ask students for strategies they used to count their beans. Did anyone think to make piles of 10 beans and then count the piles? Have students try that strategy–count out ten beans and put them in a pile. Then count another 10 and make another pile. And so on. Then count the piles. Was that an easier way to count a large amount? Why or why not?

Solve the story problems. Draw a picture if you need.

13. Dan is counting the pennies in his wallet. He puts the pennies in stacks of 10 . If he makes 4 stacks of pennies, how many pennies does he have?

15. Sally put 3 stickers on each of her ﬁ ngers. How many stickers did she use?

Struggling Learners

Provide base-10 rods to represent groups of 10. Encourage students to count out the number of rods they need to make the equation. Use the rods to help skip count by 10s to get the answer to the x10 facts.

Early Finishers

Review. Multiply to write the product.

14. Roberta is arranging fl owers in vases. She has 6 vases. She puts 10 fl owers in each vase. How many fl owers does she need?

16. Isaac owns a bicycle shop. He has 10 bicycles in the front room. How many bicycle tires are in that room?

Have students illustrate two of the story problems. Their illustrations should show the problem and the answer clearly.

Challenge and Explore

Challenge students to solve the following problems:

13 x 10 = [130]

14 x 10 = [140]

21 x 10 = [210]

Discuss how they knew the answer or what strategies they used to solve. [answers will vary. Students may have counted by 10 or multiplied the numbers by 1 and then added a zero to the end of the product]

Apply and Develop Skills (Practice / Exercise page)

Read the instructions together. In problems 1-9, students will need to find the missing factor. Remind students that factors are the numbers we multiply together to get a product. Encourage students to look at the product to help them determine what the missing factor will be. How many groups of 10 are in the product? In problems 10-12, students will need to solve for the product. Take a look at the word problems. Have students draw a picture of the problem to help them solve.

The review problems go over multiples of 9, 3 and 7. Students are to write the products in the outer circle. Encourage students to use the strategies they’ve learned to solve.

Common Errors

Some students may find it difficult to multiply by 10 when they get to higher numbers like 11 and 12. Watch for students who say 11 x 10 is 101 instead of 110. Encourage students to count by 10s to find the products.

Assess

Play Times Table War to practice multiplying by 10. p. 315

Check work for problems 8-16.

Level C Chapter 4-7

Objective and Learning Goals

y Multiply by the factors of 6 - 9 by using strategies such as equal groups, arrays, repeated addition and skip counting

Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Repeated addition - a multiplication strategy in which groups are added

y Skip counting - counting by multiples of a certain number

y Factors - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

Materials

y Hundreds charts

y Crayons or colored pencils

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up Guiding Questions

Practice multiplying by factors 0-5.

2 x 7 = [14]

3 x 4 = [12]

5 x 7 = [35]

4 x 4 = [16]

1 x 6 = [6]

3 x 5 = [15]

4 x 0 = [0]

Guiding Questions

1. How can we solve a multiplication fact we don’t know?

[skip count, draw equal groups, make arrays or use repeated addition]

Review the strategies in the chart with the students. Do the problems in Try it Together with the students. For each problem 1-4, have a couple of students suggest different strategies, and show it both ways. On the multiplication wheels, have students help you fill them out by having students call out the answers. When you come to a fact that students either hesitate on or disagree on the answer, have a student suggest a strategy, and use that strategy to find or check the answer. For example, if you ask the students: “What is 6 x 7?” for the first wheel, and no one answers right away, or one student calls out 42 but another calls out a different number, stop and solve the problem using a strategy. Continue to fill in the rest of the wheels quickly until there is another hesitation or disagreement.

Activities

Give students a hundreds chart. Tell students to choose 4 different colors. Have them color in all of the multiples of 6 in one color, multiples of 7 in a different color, multiples of 8 in a third color and multiples of 9 in the last color. Then practice asking partners multiplication facts 6-9 using the chart they colored to help them.

Fill in the missing factor.

Struggling Learners

Provide counters to make equal groups, grid paper to make arrays and number lines and hundreds charts to skip count on for students.

Match the equation with its array, equal groups or repeated addition. Write the product.

Early Finishers

Go back to problems 10 - 15. These problems are all shown with arrays, equal groups or repeated addition. Show each problem in a different way than it is already shown. You can also use skip counting or a “trick” that you know.

Multiply

Challenge and Explore

Have students look at the tables in the Challenge problem. Explain that the first table shows the cost to buy one of each item. The second table tells them the number of each item that someone ordered. They need to figure out the total cost, and write the equation they will use. Start the first one together. Tell students: “They want to order 5 hammers. Hammers cost $2 each, so we need to multiply 5 x 2.” Have students fill in the rest of the chart. Make sure they understand that they will need to add the 3 totals to get the final total at the bottom of the table.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Do number 1 with them. Remind them that on missing factor problems, they should ask themselves “What times 3 equals 9?” or “Three groups of what equals 9?” [3] Do number 10 with the students. Ask: “Which picture shows 3 groups of 5?” [3 rows of 5 blue stars] For numbers 16 - 31, tell the students to fill in any products they know by heart and then to choose any strategy they want to solve the ones they aren’t sure about.

Common Errors

Some students will think they have a product memorized, but they might be confused and write down the wrong answer. Have them use a strategy to check their answer. Some students will need a more concrete way of figuring out the products, such as using counters to make equal groups.

Assess

Check work for numbers 16-31.

Objective and Learning Goals

y Review

y Strategies for multiplying factors 0-10 Vocabulary

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Repeated addition - a multiplication strategy in which groups are added

y Skip counting - counting by multiples of a certain number

y Multiples - the product of multiplying one whole number by another

y Factors - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

Pre-Lesson Warm-up

Guiding Questions

Practice skip counting. Have students skip count aloud together by 2, 3, 4, 5, 6, 7, 8, 9 and/ or 10. Choose a couple of factors that will be easier for them and a couple that will be more challenging.

Guiding Questions

1. Which numbers are easy to skip count? [answers will vary. Possible answers: 2, 5, 10]

2. Which numbers are hard? [Answers will vary. Possible answers: 6, 7, 8, 9]

3. How can we find the next number when skip counting the hard numbers? [count up, multiply, add the number we are skip counting by]

4. How can we solve a multiplication fact we don’t know? [skip count, make an array, draw equal groups, use repeated addition]

Review the vocabulary of factors and products with the students. Introduce the fact triangle by explaining that the numbers along the two bottom corners are the “factors,” and the number at the top corner is the “product.” Draw an example of a triangle with 30 at the top and 5 and 6 along the inside bottom left and right corners. Use your hand to cover up the product (30). Write the multiplication problem: 5 × 6 =___. Ask what product is missing. [30] Solve the fact triangles in Try it Together with the students. Have students write the equations with a blank underneath each problem as is done for them in numbers 5 and 6. In number two, they should write 4 x 4 = ___, and in number 3, they should write 5 x ___ = 15. They should then fill in the blanks. [16 and 3]

Activities

Students make flashcard sets for the problems that are the hardest for them. For each problem, students will make 4 cards. Card 1 will have the problem written out with the answer on the back. Card 2 will be an array of the problem. Card 3 will be an illustration showing the number of equal groups. Card 4 can show repeated addition. Once the student is done, they will mix up the cards, and sort them into piles that show the same problem. Example of each card:

17. Susan has 6 bags of candy on her desk. Each bag has 7 pieces of candy in it. How many pieces of candy does Susan have in all?

x 7 = 42 pieces of candy

Struggling Learners

Provide counters to make equal groups, grid paper to make arrays and number lines and hundreds charts to skip count on for students.

Early Finishers

Go back and illustrate each multiplication fact in numbers 9 - 16 with equal groups or arrays.

Challenge and Explore

18. Bill has 72 books in all. His books are in a bookcase with 9 shelves. Each shelf holds the same number of books. How many books are on each shelf? Find the missing factor.

Have students look at the table in the Challenge problem. Explain that the numbers in the bottom row and the far right column are products. Show them that there is only one factor filled in, and they need to figure out the rest. The numbers in each column must multiply to equal the product on the bottom, and the numbers in each row must multiply to equal the product on the right. Tell students to ask themselves “What times 6 equals 36?” to find what goes in the top left box in the table. Once they start filling in more factors, they will be able to check that all factors correctly multiply to equal the products given. When they finish the challenge, have students create a new number puzzle with a partner. Exchange it with another group and solve each others puzzles.

Apply and Develop Skills (Practice / Exercise page)

Read the directions on the page. Remind students in problems 1-8 to put the factors on the bottom of the triangle and the product at the top. In problems 9-16 they will find the missing factor. Encourage students to say to themselves “4 times what is 32?” or “what times 9 is 18?” They can also refer to strategies of skip counting, using arrays, repeated addition, making equal groups, etc. to help them solve. In problems 17 and 18, read the problems carefully and circle the important information. What are you asked to find? Draw a picture to help you understand the problem and solve. To extend, have students reverse the order of the factors. Rewrite 4 x 8 as 8 x 4. Is the product still the same?

Common Errors

Assess

Play Brain vs. Hand to practice multiplication facts. p. 308

Check work for numbers 9 - 18.

Chapter 5 Chapter 5

In

Chapter 5, we will learn more about properties and patterns in multiplication.

• Recognize patterns with 10 s, 100 s, 1000 s

• Use the commutative property and “turn around” facts

• Understand the associative property—factors can be grouped and multiplied in any order

• Identity property

• Zero property

• Round to tens or hundreds and estimate

Objective and Learning Goals

y Understand and use the commutative property to multiply

Vocabulary

y Commutative property - changing the order of the factors does not change the product

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Factors - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

Materials

y Grid paper

y Counters, beans or other small objects

y Dice and number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up Guiding Questions

Practice the commutative property with addition facts.

3 + 4 = [7] 4 + 3 = [7]

6 + 8 = [14] 8 + 6 = [14]

5 + 4 = [9] 4 + 5 = [9]

9 + 3 = [12] 3 + 9 = [12]

2 + 8 = [10] 8 + 2 = [10]

Guiding Questions

1. How can we use the commutative property to solve multiplication equations? [if you don’t know a multiplication fact, you may know its turn-around fact. For example, if you know 2 x 8, you also know 8 x 2]

Read the information and example in Let’s Learn to the students, and go through the Try it Together problems with them. Pass out a sheet of grid paper to the students. For each example, have the students make arrays for each fact and its “turn-around” fact. For example, in number 1, have them color in 2 rows of 4 to show 2x4, and then next to that, color in 4 rows of 2 to show 4x2. Help them to realize that the array is exactly the same except that it is turned over on its side. This will help students to see that it doesn’t matter which order the factors are in; the product is the same. This is the commutative property.

To help students write the correct equations to go with each array, have them say out loud, “2 times 4 is 2 rows of 4, 4 times 2 is 4 rows of 2.”

Activities

Give students a container of counters, beans or other small objects. Have them choose a multiplication equation and make groups with the objects. For example, if they choose 3 x 8, they should make 3 groups of 8 counters. Students should draw the groups on a piece of paper and label their drawing with the equation (3 x 8 = 24). Then have them make groups to show the turn-around fact. In this example, they should now make 8 groups with 3 in each group. They should draw that and label it with the turn-around fact (8 x 3 = 24) next to the first fact. Continue to make and draw equal groups for turn-around facts as time allows.

Use the commutative property. Write the ‘turn around’ fact. Then write the product.

Complete the chart to review multiplication facts.

Multiply to write the product.

Using the commutative property, write in the partner equation.

How did earlier problems help you solve this one?

Earlier problems help me understand that turn around facts are equal.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. In the first set of problems, explain that they are to write the “turn-around” fact, or simply switch the order of the factors, on the first line. Then after the equal sign, they should write the product. Emphasize that both of these equations have the same product, which is why there is only one answer line.

Struggling Learners

For students who are struggling to see how the turn-around facts are the same, have them cut out one of the arrays and turn it around to match the other one.

Early Finishers

Draw arrays or equal groups for the pairs of turn-around facts in problems 1-10.

Challenge and Explore

Read the Challenge problem to the students. Tell them that the “partner equation” is the same as a “turn-around” fact. Help them to understand that it doesn’t matter how large the numbers that they are multiplying are, it still does not matter which order the factors are in.

Give students some other larger multiplication facts, and ask them to write or say the partner facts.

54 x7 [7 x 54]

5 x 38 [38 x 5] 42 x 9 [9 x 42]

Review how the chart in number 11 works. Do the example with them, and encourage them to go straight across, continuing to multiply each number on the top times 5. Then move down to the next row, and multiply each top number by 6, and so on. This will help them to keep track of their work.

Review how the multiplication wheels work, and do the example problem in number 12 with the students.

Common Errors

Watch for students who simply write the same equation again instead of reversing the order of the factors. Some students may also draw the same array for turn-around facts instead of turning the array on its side.

Assess

Games

Play Go Fishing to practice making equal groups. p. 314

Check work for numbers 2, 4, 6, 8 and 10.

Objective and Learning Goals

y Use the associative property to multiply 3 numbers

Vocabulary

y Associative property - in multiplication, when 3 or more numbers are multiplied, they can be grouped in any order, and the product will be the same

y Arrays - an arrangement of objects in equal rows and columns used as a multiplication strategy

Materials

y Counters, beans or other small objects

y Dice and number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Review the associative property of addition. Remind students that when they add 3 numbers, they can group them and add in any order. Present the following equations, and ask students to tell which numbers they grouped and added first.

3 + 4 + 7 = [14]

8 + 6 + 2 = [16]

5 + 8 + 5 = [18]

4 + 6 + 7 = [17] [any order is acceptable, but students may have found it easier to add the combinations of 10 first, and then add the 3rd number. For example, in the first problem add 3 + 7 = 10, and then add 10 + 4 = 14]

Guiding Questions

1. How can we use the associative property to multiply 3 numbers together? [we can group the numbers and multiply in any order]

The associative property in multiplication tells us that when we multiply 3 or more numbers, we can group the numbers, and multiply them in any order and we will get the same answer. Look at the arrays below. The two groups of arrays have the same number of total counters.

6 × (3 × 2) = 36

Six groups of 3 by 2 arrays 3 × 2 = 6 6 × 6 = 36 (6 × 3) × 2 = 36

Two groups of 6 by 3 arrays 6 ×

When you have an equation with parentheses, always do the part in parentheses ﬁrst.

Match the equation to the group of arrays.

Introduce the Lesson (Try it Together)

Read the Let’s Learn section to the students. Remind them that when they see parentheses in an equation, they should do that part first. In the second example, have students circle 2 rows of 3 in each of the larger arrays to show that there are still six 2x3 arrays even though they are arranged into two 6x3 arrays now. Do the Try it Together problems with the students. For number 1 ask: “Which part should we do first?”[4 x 6] Make a 4 by 6 array. Then they are multiplying that by 3, so ask: “How many 4 by 6 arrays will there be?” [3] For number 2, ask: “Which part should we do first?” [6 x 3] Make a 6 by 3 array. Then they are multiplying by 4, so ask: “How many 6 by 3 arrays will there be?” [4]

For the rest of the problems, ask students to help you fill in the blanks to solve the equations. For number 3, ask: “What is 5 x 1?” [5] Write it in the blank, and ask: “Now what it is 5 x 3?” [15] Say: “So 5 x 1 x 3 is 15.”

Activities

Give students counters, beans or other small objects and the following equations. If you want them to work independently, write the equations on index cards to leave at the center. For each equation, have them make arrays with counters to match the equation. You can have them copy the arrays they make onto paper with the equations as well.

(3 x 4) x 2 = [24]

3 x (4 x 2) = [24]

(2 x 2) x 6 = [24]

2 x (2 x 6) = [24]

2 x (5 x 4) = [40]

(2 x 5) x 4 = [40]

(3 x 3) x 2 = [18]

3 x (3 x 2) = [18]

Match the equation to the group of arrays.

Struggling Learners

Provide students with counters to make arrays to help them solve the problems and count up their answers if they do not have multiplication facts memorized yet.

Early Finishers

Multiply.

Make up your own multiplication problems with 3 numbers. Choose where to put the parentheses. Draw arrays, and solve your problems.

Challenge and Explore

Read the Challenge problem to the students. For the first problem ask: Which array are you going to make first? [2 by3] How many are you going to make? [4] Guide them through the second problem in this way as well if needed.

Draw arrays to match the equations and solve.

Apply and Develop Skills (Practice / Exercise page)

Read the directions on the page. Ask students: “Which part do you always do first?” [the part in parentheses] Ask a student to describe what the arrays should look like for the first equation in number 1. [two 4 by 5 arrays] Do number 3 with the students to remind them how to fill in the blanks. Say: We must do the part in parentheses first. What is 3 x 2? [6] Now we can finish the problem. What is 0 x 6? [0]

Games

Play Go Fishing to practice making equal groups. p. 314

Common Errors

Watch for students who ignore parentheses. Make sure they always draw that part or find and write that product first.

Assess

Check work for numbers 9, 10 and 11.

Level C Chapter 5-3

Objective and Learning Goals

y Solve larger multiplication problems using the identity and zero properties

Vocabulary

y Identity property - when multiplied by one, a number keeps its identity

y Zero property - multiplying by zero always results in zero

Materials

y Counters, beans or other small objects

y Dice

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Practice multiplication using the identity and zero properties.

9 x 0 = [0]

1 x 6 = [6]

0 x 2 = [0]

4 x 1 = [4]

1 x 8 = [8]

7 x 0 = [0]

Guiding Questions

1. How can we use the identity property to multiply larger numbers?

[we know that any number, no matter how large, times 1 will always keep its identity and equal that same number]

2. How can we use the zero property to multiply larger numbers?

[we know that any number, no matter how large, times zero will equal zero]

There are 25 lollipops in a bag. Mrs. Jones has 1 bag of lollipops. How many lollipops does she have?

There are 15

There

Read the examples in Let’s Learn to the students. Point out that they have not learned how to multiply by 15 or 25 yet, but they can multiply these larger numbers by 1 and zero because they know the identity property and the zero property. These properties are true with all numbers, no matter how large. Go through the problems in Try it Together with the students. Occasionally ask students to think about what the problem means by asking questions like “If there are 64 classrooms with 0 students in each, how many students are there?” or “If there are 32 classrooms with 1 teacher in each classroom, how many teachers are there?”

Activities

Have students play a modified version of the Go Fishing game they have played. In the game, they will draw 2 cards to make a 2-digit number. They will draw that many circles or “ponds.” Then when they roll the dice, even numbers will represent 0, and odd numbers will represent 1. Students will put either 1 or 0 fish in each “pond.”

31. There are 24 bottles of soda in a case. Jacob has 0 cases. How many bottles of soda does Jacob have?

33. There are 48 crackers in each box. Andy has 1 box of crackers. How many crackers does Andy have?

32. Brandy puts 1 cookie on each plate. She has 37 plates. How many cookies did Brandy put on plates?

Struggling Learners

Have students think of concrete scenarios to help them solve the problems. For example, if I think of 1 x 23 as 1 group of 23 candies, I know I have 23 candies. If I think of 36 x 0 as 36 jars with 0 candies in each jar, I know I have 0 candies.

Early Finishers

Choose some of the problems, and write your own word problems to go with the equations. Draw pictures to illustrate your word problems.

Challenge and Explore

Read the word problems to the students. In each problem, ask them to think about whether the scenario is demonstrating the identity property or the zero property to help them figure out the equation to write. Ask, “Is this problem talking about groups of zero or zero groups? Or is it talking about groups of 1 or 1 group?”

34. There are 85 quarters in each jar. Sarah has 0 jars. How many quarters does Sarah have?

Apply and Develop Skills (Practice / Exercise page)

Tell students to use the identity and zero properties to multiply by 1 and 0 on this page. Point out that they will also be asked to solve multiplication facts that they have already learned. Remind them to use any of the strategies they have learned if they do not have a fact memorized yet (equal groups, arrays, skip counting, repeated addition, etc.)

Games

Play Brain vs. Hand to practice multiplication facts. p. 308

Common Errors

Students often will confuse the identity and zero properties if they don’t stop to think of what the problem actually means. They may say that 26 x 0 is 26. Point out to them that this means 26 groups of 0.

Assess

Check work for problems 25 - 30.

Objective and Learning Goals

y Understand and apply the distributive property over addition

Vocabulary

y Sum - the answer to an addition problem

y Addend - a number that is being added

y Product - the answer to a multiplication problem

Materials

y Square tiles or objects of the same size and shape (ex. coins)

y Sticks or pencils to use as a divider

y Dice

y Roll and Distribute graphic organizer

Pre-Lesson Warm-up Guiding Questions

Arrange the desks in the classroom into an array. Ask students to count the number of rows and columns.

Guiding Questions

1. By just counting the number of rows and columns, how many students are in the classroom? How do you know? [Answers vary according to class size. They should find their result by multiplying the number of rows by the number of columns.]

2. If we split the class in half so that we have two arrays with the same number of rows but only half the number of columns in each array, how many students are in the classroom? How do you know? [The same number of students. Students should multiply the number of columns times the number of rows in each array and add them together resulting in the same amount.]

Introduce the Lesson (Try it Together)

Look at the arrays of objects. Ask students how to find the product of the first array. [multiply the number of rows by the number of columns] Direct students to look at the second array of objects that has been separated. Ask students to fill in the multiplication problem with the number of arrays and columns. Walk around to check students’ work. Next, have students multiply each product, and finally simplify by adding the products together. Ask students what they notice about the number of objects here compared to the first array. [there are the same number of objects] Ask students to discuss with a partner how the distributive property can help us when multiplying larger numbers. [we can separate one number into two addends and multiply]

Activities

Students are given a graphic organizer entitled “Roll and Distribute” and a die. They will roll the die three times, each time filling a space in the graphic organizer with the number on their die. They will then use the numbers that they rolled to distribute according to the order they are in. Between each new set of numbers, walk around the classroom to ensure students are arriving at the correct answers, as their answers will vary.

Story Problems.

9. Kyle wants to bring cookies to school to share with others. There are 9 boys including himself and 3 teachers that he works with during the day. If he would like to bring enough cookies for everyone to have 2 , how many does he need to bring?

10. Joshua is a newspaper delivery boy. His delivery route covers two roads. Each road has 7 houses on the right side of the road and 6 houses on the left side of the road. If he delivers a newspaper to each house every morning, how many newspapers does he deliver?

Level C Chapter 5-4

Struggling Learners

Provide students with square tiles or several objects of the same shape (ex. coins) and a stick. Have students arrange the items into an array on their desk. Have students count the number of objects. After counting the number of objects, have students divide the array in half by using the stick as a divider. Have students multiply the rows by columns and add the totals together, noticing that they get the same result. Repeat this process several times changing the position of the dividing stick.

Early Finishers

Students can continue exploring the distributive property by dividing large multipliers (numbers greater than 10) into smaller addends and apply the distributive property in order to find the product.

Challenge and Explore

Roll and distribute. Divide the class into pairs, and give each pair a set of dice. Use the Roll and Distribute worksheet to organize their work.

Apply and Develop Skills (Practice / Exercise page)

In numbers 1-4 of the independent work page, instruct students to fill in the blanks according to the distributive property. For example in #1, if we have 3 x (4+5) we will distribute and multiply the 3 by the 4 as well as the 3 by the 5. In numbers #5-8, students gain a little bit more independence as they fill in the blanks resulting from distributing the first number to the numbers inside the parentheses. They then perform the multiplication and write the products on the next line. Their final line of work should be the sum of the two products. In #9 and #10 read through the story problems with the students once. Encourage students to highlight or underline any key information. Then have students use this key information to fill in the blanks and continue to distribute as they have done in the previous practice problems.

Common Errors

Students may only multiply one of the addends when distributing rather than distributing to both terms inside the parentheses. When teaching this, arrows can be used from the multiplier to each addend to remind students to multiply both. Students may also add the multiplier rather than multiplying it to the numbers inside. Using graphic organizers that include blanks and multiplication signs can help students to organize their work and perform the correct operation on the numbers.

Discuss the results by asking the following questions:

1. What is the total if you add the addends before multiplying? [answers may vary]

2. What is the total if you multiply the outside digits by each addend and add their totals? [answer should be the same as question #1]

3. Are the answers in #1 and #2 the same? Why do you think this is? [answers will vary]

Assess

Check problems 5-8 to assess whether students are using the distributive property. Ask them to draw arrows to show which numbers they are distributing and multiplying. Students can draw arrays for problem #5 to show how 3x2 and 3x3 is equal to 3x5.

Objective and Learning Goals

y Students will use the distributive property to solve multiplication problems

Vocabulary

y Distributive property- breaking one factor up to make the multiplication problem easier to solve.

y Product- the answer to a multiplication problem.

y Factors- the numbers you multiply together.

y Addend- the numbers you add together.

y Sum- the answer to an addition problem.

Materials

y Dry-erase board and marker

y Base-10 rods

y Deck of cards for game

Pre-Lesson Warm-up

Guiding Questions

Review multiplication facts from previous lessons.

6 x 8 = [48] 5 x 9 = [45]

7 x 4 = [28] 3 x 8 = [24]

8 x 7 = [56] 4 x 2 = [8]

Guiding Questions

1. Which combination for 11 was easier for you to solve?[Answers will vary. Any answer is correct as long as students can explain what made it easier to solve.]

2. Which combination for 12 was easier for you to solve? [Answers will vary. Any answer is correct as long as students can explain what made it easier to solve.]

Ask students to look at the problem 3 x 11 at the top of the page. Explain to students that today we will use the distributive property to solve multiplication problems. Lead students through it step by step. First, we need to break apart one of the factors. Since 11 is a bigger number to multiply, we will break apart the 11. Model thinking aloud different combinations that equal ll. Since multiplying by 10 is easy, I’m going to break 11 into 10 +1. Have students trace the 10 and 1. Now, the 3 has to have a turn to be multiplied by the 10 and the 1. Have students trace the 10 and 1 inside the parentheses. Now, work with students to complete the two multiplication problems. Then, explain that we need to add the two products together to get our answer. Repeat these same steps for all the problems in Let’s Learn. Ask students the Guiding Questions. Now as you move into Try it Together, work with students to fill in the missing addend. Then, work through the remaining steps to solve. When students list the combinations of addends that equal 11 and 12 there is not space for students to put 0+11 or 0+12. If students write those facts, tell them that they are correct that the sum is 11 or 12. However, those facts won’t help us with the distributive property because the 11 and 12 aren’t broken up into other numbers.

Activities

Practice making groups of tens using base-10 rods. Call out (or have partners call out to each other) a x10 fact. Have the students demonstrate the problem with base-10 rods, and then tell the product. For example, if you say 4 x 10, the students should get 4 rods. They should then say 4 x 10 equals 40. Encourage them to count the rods by 10s.

Use the distributive property to solve each problem.

1. 11 x 5

Think Which factor will I split apart? Cross that factor out.

Split the factor into 2 addends +

Now, multiply the factor you didn’t split with each addend.

( × )+( × )

Now, add the two products together + So, 11 × 5 =

Read each problem. Solve.

3. Mr. Smith hiked 12 miles each day for 12 days.How many miles did Mr. Smith hike?

Think

Split the factor into 2 addends +

Now, multiply the factor you didn’t split with each addend.

Now, add the two products together

4. Mrs. Kline has 6 children. Each child has 11 stickers. How many stickers do her children have?

Struggling Learners

Students may need a multiplication chart to help them with their facts.

Early Finishers

Choose multiplication facts from the multiplication wheel to write word problems for. Students can give their problems to a classmate to solve.

Challenge and Explore

Give students the following larger problems. Have them use the distributive property to solve:

9 x 17= [153]

15 x 8 = [120]

5 x 19 = [95]

Apply and Develop Skills (Practice / Exercise page)

Discuss the results by asking the following question:

1. How did using the distributive property make the problems easier to solve? [answers will vary but should be similar to it was easier to solve because I was able to break the larger factor into numbers that were easy for me to multiply.]

Depending on the level of your class, students can complete this page as a whole class, with a partner or independently. Remind students that they can refer back to the addition facts they listed on the previous page to help them decide how to break apart the factor. Students may also need to be reminded that they should break the factor up into numbers that are easy for them to multiply. When students get to the multiplication wheels, students will need to use their dryerase boards to do their work. Walk around while students are working to make sure students are using the distributive property correctly.

Students may not multiply the factor by both of their addends. Students may also try to multiply the two products instead of adding them together. Common Errors

Assess

Games

Play Times Table War to practice multiplying by 11 or 12. p. 315

Use numbers 3-6 to assess understanding.

Level C Chapter 5-6

Objective and Learning Goals

y Use patterns to multiply by 10s, 100s and 1,000s

Vocabulary

y Product - the answer to a multiplication equation

Materials

y Base-10 blocks

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplying by 10.

5 x 10 = [50]

2 x 10 = [20]

7 x 10 = [70]

9 x 10 = [90]

4 x 10 = [40]

Guiding Questions

1. How can we use patterns to multiply by multiples of 10, 100 and 1,000? [multiply the number by the first digit in the multiple of 10, 100 or 1,000, and then add 1 zero if multiplying by 10s, 2 zeros if multiplying by 100s and 3 zeros if multiplying by 1,000s]

36,000 12,000 20,000 32,000 36,000 40,000 3,600

Have students examine the problems in Let’s Learn to look for patterns, and discuss what they find. Demonstrate each problem with base-10 blocks. For the first example, show 5 rods for 5 x 10, and have students count by 10s. Then show 5 flats for 5 x 100, and have students count by 100s. Last, show 5 large cubes for 5 x 1,000, and have students count by 1,000s. For the second example, show 4 groups of 5 of each - small cubes(ones), rods (tens), flats (hundreds) and large cubes (thousands). If you don’t have enough of any of the blocks, you can draw them on the board. Explain to students that if they know that 4 groups of 5 is 20, then they also know that 4 groups of 5 tens is 20 tens, 4 groups of 5 hundreds is 20 hundreds and 4 groups of 5 thousands is 20 thousands. Help students to see the pattern, that they can multiply the 1-digit number times the number of tens, hundreds or thousands, and then add 1 zero for tens, 2 zeros for hundreds or 3 zeros for thousands. Go through the Try it Together problems with the students. Have students explain the pattern, and encourage them to use place value language (talk about groups of tens, hundreds or thousands).

Activities

Give students base-10 blocks (or have them draw them if you don’t have enough) to demonstrate multiplying by 10s, 100s and 1,000s. Have them show the following problems.

9 × 100 = 900

9 × 1,000 = 9,000

5 × 60 = 300

5 × 600 = 3,000

5 × 6,000 = 30,000

8 × 80 = 640

8 × 800 = 6,400

8 × 8,000 = 64,000

Struggling Learners

Have students circle the zeros in the problem to help them remember how many zeros to add to their answer. Tell them to multiply the first factor times the first digit in the other factor, write down the product, then look at the problem to see how many zeros they circled and add them to the end of the product they wrote down.

Early Finishers

Choose equations from problems 1-9, and write your own story problems to go with the equations.

Challenge and Explore

Solve the story problem.

James collected 5 books of stamps. Each book contained 300 stamps. How many stamps did James have altogether? × = stamps

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Do the example problems with the students, reminding them to use the pattern they learned. Tell students that the wheels in numbers 10-12 work just like the ones they are used to, only these will have larger numbers to multiply. They should use the same patterns as the problems above to help them.

Read the story problem to the students. To fill in the equation, have students think “groups of.” James has 5 books or 5 groups of 300 stamps, so the equation the students need to solve is 5 x 300. Remind them to use the pattern and multiply 5 x 3 = 15. Then ask: How many zeros are in the problem? [2] So, add 2 zeros to the end of the product, and what is the answer? [1,500 stamps]

Common Errors

Watch for students adding the incorrect number of 0s to the products. This can be especially tricky for students when the product already ends in a zero. For example, in 2 x 500, students may multiply 2 x 5 = 10 and then only add 1 zero since 10 already ends in a zero. They may say that 2 x 500 is 100 instead of 1,000. Help them to see that that is impossible, and remind them to write the product and then add the zeros even if there is already a zero in the product.

Assess

Check work for numbers 6, 7, 8 and 9.

Level C Chapter 5-7

Objective and Learning Goals

y Round to the nearest 10 or 100 to estimate multiplication

Vocabulary

y Round - find a close but easier to work with number to a given number

y Estimate - to find a close enough answer when the exact answer is not needed

Materials

y Dice

y Number cards 1-9

Pre-Lesson Warm-up

Guiding Questions

Practice rounding to the nearest 10 and 100.

Round to the nearest 10:

67 [70]

43 [40]

81 [80]

Round to the nearest hundred:

176 [200]

539 [500]

762 [800]

Guiding Questions

1. How can we use estimation to multiply a 1-digit number by a larger number when we do not need the exact answer? [round the larger number to the nearest 10 or hundred, then multiply the tens or hundreds by the 1-digit number]

We can use estimation to help! If there were 39 students in each class, we would round to

If there were 220 students we round

Estimate and multiply.

1. If there are 39 students in each class, about how many chairs would be needed for 6 classes? First, we must round 39

If 39 rounds to 40 , we can multiply 40 by the number of classes to estimate how many chairs we need. 40 × 6 = 240 chairs, so about 240 chairs are needed.

About how many? Round to the nearest 10 or 100.

Remind students that they have used rounding and estimation to find “close enough” answers when an exact answer is not needed. Draw students’ attention to the illustration and speech bubbles. Ask students: “What is the key word in these questions that tells us we do not need an exact answer?” [about]

Tell students: “In the last lesson we learned how to multiply by multiples of 10 and 100. So, if we round larger numbers to the nearest 10 or 100, we can use estimation to multiply larger numbers.”

Read through the information and examples in Let’s Learn and Try it Together. For numbers 2 - 5, help students to first round the larger number, then multiply the “easier” number. For example, in number 2, say: “First round the larger number to the highest place value. What is 49 rounded to the nearest 10?” [50] “If you know 6 x 5, then you know 6 x 50.” Circle the 0 in 50. Ask: “What is 6 x 5?” [30] “How many zeros do we add?” [1] “So, what is 6 x 50?” [300] Continue with the other problems in this manner.

Activities

Students will practice rounding and multiplying by tens and hundreds. Give students a die and number cards 1-9. Students should draw 2 or 3 cards and put the digits in any order they wish to make a 2 or 3-digit number. Then roll the die. The number they roll is the number they should multiply their 2 or 3-digit number by. Round the 2 or 3-digit number to the nearest ten or hundred, and then multiply to find the estimate.

Estimate. Show your equation and answer.

9. About how many tickets are

for all 3 classes?

Struggling Learners

Provide or draw number lines for students to use to round. If students do not have basic facts memorized yet, consider giving them a multiplication chart to use to look up the products before adding zeros.

11. About how many tickets are needed for all 7 classes?

10. About how many tickets are needed for all 5 classes?

Early Finishers

Choose equations from numbers 13-24, and write your own word problems to go with the equations that do not need an exact answer and can use estimation.

Solve the equation using estimation.

12. About how many tickets are needed for all 8 classes?

Challenge and Explore

Challenge students to round to the nearest thousand and estimate the following problems:

3,278 x 6 = [3,000 x 6 = 18,000]

6,842 x 3 = [7,000 x 3 = 21,000]

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. For numbers 1-8, tell students that they should round the larger factor to its highest place value. Ask a student to explain how they can use the number line to help them round number 1. [find 29 on the number line, and see that it is higher than 25 and much closer to 30 than to 20] For the rest of the problems on the page, remind students that the first step is to round the larger factor on top to its highest place value. Then multiply, and add the correct number of zeros. Encourage students to circle the zeros in their rounded numbers if they aren’t sure how many to add to the product. Also, remind students to think about place value. For example, in number 9, if 3 x 4 is 12, then 3 x 40 is 12 tens or 120.

Common Errors

Watch for students who are still making rounding errors, especially to the nearest hundred. Have them underline the target digit and circle the digit to the right. Remind them of the rhyme they learned in earlier chapters. Some students may add an incorrect number of zeros to the product of the 1-digit numbers they multiply. Have them circle the zeros in the rounded number to help them see how many they need to add.

Games

Play Draw and Round to practice rounding to the nearest 10 and 100. p. 310

Assess

Check work for numbers 21 - 24.

Objective and Learning Goals

y Review

y Commutative, associative, identity and zero property of multiplication, patterns of multiplying by tens, hundreds and thousands Vocabulary

y Associative property - in multiplication, when 3 or more numbers are multiplied, they can be grouped in any order, and the product will be the same

y Commutative property - changing the order of the factors does not change the product

y Identity property - when multiplied by one, a number keeps its identity

y Zero property - multiplying by zero always results in zero

y Equal groups - a multiplication strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication strategy

y Factors - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

y Repeated addition - a multiplication strategy in which groups are added

y Skip counting - counting by multiples of a certain number

y Round - find a close but easier to work with number to a given number

y Estimate - to find a close enough answer when the exact answer is not needed

Materials

y Grid paper

y Crayons or colored pencils

Pre-Lesson Warm-up Guiding Questions

Practice multiplication facts. Have students call out answers or write them on a dry-erase board or piece of paper to show you.

2 x 8 = [16]

10 x 4 = [40]

3 x 0 = [0]

6 x 7 = [42]

9 x 3 = [27]

7 x 1 = [7]

5 x 6 = [30]

4 x 8 = [32]

Guiding Questions

Let’s review some properties and patterns of multiplication.

The commutative property tells us that the order we multiply two numbers in does not change the product.

The associative property in multiplication tells us that when we multiply 3 or more numbers, we can group the numbers and multiply them in any order.

The identity property multiplying by 1 does not change the answer.

When we multiply by multiples of 10 , 100 , and 1000 we see a distinct pattern:

3 ×

The zero property multiplying by 0 always results in 0

Use the commutative property. Write the turn around fact and the product.

1. How can we use properties and patterns to help us solve multiplication equations? [We can use the identity and zero properties to solve anything times 1 or 0. We can use the associative property to group numbers in any order when multiplying 3 or more numbers. We can use the commutative property to solve turnaround facts. We can use the patterns to solve multiplication by tens, hundreds and thousands by simply adding zeros to the products]

Activities

(Try

Review the four properties that students have learned, and go over the examples of each in Let’s Learn. Then have students look at the example problem for multiplying by multiples of 10, 100 and 1,000. Ask a student to describe the pattern we see in these types of problems. [when you add a zero to one of the factors, you add a zero to the product as well] Do the problems in Try it Together with the students to review.

Color arrays on grid paper that show the associative property. Give students equations to draw arrays. For example, (2 x 4) x 3. Have students color three 2 by 4 arrays all connected together. Color each of the 2 by 4 arrays a different color to make them stand out from each other. Then solve the problem for the total. [24]

Equations:

(2 x 4) x 3 = [24]

6 x (3 x 2) = [36]

(5 x 4) x 2 = [40]

4 x (2 x 2) = [16]

(5 x 2) x 3 = [30] Introduce the Lesson

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. For the first two problems, tell the students to fill in the blanks with how many rows and how many in each row. Then solve for the product.

Struggling Learners

Give students tools such as counters and grid paper to help them solve multiplication facts. For students who need help rounding, provide number lines or hundreds charts.

Early Finishers

Write and solve your own problems that have parentheses in them.

Challenge and Explore

Solve the following problem. Write an equation with parentheses.

James was helping his teacher sort supplies. There were 8 markers in each box. He put 5 boxes of markers on each table There were 6 tables. How many total markers did James put on tables?

First, how many markers did he put on each table?

[5] boxes x _______ [8] markers in each box = [40]

Next, how many markers did he put on all 6 tables?

[6] tables x _______ [40] markers on each table = [240 markers]

For numbers 9-14, remind students to always do what is in parentheses first. Encourage students to use patterns to solve 15-17. Tell the students that they should round the larger factor to its highest place value on the estimation problems at the bottom of the page.

Common Errors

Watch for students who guess the products of multiplication facts and fail to use a strategy to check their work. Some students will still make rounding errors when estimating or become confused about the number of zeros needed in the products of multiplication by multiples of 10, 100 and 1,000.

Assess

Write an equation with parentheses: (____ x _____) x _______ = _______ [(5 x 8) x 6 = _____ 40 x 6 = 240]

Games

Choose a game to play to practice multiplication or rounding.

Check work for numbers 2, 14, 17 and 21.

Chapter 6 In Chapter 6, we will learn about division using divisors 0-5.

• Understand that division is the inverse operation of multiplication and is used to solve problems

• Separate items into equal groups to ﬁnd the total number of objects in each group

• Use pictures to draw total quantities and circle groups to help calculate division totals

• Use arrays to help visualize how equal groups can be arranged to quickly calculate totals

• List multiples of each divisor to ﬁnd the quotient quickly

• Dividing by 1 results in the identical quotient as the dividend

• Dividing a group of 0 results in a quantity of 0

• Use manipulatives and counting games to make division a more concrete concept

• Notice and connect patterns of multiplication to solve division equations accurately and e iciently

Objective and Learning Goals

y Divide using divisors 0-5

Vocabulary

y Divide - to split a number into equal groups

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication or division strategy

Materials

y Counters, beans or other small objects

y Small containers such as jars, cans or small paper or plastic cups, plates or bowls

y Dice and number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Ask “equal groups” questions for students to solve mentally.

How many groups of 4 are there in 8? [2]

How many groups of 4 are there in 16? [4]

How many groups of 3 are there in 15? [5]

How many groups of 3 are there in 18? [6]

How many groups of 5 are there in 35? [7]

How many groups of 5 are there in 45? [9]

Guiding Questions

1. How can we divide things into equal groups? [start with the total number of objects, think about how many groups you are dividing into and then draw objects in groups one at a time until you have the total number of objects]

Let’s learn!

David has six cookies and wants to give each of his friends the same amount of cookies. Divide his six cookies into three groups to give his friends.

How many groups?

How many in each group?

How

How many rows?

How many in each row?

Divide into equal groups. 1. Divide 12 into four equal groups. 2. Divide 9 into three equal groups.

How

How many groups?

How many in each group?

How many in all?

How many rows?

How many in each row?

Introduce the Lesson (Try it Together)

Read through Let’s Learn with the students. Use counters or other objects to show the students how to divide the cookies in the example problems. Say: “We have 6 cookies we need to divide into 3 groups. Let’s share them equally. Count the cookies 1 to 6 as you put one in each group.” Put cookies in each of the 3 groups 1 at a time while counting 1, 2, 3, and then put a second cookie in each group one at a time while counting 4, 5, 6 to show the students how to share the cookies equally. Repeat this process of equal sharing with the other example problems in Try it Together.

Activities

Students will divide counters into equal groups. Give students counters and several small containers. Tell students to take out a certain number of counters, and then divide them equally among a certain number of containers. Ask how many counters are in each container.

Divide 25 counters equally among 5 containers.[5]

Divide 24 counters equally among 6 containers. [4]

Divide 10 counters equally among 5 containers. [2]

Divide 12 counters equally among 4 containers. [3]

Divide 18 counters equally among 3 containers. [6]

Divide 18 counters equally among 2 containers. [9]

Struggling Learners

Give students counters or objects to make the division more concrete.

Early Finishers

Write word problems about dividing or sharing things equally using the equations on this page.

Challenge and Explore

Read the Challenge problem to the students. Give each student 12 counters to represent David’s pieces of candy. Give the students some time to make equal groups as many ways as they can. Bring the class together, and discuss their strategies as well as all of the different ways to make equal groups.

If David had 12 pieces of candy, what are all the possible ways that David could separate his 12 candies into equal groups?

groups of groups of groups of groups of groups of groups of

Apply and Develop Skills (Practice / Exercise page)

Read the directions, and do number 1 with the students. Say: “The first problem is 6 divided by 3. Which picture shows 6 total objects divided into 3 equal groups?” [the footballs] “Draw a line to the footballs. How many footballs are in each group?” [2] “6 divided by 3 is 2. Write a 2 after the equal sign.” Get students thinking about number 2 by asking: “How many total objects and how many groups should you look for in number 2?” [20 total objects in 5 groups]

Read the directions for 6 - 11, and do number 6 with the students. Show students how to draw objects in arrays until they reach the total number of objects. Say: “8 divided by 4 is the problem. We are going to draw 8 total objects. Let’s draw groups of 4.” Draw the first row, counting 1, 2, 3, 4, and then the second row counting 5, 6, 7, 8. Say: “We drew 8 objects in groups of 4. How many groups did we draw?” [2] “8 divided by 4 is 2.”

Common Errors

When dividing and sharing equally, some students try to put more than one object in a group at a time. Some students forget to count the objects they are sharing to make sure they share the correct total number.

Assess

Games

Play Go Fishing to practice making equal groups. p. 314

these problems. Draw an array or equal groups to help you.

Objective and Learning Goals

y Divide by 0 and 1

Vocabulary

y Divide - to split a number into equal groups

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

Materials

y Counters, beans or other small objects

y Small containers such as jars, cans or small paper or plastic cups, plates or bowls

y Dice and number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplication by 0 and 1.

3 x 1 = [3]

0 x 6 = [0]

7 x 0 = [0]

1 x 8 = [8]

9 x 0 = [0]

5 x 1 = [5]

1 x 4 = [4]

0 x 2 = [0]

Guiding Questions

1. What happens when we divide by 1 and 0? [when we divide by 1, the answer is always the number you are dividing because if you divide it into 1 group, you still have the whole amount. When we divide by 0, the answer is always 0 because you will have nothing in the groups]

Let’s learn!

Divide these cookies onto the plate. Now here are some treats. Divide these treats onto the plate.

How many in all?

How many groups?

How many in each group?

How many in all?

How many groups?

How many in each group?

When your dividend is zero, your answer will always be zero because there is nothing to divide! You don’t have any cookies to give your friends.

Try it together!

How many in all?

How many groups?

How many in each group?

Solve these division equations.

How many in all?

How many groups?

How many in each group?

Introduce the Lesson (Try it Together)

Model with students to show when dividing by 1, you’re taking what you have and splitting it into 1 group. You can use students, counters or beans. Students should see when you try to break up anything into one group, the quotient is the same as what you started with. Then, model with students that when you start with 0 and try to divide it into groups, there is always 0 as your quotient because you started with nothing. Work through the Try it Together problems with students. Provide counters or beans for students to use, if necessary.

Activities

Give students counters and containers to practice dividing, just like in the last lesson. However, in this activity, we will practice dividing by 1 and 0. Ask how many counters are in each container. Have students write a division equation for each.

Divide 9 counters equally among 1 container. [9 ÷ 1 = 9]

Divide 0 counters equally among 4 containers. [0 ÷ 4 = 0]

Divide 7 counters equally among 1 container. [7 ÷ 1 = 7]

Divide 0 counters equally among 3 containers. [0 ÷ 3 = 0]

Divide 0 counters equally among 6 containers. [0 ÷ 6 = 0]

Divide 3 counters equally among 1 container. [3 ÷ 1 = 3]

0 Divided by 6 0

0 Divided by 3

0 Divided by 9

Answers will vary. When you divide by zero the quotient is always zero. When you divide by 1 the quotient is always the other number (dividend).

Solve each division equation. Complete the supporting multiplication equation.

12. Joseph made 7 snowballs. He put the snowballs into 1 group. How many snowballs were in the group?

13. Sarah has 0 candies. She tries to share the candies with 9 people. How many candies does each person get?

7 ÷ 1 = 7 snowballs in the group 0 ÷ 9 = 0 candies for each person

Apply and Develop Skills (Practice / Exercise page)

Look at the tables at the top of the page with students. Depending on the level of your class you could do the first problem on each table with students and have them complete the rest of the table in partners or independently. Have students work through the rest of the page independently. When students finish, review the answers paying special attention to the answer to number 3.

Struggling Learners

Have students think about a scenario (such as having 0 pencils to divide among 3 students or dividing 6 apples into 1 basket) to help them remember how to divide by 0 and 1. Consider posting an example problem on an anchor chart in the classroom.

Early Finishers

Write story problems to go with 4-11. Give the problems to a classmate to solve.

Challenge and Explore

Present the following problems to the students:

5,280 ÷ 1 = [5,280]

0 ÷ 5,280 = [0]

Ask students to explain their answers. [if you divide any number, even a big one, into 1 group, the whole number will be in that group, so the whole number is the answer. If you start with 0, you will always have 0 no matter how many groups you divide it into because you started with nothing]

Common Errors

Students will get confused with adding or subtracting 0, so when they have 0 divided by a number, they think it’s that number. Students may say that a number divided by 1 is always 1 instead of the number. It is important to emphasize that numbers cannot be divided by 0. You can divide 0 by a number, but cannot divide a number by 0.

Assess

Check work for numbers 9 - 12.

Level C Chapter 6-3

Objective and Learning Goals

y Divide by 2 using equal groups, arrays and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication or division strategy

Materials

y Counters, beans or other small objects

y Multiplication x 2 flashcards (for game)

Pre-Lesson Warm-up Guiding Questions

Practice multiplying by 2.

2 x 3 = [6]

2 x 6 = [12]

2 x 5 = [10]

2 x 9 = [18]

2 x 4 = [8]

2 x 7 = [14]

Guiding Questions

1. How can we divide by 2? [use the related x2 fact, make 2 equal groups out of the total or distribute the total into 2 rows in an array]

The boys want to play in a ball game together. Divide the boys into two teams.

How many in all?

How many groups?

How

in each group?

Two more boys want to join in. How would you divide the boys now to make teams?

How many in all?

How many groups?

Try it together!

Divide into equal groups using arrays or pictures.

1. Abe had 14 pieces of candy. He wanted to eat some of the candy and save an equal amount. How many pieces of candy can Abe eat?

How many in all?

How many groups?

2. Aaron had two cakes. If he put them in two boxes, how many cakes would go in each box?

How many in all?

How many groups?

Introduce the Lesson (Try it Together)

Explain to students that when we divide by 2, we split a total amount of something into two equal groups. Read the examples about the teams in Let’s Learn to the students. Relate the situations to the divided by 2 equations shown. Say: “Since we are splitting the 8 boys into 2 equal teams, we are dividing 8 by 2. There are 4 boys on each team, so 8 divided by 2 is 4.”

Go through the other examples on the page in a similar manner. Show students how the multiplication facts relate to the division facts. For number 1 in Try it Together say: When we divide 14 into 2 equal groups we get 7 in each group. We know from multiplication that 2 groups of 7, or 2 x 7, is 14.

Activities

Practice dividing a group of counters by 2. Have partners share sets of counters equally, then write the division equation to match each equal sharing situation.

Share 16 counters. [16 ÷ 2 = 8]

Share 4 counters. [4 ÷ 2 = 2]

Share 8 counters. [8 ÷ 2 = 4]

Share 18 counters. [18 ÷ 2 = 9]

Share 10 counters. [10 ÷ 2 = 5]

Share 14 counters. [14 ÷ 2 = 7]

Share 24 counters. [24 ÷ 2 = 12]

Solve each story problem below using a division array or picture.

9. Twelve boys want to play a game of ball together. Divide these boys into two teams.

10. There are twenty-four strawberries on a bush. How many would be in each of the two baskets if you divide them equally?

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Provide counters for students to divide into 2 equal groups when solving the problems.

Early Finishers

Choose two divided by 2 equations on this page. Write a number story to go with each equation, and illustrate each problem.

Challenge and Explore

Present the following problem to students. Allow students to use counters or other objects to help them.

Solve 34 ÷ 2 = [17]

How did you solve this problem? [answers will vary. Students may have counted out 34 counters and then put them into two equal rows of 17]

Read the directions for the first set of problems, and do number 1 with the students. Say: “When we split 8 into 2 equal groups, there are 4 in each group because 2 groups of 4 or 2 x 4 is 8.” For numbers 7 and 8, explain that students should divide the number in the column on the left by 2, and write the answer next to it in the column on the right. Read the directions for numbers 9 and 10, and emphasize the importance of drawing a picture to help solve the problem.

Common Errors

When writing the related multiplication equation, some students may take the divisor and dividend and make those the factors. For example, for 20 ÷ 2, they will say the related multiplication equation is 20 x 2 instead of 10 x 2.

Assess

Play Around the World to practice dividing by 2. p. 317

Solve the following two problems. Draw pictures, or arrays to show the division problem. Write the related multiplication equation.

Level C Chapter 6-4

Objective and Learning Goals

y Divide by 5 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication or division strategy

y Skip counting - counting by multiples of a certain number

Materials

y Counters, beans or other small objects

y Small containers

y Multiplication x 5 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplying by 5.

5 x 3 = [15]

5 x 6 = [30]

5 x 5 = [25]

5 x 9 = [45]

5 x 4 = [20]

5 x 7 = [35]

Guiding Questions

1. How can we divide by 5? [use the related x5 fact, make 5 equal groups out of the total or distribute the total into 5 rows in an array, skip count by 5s until you reach the total, and keep track of how many skip counts]

1. Issac wanted to sort his nails into ﬁve separate boxes. How many nails would go in each box if they all had an equal amount?

2. Use an array to support your answer for 25 ÷ 5

Games

Play Around the World to practice dividing by 5. p. 317

Try it together!

How many in all? How many in all? How many groups? How many groups? How many in each group? How many in each group?

List out the multiples of 5

10, 15, 20,

4. Issac went to the store and brought home 10 more nails for a total of 35 nails. How many nails would he now have in each of his ﬁve boxes?

5. Issac dropped his tool box and 15 nails rolled away. Now his collection has 20 nails. How many nails would he have in each of his ﬁve boxes?

List out the multiples of 5 until you get to 20 , , ,

Solve these division equations.

Explain to students that when we divide by 5, we split a total into 5 equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into boxes. For number 3, explain to students that they can use skip counting to divide as well as multiply. Tell them to make sure to keep track of how many times they skip count by 5. The number of skip counts will be their answer. Remind them how to find the related multiplication equation by thinking “What times 5 equals 25?”

Go through the Try it Together problems with the students. Ask students to choose a strategy and share with the class how to solve the problem. They can draw equal groups or arrays, skip count by 5s or think of the related multiplication equation.

Activities

Practice dividing a group of counters by 5. Have students share sets of counters equally among 5 small containers, then write the division equation to match each equal sharing situation.

Share 40 counters. [40 ÷ 5 = 8]

Share 10 counters. [10 ÷ 5 = 2]

Share 20 counters. [20 ÷ 5 = 4]

Share 45 counters. [45 ÷ 5 = 9]

Share 25 counters. [25 ÷ 5 = 5]

Share 35 counters. [35 ÷ 5 = 7]

Share 15 counters. [15 ÷ 5 = 3]

Solve each division equation. Complete the supporting multiplication equation.

Let’s play the “Race Through Dividing by Five” game. Begin at the start line and divide each block by 5 , see how fast you can race to the ﬁnish.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Provide counters for students to divide into 5 equal groups when solving the problems.

Early Finishers

Choose two divided by 5 equations on this page. Write a story problem to go with each equation, and illustrate each problem.

Challenge and Explore

Present the following problem to students. Allow students to use counters or other objects to help them.

Solve

75 ÷ 5 = [15]

How did you solve this problem? [answers will vary. Students may have counted out 75 counters and then put them into two equal rows of 15, or they may have skip counted by 5s to 75 and kept track of their 15 counts]

Read the directions to the students. Start the skip counts with the students. Point out that 10 is filled in for them. Ask: What comes first when we count by 5? [5] Fill in 5. What comes after 10? [15] Fill in 15. Tell the students to continue like this. Explain how to use the skip counts to solve the problems using the first example. Say: We can solve 10 divided by 5 if we figure out how many times we skip count by 5s to get to 10. Let’s do it. 5, 10. We skip counted 2 times, so 10 divided by 5 is 2.

Common Errors

When writing the related multiplication equation, some students may take the divisor and dividend and make those the factors. For example, for 20 ÷ 5, they will say the related multiplication equation is 20 x 5 instead of 4 x 5. Some students will struggle to keep track of their skip counts when using that strategy. Have them write down the counts or count on their fingers.

Assess

Read the directions, and do number 2 with the students. Say: To solve 50 divided by 5, we can think of the related multiplication equation. Think, what times 5 equals 50? [10]

Explain the race track problem to the students. Tell them that they should take the number in dark blue on the outside, divide it by 5 and write the answer in the corresponding light blue square. Show them how 15 ÷ 5 = 3 has been done for them.

Solve the following two problems. Draw pictures or arrays, or write the skip counts to show the division problem. Write the related multiplication equation.

25 ÷ 5 = [5, picture should show 25 total objects in 5 groups of 5 or skip count 5s to 25, 5 x 5 = 25]

40 ÷ 5 = [8, picture should show 40 total objects in 5 groups of 8 or skip count 5s to 40, 8 x 5 = 40]

Objective and Learning Goals

y Divide by 3 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication or division strategy

y Skip counting - counting by multiples of a certain number

Materials

y Counters, beans or other small objects

y Small containers

y Multiplication x 3 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplying by 3.

3 x 3 = [9]

3 x 6 = [18]

3 x 5 = [15]

3 x 9 = [27]

3 x 4 = [12]

3 x 7 = [21]

Guiding Questions

1. How can we divide by 3? [use the related x3 fact, make 3 equal groups out of the total or distribute the total into 3 rows in an array, skip count by 3s until you reach the total, and keep track of how many skip counts]

learn!

1. Joseph and his classmates were visiting a farm. He saw 12 goats in 3 pens. If the same amount of goats were in each pen, how many goats were in each pen?

How many in all?

How many groups?

2. Use an array to support your answer for 12 ÷ 3

3. List out the multiples of 3 , , , , How many multiples does it take to get to 12 ?

÷ 3 = because × 3 = 12

Divide into equal groups using arrays or pictures.

4. Joseph noticed there were 21 chickens in yard. There were three chicken coops. If the same number of chickens are in each coop, how many chickens would live in each coop?

How many in all?

How many groups?

How many in each group?

5. There were 30 cows in the ﬁeld. If there were three milking barns with the same number of cows in each, how many cows would be in each milking barn?

List out the multiples of 3 until you get to 30

, , , , , , , , How many multiples does it take to get to 30 ?

Introduce the Lesson (Try it Together)

Explain to students that when we divide by 3, we split a total into 3 equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into groups. Have a student suggest a way to make the array for number 2. Be sure to show students that they need to have 12 total objects in 3 rows and will end up having 4 objects in each row. For number 3, remind students that they can use skip counting to divide as well as multiply, and they need to make sure to keep track of how many times they skip count by 3. Remind them how to find the related multiplication equation by thinking “What times 3 equals 12?” Go through the Try it Together problems with the students. Ask students to choose a strategy, and share with the class how to solve the problem. They can draw equal groups or arrays, skip count by 3s or think of the related multiplication equation.

Activities

Practice dividing a group of counters by 3. Have students share sets of counters equally among 3 small containers, then write the division equation to match each equal sharing situation.

Games

Play Around the World to practice dividing by 3. p. 317

Share 24 counters. [24 ÷ 3 = 8]

Share 6 counters. [6 ÷ 3 = 2]

Share 12 counters. [12 ÷ 3 = 4]

Share 27 counters. [27 ÷ 3 = 9]

Share 15 counters. [15 ÷ 3 = 5]

Share 21 counters. [21 ÷ 3 = 7]

Share 9 counters. [9 ÷ 3 = 3]

Solve each division equation. Match the equation to the picture, array or multiples list that supports your answer.

Struggling Learners

Provide counters for students to divide into 3 equal groups when solving the problems. Consider writing out the multiples of 3 for the students, or have them help you write them out on the top of their paper to use to solve the problems.

Early Finishers

Solve each division equation. Complete the supporting multiplication equation.

There are three animal barns on the

and the same number of animals go in each barn. Solve each division problem to see how

Choose two divided by 3 equations on this page. Write a number story to go with each equation, and illustrate each problem.

Challenge and Explore

Present the following problem to students. Allow students to use counters or other objects to help them.

Solve

42 ÷ 3 = [14]

How did you solve this problem? [answers will vary. Students may have counted out 42 counters and then put them into two equal rows of 14, or they may have skip counted by 3s to 42 and kept track of their 14 counts]

Apply and Develop Skills (Practice / Exercise page)

Read the directions at the top of the page. Tell students: “To find 15 divided by 3, I can count by 3s until I get to 15. 3, 6, 9, 12, 15. I skip counted 5 times, so 15 divided by 3 is 5.” Ask students to describe what a picture of this problem might look like. [there would be 3 rows of 5 objects or 3 groups of 5 objects]

Read the next set of directions, and do number 7 with the students. Say: To solve 30 divided by 3, I need to think “What times 3 equals

Common Errors

Some students will struggle to keep track of their skip counts when using that strategy. Have them write down the counts or count on their fingers. Students may still struggle with skip counting by 3s. They can use a number line or hundreds chart to help them.

Assess

30?” I know 10 x 3 equals 30, so 30 divided by 3 equals 10. Read the directions to the last set of problems, and tell students they can circle groups of objects to help them solve the problem. Do number 13 with the students. First circle 3 groups of 2 cats. Say: There are 6 cats. If I divide them into 3 groups, there are 2 in each group, so 6 divided by 3 is 2. Now, you will divide the 9 ducks into 3 groups.

Solve the following two problems. Draw pictures arrays, or write the skip counts to show the division problem. Write the related multiplication equation.

15 ÷ 3 = [5, picture should show 15 total objects in 3 groups of 5 or skip count 3s to15, 5 x 3 = 15]

24 ÷ 3 = [8, picture should show 24 total objects in 3 groups of 8 or skip count 3s to 24, 8 x 3 = 24]

Objective and Learning Goals

y Divide by 4 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication or division strategy

y Skip counting - counting by multiples of a certain number

Materials

y Counters, beans or other small objects

y Small containers

y Division by 4 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplying by 4.

4 x 3 = [12]

4 x 6 = [24]

4 x 5 = [20]

4 x 9 = [36]

4 x 4 = [16]

4 x 7 = [28]

Guiding Questions

1. How can we divide by 4? [use the related x4 fact, make 4 equal groups out of the total or distribute the total into 4 rows in an array, skip count by 4s until you reach the total, and keep track of how many skip counts]

1. Jacob and his family were visiting the aquarium. During the dolphin show there were four star dolphins. If there were 16 ﬁsh to feed the dolphins, how many ﬁsh did each dolphin receive?

How many in all? How many groups? How many in each group?

16 ÷ 4 =

2. Draw an array to support your answer for 16 ÷ 4.

List out the multiples of 4 , , , , How many multiples does it take to get to 16 ?

÷ 4 = because × 4 = 16

Divide into equal groups using arrays or pictures.

4. Jacob went to see the seals next. There were 4 seals. If there were 8 ﬁsh to give the seals, how many ﬁsh would each seal receive?

5. The next exhibit showed 28 fish. These fish were separated evenly into 4 tanks. How many fish were in each tank?

= How many in all? How many groups? How many in each group? List out the multiples of 4 until you get to 28

Explain to students that when we divide by 4, we split a total into 4 equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into groups. Have a student suggest a way to make the array for number 2. Be sure to show students that they need to have 16 total objects in 4 rows and will end up having 4 objects in each row. For number 3, remind students that they can use skip counting to divide as well as multiply, and they need to make sure to keep track of how many times they skip count by 4. Remind them how to find the related multiplication equation by thinking “What times 4 equals 16?”

Go through the Try it Together problems with the students in a similar manner.

Activities

Practice dividing a group of counters by 4. Have students share sets of counters equally among 4 small containers, then write the division equation to match each equal sharing situation.

Share 24 counters. [24 ÷ 4 = 6]

Share 8 counters. [8 ÷ 4 = 2]

Games

Play Around the World to practice dividing by 4. p. 317

Share 16 counters. [16 ÷ 4 = 4]

Share 36 counters. [36 ÷ 4 = 9]

Share 20 counters. [20 ÷ 4 = 5]

Share 28 counters. [28 ÷ 4 = 7]

Share 12 counters. [12 ÷ 4 = 3]

Solve each division problem. Then help each shark find the right fish by drawing a line from the shark to his fish.

Solve each division equation. Complete the supporting multiplication equation.

Solve each story problem below using a division array or picture.

13. At the seal exhibit there were 36 ﬁsh to feed the new seal pups. If there were four new seal pups, how many ﬁsh would each seal pup receive?

How many in all?

How many groups?

14. There are eight dolphins that perform in the dolphin show. If there are four trainers, how many dolphins would each trainer work with if you divide them equally?

How many in all?

How many groups?

How many in each group? How many in each group?

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Provide counters for students to divide into 4 equal groups when solving the problems. Consider writing out the multiples of 4 for the students, or have them help you write them out on the top of their paper to use to solve the problems.

Early Finishers

Go back to problems 1 - 6, and write the related multiplication equation for each division equation. If you have time, choose 1 equation to write and illustrate a story problem for.

Challenge and Explore

Present the following problem to students. Allow students to use counters or other objects to help them.

Solve

52 ÷ 4 = [13]

How did you solve this problem? [answers will vary. Students may have counted out 52 counters and then put them into four equal rows of 13, or they may have skip counted by 4s to 52 and kept track of their 13 counts]

Read the directions at the top of the page, and point out that the first problem has been solved for them. 8 ÷ 4 = 2, so the line was drawn to the fish with 2 on it. Tell students to use any strategy they wish to solve the rest of the division problems, and ask students to remind the class of the different strategies they know. [skip counting, drawing equal groups or arrays, thinking of the related multiplication equation] Read the directions for numbers 7-12, and show the students how number 7 was solved by saying: “To solve 24 divided by 4, we can think “What

Common Errors

Some students will struggle to keep track of their skip counts when using that strategy. Have them write down the counts or count on their fingers. Students may still struggle with skip counting by 4s. They can use a number line or hundreds chart to help them.

Assess

times 4 equals 24?” I know that 6 x 4 = 24, so 24 ÷ 4 = 6. Read the directions for numbers 13 and 14 to the students, and read the story problem in number 13. Get the students started on this problem by asking them: “How many fish are there in all?” [36] Fill in the first blank with 36, and have students do the same. Then ask: “How many seals are there to feed fish to?” [4] “So we are starting with 36 fish and dividing them by 4 seals. Now you need to use a strategy to find how many are in each group, or what 36 divided by 4 is.”

Solve the following two problems. Draw pictures arrays, or write the skip counts to show the division problem. Write the related multiplication equation.

20 ÷ 4 = [5, picture should show 20 total objects in 4 groups of 5 or skip count 4s to 20, 5 x 4 = 20]

32 ÷ 4 = [8, picture should show 32 total objects in 4 groups of 8 or skip count 4s to 32, 8 x 4 = 32]

Level C Chapter 6-7

Objective and Learning Goals

y Divide by 0-5 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication or division strategy

y Skip counting - counting by multiples of a certain number

Materials

y Grid paper

Let’s learn!

1. Nathaniel and his classmates were visiting the zoo. He saw that there were twenty-four gira es and four feeding stations. If the same amount of gira es were at each feeding station, how many gira es are at each feeding station?

3. List out the multiples of 4 , , , , , How many multiples does it take to get to 24 ?

2. Use an array to support your answer for 24 ÷ 4

Pre-Lesson Warm-up

Guiding Questions

Practice skip counting by 2s, 3s, 4s and 5s. Have the students count out loud by each multiple.

Guiding Questions

1. What strategies can we use to solve an unknown division fact 0-5?

[make equal groups of objects or arrays, skip count by the dividend until you reach the divisor or think of the related multiplication fact]

Nathaniel noticed that there were 2 cages and 8 tigers. There were the same amount of tigers in each cage. How many tigers were in each cage?

How many in all? How many groups? How many in each group?

5. In the zebra habitat there were 20 straw bales. If there were 5 zebras, how many straw bales would each zebra eat if they shared them equally?

List out the multiples of 5 until you get to 20 , , , How many multiples does it take to get to 20 ? 20 ÷ 5 = because × 5 = 20

Introduce the Lesson (Try it Together)

Remind students that when we divide, we split a total into equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into groups. Have a student suggest a way to make the array for number 2. Be sure to show students that they need to have 24 total objects in 4 rows and will end up having 6 objects in each row. For number 3, remind students that they can use skip counting to divide as well as multiply, and they need to make sure to keep track of how many times they skip count by 4. Remind them how to find the related multiplication equation by thinking “What times 4 equals 24?”

Go through the Try it Together problems with the students in a similar manner.

Activities

Practice making arrays to solve division equations. Give students grid paper and some division 1-5 facts to solve. Have them write the division fact on the grid paper, and then make an array underneath to solve the fact. For example, 18 ÷ 3: Students should write 18 ÷ 3, and then underneath that, color in rows of 3 until they have colored 18 total squares. Then count to see how many rows they colored. They should end up with 6 rows of 3 to get 18, and write 18 ÷ 3 = 6.

16 ÷ 4 = [4, the array should show 4 rows of 4]

14 ÷ 2 = [7, the array should show 7 rows of 2]

25 ÷ 5 = [5, the array should show 5 rows of 5]

20 ÷ 4 = [5, the array should show 5 rows of 4]

12 ÷ 3 = [4, the array should show 4 rows of 3]

10 ÷ 2 = [5, the array should show 5 rows of 2]

Solve each problem using a picture or an array.

Notes

Apply and Develop Skills (Practice / Exercise page)

Read the directions at the top of the page, and do number 1 with the students. Ask a student to use any strategy to solve 12 ÷ 2 = . [6] Have students draw a line from the lion to the cage with the number 6 under it.

Read the directions for numbers 6 - 11. For number 6, tell students: “Since I know 2 x 2 = 4, I know 4 ÷ 2 = 2.”

Struggling Learners

Provide counters for students to divide into equal groups when solving the problems or grid paper for them to make arrays. For students struggling to skip count, provide number lines or hundreds charts to circle or color in the skip counts on.

Early Finishers

Choose two division equations on this page. Write a story problem to go with each equation, and illustrate each problem.

Challenge and Explore

Present the following problem to the students:

There are 24 students in a class. The teacher wants to divide them into tables with the same number of students at each table. How many students will be at each table if she has 2 tables? 3 tables? 4 tables? Use counters, arrays, skip counts or any strategy you want. Write the division equations for each and solve.

2 tables - [12, 24 ÷ 2 = 12]

3 tables - [8, 24 ÷ 3 = 8] 4

Remind students how to complete the tables in numbers 12-14 by showing them how the first row of number 12 has been written down for them. Say: “Take the number on the left, 9, divide it by 3, and write the answer, 3, on the right.” Tell students that it’s great if they have some of the facts memorized already but that they should use any strategy they want to figure out or check division equations that they are not sure about.

Common Errors

Some students will try to skip count but may get the counts wrong, especially for 3s and 4s, which they may not be as familiar with. Watch for students who try to put objects into equal groups but don’t keep track of how many total objects they are putting into those groups.

Assess

Check work for numbers 15 - 26.

Level C Chapter 6-8

Objective and Learning Goals

y Review

y Use equal groups, arrays, skip counting and related multiplication to divide by 0-5

Vocabulary

y Divide - to split a number into equal groups

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication or division strategy

y Skip counting - counting by multiples of a certain number

y Dividend - the number that you start with in a division equation

y Divisor - the number of equal groups you divide the dividend into in a division equation

y Quotient - the answer to a division equation

Materials

y Counters, beans or other small objects

y Small containers such as jars, cans or paper or plastic cups, bowls or plates

Pre-Lesson Warm-up Guiding Questions

Practice multiplication facts through 5.

5 x 3 = [15]

3 x 6 = [18]

4 x 7 = [28]

2 x 9 = [18]

5 x 4 = [20]

3 x 7 = [21]

Guiding Questions

1. What strategies can we use to solve an unknown division fact 0-5? [make equal groups of objects or arrays, skip count by the dividend until you reach the divisor or think of the related multiplication fact]

Dividend Divisor Quotient

Solve the division equation in three di erent ways to complete the chart below: Samuel is helping at his family’s fruit stand. He has 30 apples and must divide them into 5 baskets equally. How many apples go in each basket?

Draw an array or list the multiples to help solve the division equation and check it with a correct multiplication equation.

Solve these division equations.

Explain to students that the number they are dividing into groups is called the dividend, and have them write it on the line. Then tell them that the number they are dividing by is the divisor, and have them write that on the line. Tell students that the answer to a division equation is called the quotient, and have them write that on the last line. Remind students of the different strategies they have learned to solve division facts, and have them help you fill in the chart to solve 30 ÷ 5 in 3 different ways. For the picture or array, ask a student to suggest a drawing. Make sure you draw 30 total objects in groups of 5 or an array with rows of 5. There should be 6 groups or rows. Then, for the multiples strategy, tell students that since we are dividing by 5, we need to skip count by 5s until we get to 30. Have them write in the counts with you, and ask: “How many times did we skip count by 5 to get to 30?” [6] Then ask: “What times 5 equals 30?” [6] “So 30 ÷ 5 = 6.” Do the Try it Together problems with the

students. Tell students that it is great if they have the division facts memorized already but that they should always be able to prove it or check their work with a strategy.

Activities

Practice dividing a group of counters. Have students share sets of counters equally among small containers, then write the division equation to match each equal sharing situation.

Share 24 counters among 3 containers. [24 ÷ 3 = 8]

Share 10 counters among 2 containers. [10 ÷ 2 = 5]

Share 15 counters among 5 containers. [15 ÷ 5 = 3]

Share 36 counters among 4 containers. [36 ÷ 4 = 9]

Share 20 counters among 5 containers. [20 ÷ 5 = 4]

Share 21 counters among 3 containers. [21 ÷ 3 = 7]

Share 16 counters among 2 containers. [16 ÷ 2 = 8]

Solve each story problem below.

20. Nathaniel had 40 lemons and 4 baskets. How many lemons would go into each basket if he divided them equally?

Struggling Learners

Early Finishers

Go back and write the related multiplication fact for numbers 4 - 19.

Challenge and Explore

Extend problem 21:

Nathaniel forgot that he also has 30 raspberries to put in the bins! After he mixes his raspberries with the blueberries and strawberries, how many berries would go in each bin? Explain how you solved the problem.

21. There were 25 blueberries and 20 strawberries. If Nathaniel mixed the two berries together to put into 5 bins, how many berries would go into each bin?

[15 berries; 45 + 30 = 75, 75 ÷ 5 = 15; strategies will vary. Some students may divide 30 by 5 to find that there will be 6 more berries in each bin, and then add 6 to 9 to get 15. Other students might add 30 to 45 to get 75, and then divide 75 by 5 by drawing a picture or array or skip counting]

Apply and Develop Skills (Practice / Exercise page)

Read the directions at the top of the page to the students. Draw their attention to the chart in the Let’s Learn section, and remind them how they solved the problem using the 3 strategies. Tell them to use this as a guide to fill out the chart on this page. Then tell students that they can use these examples of strategies to help them solve any of the other division facts on the page that they do not have memorized yet.

Games

Play Brain vs. Hand to practice division facts 0-5. p. 308

Common Errors

Assess

Check work in the chart for numbers 1-3.

Chapter 7

In Chapter 7, we will learn about division using divisors 6-9 conceptually and numerically. We will understand that division is the inverse operation of multiplication and is used to solve problems.

5 6 ) 30

• Recall that division equations have three parts: dividend, divisor, quotient

• Understand that division problems can be written in di erent ways, called notations

• Notice and connect patterns of multiplication to solve division equations accurately and e iciently

• Separate items into equal groups to ﬁnd the total number of objects in each group of 6 , 7 , 8 and 9

• Use arrays to help us visualize how equal groups can be arranged to quickly calculate totals

• List multiples of each divisor to help ﬁnd the quotient quickly

• Use manipulatives and counting games to make division a more concrete concept

Vocabulary Words

Level C Chapter 7-1

Objective and Learning Goals

y Write and solve division problems in both number sentences and long division notation

Vocabulary

y Divide - to split a number into equal groups

y Division - the act of dividing or splitting a total into equal groups

y Dividend - the number that you start with in a division equation

y Divisor - the number of equal groups you divide the dividend into in a division equation

y Quotient - the answer to a division equation

y Division notations - different ways of writing a division equation

y Long division - a division notation where the dividend is inside the division symbol, allowing students to handle larger quantities

Materials

y Dry-erase boards

y Dry-erase markers

y Division by 0-5 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice division facts through 5:

35 ÷ 5 = [7]

20 ÷ 4 = [5]

18 ÷ 3 = [6]

14 ÷ 2 = [7]

27 ÷ 3 = [9]

32 ÷ 4 = [8]

12 ÷ 3 = [4]

15 ÷ 5 = [3]

Guiding Questions

each

problem as a number sentence and then in long division notation.

Divisor:

Quotient: How many in each group?

Dividend: How many in all?

Divisor: How many groups?

Quotient: How many in

1. How can we write division problems in different ways?

[write the number sentences that we have been writing, or write the problem in long division notation to prepare for dividing larger quantities]

Review the definitions of dividend, divisor and quotient with the students. Use the cookie problem to show what each means. Then show students the two different ways - number sentence and long division notation - to write the same problem. Help students to remember which number goes where in the long division notation by explaining that the number INside the symbol is the number that you are dividing INto. The number on the outside is trying to get in! The answer goes on top.

Go through the examples in Try it Together with the students referring to this explanation to help them set up each problem correctly.

Activities

Students practice writing division problems both ways with a partner. Have one student write a division fact through 5 in a number sentence on a dry-erase board, and show it to their partner. The partner should then write the same division fact in long division notation. The first partner checks the 2nd partner’s work and helps them to correct any mistakes. Then students switch, and the 2nd student writes a number sentence for the 1st student to write in long division notation.

Solve each division problem and write the missing notation to complete the table.

Apply and Develop Skills (Practice / Exercise page)

Read the directions and show students how the first problem has been matched for them. Tell students that both of these problems say 28 divided by 4 equals 7. Read the directions for numbers 7 and 8 and tell students that they can refer to the learning page to help them fill in the blanks.

Struggling Learners

Make and hang up an anchor chart that shows the student a problem written in both notations. Refer to the chart often, and have students use it to remind them which numbers go where in long division notation.

Early Finishers

Choose 2 division equations on this page. Write a story problem to go with each equation and illustrate each problem. Write the equation in both a numbers sentence and long division notation for each problem. Label the dividend, divisor and quotient.

Challenge and Explore

Solve the following problem. Write both a division number sentence and long division notation.

My brother collected 36 stamps. He put an equal number of stamps on each of the 4 pages in his stamp book. How many stamps were on each page?

[9; Number sentence: 36 ÷ 4 = 9

Long division notation:

Explain the tables at the bottom of the page to the students. Tell them that they will have to find the quotient for each division problem, and then write the entire problem in the other notation. Show them how the first one was done for them. Say: “This problem says 9 divided by 1. It has been solved, and the quotient on top is 9 because 9 divided by 1 is 9. Then in the other column, it has been written in a number sentence - 9 ÷ 1 = 9.

Common Errors

It is easy for students to confuse where to put the dividend, divisor and quotient in long division notation at first. Watch for students who put the divisor on top instead of to the left of the dividend. Some students may also write the dividend in the wrong location since they are used to reading left to right and in a number sentence the dividend comes first, but not in long division notation.

Games

Play Around the World to practice division facts 0-5. p. 317

Assess

Check work for numbers 12, 13, 17 and 18.

Level C Chapter 7-2

Objective and Learning Goals

y Understand and explain how multiplication and division are related

y Write fact families for multiplication and division

Vocabulary

y Division - the act of dividing or splitting a total into equal groups

Materials

y Index cards

y Division by 0-5 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice writing addition and subtraction fact families. Give students an addition or subtraction fact, and have them write the other 3 facts in the fact family on a dry-erase board or piece of paper.

5 + 2 = 7 [2 + 5 = 7, 7 - 2 = 5, 7 - 5 = 2]

9 - 4 = 5 [ 9 - 5 = 4, 4 + 5 = 9, 5 + 4 = 9]

6 + 7 = 13 [ 7 + 6 = 13, 13 - 7 = 6, 13 - 6 = 7]

15 - 8 = 7 [ 15 - 7 = 8, 7 + 8 = 15, 8 + 7 = 15]

Guiding Questions

1. How are multiplication and division connected?

[multiplication combines equal groups to find a total, and division splits a total into equal groups. You can find an unknown quotient by thinking about the multiplication fact that tells you how many groups of objects are in the total]

Multiplication and Division are Connected!

Multiplication combines groups together:

Division breaks a total into separate groups:

You can use a fact triangle to show multiplication and division working together.

Use this connection to ﬁnd missing factors: ? × 2 = 8 Think : 8 ÷ 2 = 4

Use this connection to ﬁnd missing quotients: 8 ÷ 4 = ? Think : 2 × 4 = 8

Use this connection to check your work: = 4 4 × 2 = 8

Solve for the missing numbers in each triangle. Then write out the division and multiplication equations that you could solve.

Solve each of these division problems and write a corresponding multiplication equation.

Introduce the Lesson (Try it Together)

Read the information and example in Let’s Learn to the students. Have students work with you to write the 4 facts in the fact family for the fact triangle shown. [2 x 4 = 8, 4 x 2 = 8, 8 ÷ 4 = 2, 8 ÷ 2 = 4] Show students how the fact triangle works by covering up each number one at a time and saying the equation that they need to solve for the missing number. For example, cover the 8, and say: “What is 2 x 4?” [8] Uncover the 8. Then cover the 4, and say: “What is 8 ÷ 2?” [4] Uncover the 4. Then cover the 2, and say: “What is 8 ÷ 4?” [2] Uncover the 2. Do the rest of the examples on the page with the students. Remind the students how to figure out the multiplication equation by saying for number 3: “This is 16 divided by 4, so we ask ourselves “What times 4 equals 16?” [4]

Activities

Make fact triangles and practice multiplication and division facts using the triangles. Cut index cards into triangles. Write the products of multiplication facts up to 5 at the top of the triangle. In the bottom corner, write the two factors. With a partner, practice by covering up one of the numbers. The partner needs to say the multiplication or division fact that they are solving, not just the product or quotient when they answer. (For example, if the triangle has 6 at the top and 2 and 3 in the bottom corners.) If the 6 is covered up, the partner should say: “2 times 3 equals 6” or “3 times 2 equals 6.” If the 2 is covered up, they should say: “6 divided by 3 equals 2.” If the 3 is covered up, they should say: “6 divided by 2 equals 3.”

Solve each division equation. Complete the supporting multiplication equation.

Struggling Learners

Make and display an anchor chart for students to refer to that helps them understand the relationship between multiplication and division. This could be a large fact triangle with the fact family written out next to it.

Early Finishers

Go back to numbers 9 - 16, and write out all 4 facts in the fact families related to these problems.

Challenge and Explore

Solve each fact triangle.

Read the Challenge problem to the students. Tell students that they can use division to help them with multiplication the same way they use multiplication to help them with division. Remind students that there are 4 facts in a fact family, so they need to write 3 more facts. Tell them to think of a fact triangle to help them come up with the facts.

If you know that 12 ÷ 4 =3 , what other multiplication and division problems do you know the answer to?

Apply and Develop Skills (Practice / Exercise page)

Read the directions and show the students how number 1 was done for them. Say: “I know that 6 x 1 = 6, so 6 ÷ 1 = 6.” Read the directions and do number 9 with the students in a similar manner. Show students how the fact triangle in number 13 had one corner blank and the blank has been filled in. Ask students to tell you the equation that was used to solve for the blank. [5 x 7 =35] Then ask students what equation they will need to solve to fill in the blank spot on the fact triangle in number 14. [24 ÷ 8 = 3]

Common Errors

Watch for students who write the dividend and divisor as the two factors in a related multiplication equation. For example, when asked for a related multiplication equation for 15 ÷ 3 = 5, they write 15 x 3 = 5.

Assess

Objective and Learning Goals

y Divide by 6 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Division - the act of dividing or splitting a total into equal groups

Materials

y Counters, beans or other small objects

y Small containers

y Division by 6 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplying by 6.

6 x 3 = [18]

6 x 6 = [36]

6 x 5 = [30]

6 x 9 = [54]

6 x 4 = [24]

6 x 7 = [42]

Guiding Questions

1. How can we divide by 6? [use the related x6 fact, make 6 equal groups out of the total or distribute the total into 6 rows in an array, skip count by 6s until you reach the total and keep track of how many skip counts]

Let’s learn!

1. Joshua was helping put away toys. He put away 12 toy cars in 6 di erent rows. If there were the same number of cars in each row, how many cars were in each row? How many in all? How many groups? How many in each group?

6)12

Use an array to support your answer for List out the multiples of 6 , How many multiples does it take to get to 12? because × 6 = 12

6)12

Try it together!

6)12

Divide into equal groups using arrays or pictures.

2. Joshua had 30 blocks which were placed on 6 stacks. If he placed the same amount on each stack, how many blocks were on each stack?

÷ 6 = because × 6 = 30

3. Joshua saw that there were 42 marbles. They were in 6 di erent bags. If the same number of marbles were in each bag, how many marbles were in each bag?

6)42 because × 6 = 42

Introduce the Lesson (Try it Together)

Explain to students that when we divide by 6, we split a total into 6 equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into groups. Have a student suggest a way to make the array. Be sure to show students that they need to have 12 total objects in 6 rows and will end up having 2 objects in each row. Remind students that they can use skip counting to divide as well as multiply, and they need to make sure to keep track of how many times they skip count by 6. Remind them how to find the related multiplication equation by thinking “What times 6 equals 12?” Go through the Try it Together problems with the students in a similar manner.

Activities

Practice dividing a group of counters by 6. Have students share sets of counters equally among 6 small containers. Write the division equation to match each equal sharing situation.

Share 24 counters. [24 ÷ 6 = 4]

Share 12 counters. [12 ÷ 6 = 2]

Share 48 counters. [48 ÷ 6 = 8]

Share 54 counters. [54 ÷ 6 = 9]

Share 30 counters. [30 ÷ 6 = 5]

Share 42 counters. [42 ÷ 6 = 7]

Share 18 counters. [18 ÷ 6 = 3]

Solve each division problem. Then help

Struggling Learners

Consider allowing students to use a “cheat sheet” that lists the multiples of 6. Also, provide counters and grid paper for making equal groups and arrays more concrete for students.

Early Finishers

Solve each fact triangle.

Go back and write a related multiplication equation for numbers 11 - 20.

Challenge and Explore

Extend problem number 22 by asking: “What if there are 84 books to divide among the 6 shelves? Now, how many books will be on each shelf?” Tell students to use pictures, arrays, skip counts or any strategy they want to solve the problem.

[14 books on each shelf]

Solve each story problem below using a division array or picture.

21. There are 36 wooden figures. There are 6 buckets to store the wooden figures. If the same number goes in each bucket, how many wooden figures are in each bucket?

22. There are 60 books that are organized on the bookshelf. If the same number of books is on each shelf, and there are 6 shelves, how many books are on each shelf?

Apply and Develop Skills (Practice / Exercise page)

Read the directions for problems 1-6 and show students how number 3 has been done for them. Encourage students to use any strategy they want to solve the problem before deciding where to draw the line to. Remind students how fact triangles work and ask a student to tell the class what equation they needed to solve to find the missing number in problem 7. [42 ÷ 7 = 6] Point out the two different division notations in numbers 11 - 20. Remind students that in long division notation, the answer goes on top.

Games

Play Around the World to practice dividing by 6. p. 317

Common Errors

Some students will struggle to keep track of their skip counts when using that strategy. Have them write down the counts or count on their fingers. Students may still struggle with skip counting by 6s. They can use a number line or hundreds chart to help them.

Assess

Check work for numbers 11 - 20.

Objective and Learning Goals

y Divide by 7 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Division - the act of dividing or splitting a total into equal groups

Materials

y Counters, beans or other small objects

y Small containers

y Division by 7 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplying by 7.

7 x 3 = [21]

7 x 6 = [42]

7 x 5 = [35]

7 x 9 = [63]

7 x 4 = [28]

7 x 7 = [49]

Guiding Questions

1. How can we divide by 7? [use the related x7 fact, make 7 equal groups out of the total or distribute the total into 7 rows in an array, skip count by 7s until you reach the total and keep track of how many skip counts]

1. Daniel was going to the candy shop! He wants to buy 28 lollipops, but they are sold in groups of 7 . How many groups does Daniel have to buy to get 28 lollipops?

Use an array to support your answer for

List out the multiples of 7 , , , How many multiples does it take to get to 28? because × 7 = 28

How many in all? How many in each group? How many groups? 7)28 7)28 7)28

Solve each fact triangle.

Draw an array or list the multiples to help solve the division problem and check it with a correct multiplication equation. Try it together!

Introduce the Lesson (Try it Together)

Explain to students that when we divide by 7, we split a total into 7 equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into groups. Have a student suggest a way to make the array. Be sure to show students that they need to have 28 total objects in 7 rows and will end up having 4 objects in each row. Remind students that they can use skip counting to divide as well as multiply, and they need to make sure to keep track of how many times they skip count by 7. Remind them how to find the related multiplication equation by thinking “What times 7 equals 28?” Go through the Try it Together problems with the students. Remind students how fact triangles work and have them think about the related multiplication fact to solve the division problems. For example, in number 1, to find 42 ÷ 7, think: “What times 7 equals 42?” [6]

Activities

Practice dividing a group of counters by 7. Have students share sets of counters equally among 7 small containers. Write the division equation to match each equal sharing situation.

Share 28 counters. [28 ÷ 7 = 4]

Share 14 counters. [14 ÷ 7 = 2]

Share 7 counters. [7 ÷ 7 = 1]

Share 42 counters. [42 ÷ 7 = 6]

Share 35 counters. [35 ÷ 7 = 5]

Share 49 counters. [49 ÷ 7 = 7]

Share 21 counters. [21 ÷ 7 = 3]

Solve each division equation. Complete the supporting multiplication equation.

Candy Grab! Begin at the start line and solve each square. Can you make it to the end to win the pile of candy?

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Consider allowing students to use a “cheat sheet” that lists the multiples of 7. Also, provide counters and grid paper for making equal groups and arrays more concrete for students.

Early Finishers

Draw pictures of equal groups or arrays to illustrate the division facts in numbers 2 - 11.

Challenge and Explore

Present the following problem to students. Allow students to use counters or other objects to help them.

Solve

91 ÷ 7 = [13]

1. How did you solve this problem? [answers will vary. Students may have counted out 91 counters and then put them into seven equal rows of 13, or they may have skip counted by 7s to 91 and kept track of their 13 counts]

Read the directions and write the first few multiples of 7 with the students to get them started. Then show them how the list of multiples can be used to solve number 1. Ask: “How many times do we skip count by 7s to get to 28?” [4] Have the students count with you “7, 14, 21, 28, that’s 4 times, so 28 ÷ 7 = 4.” Read the directions and do number 12 with the students. Say: “I know 10 x 7 = 70, so 70 ÷ 7 = 10.”

Read the directions for number 16. Remind the students to write the quotient, or answer, on the top in long division notation.

Common Errors

Some students will struggle to keep track of their skip counts when using that strategy. Have them write down the counts or count on their fingers. Students may still struggle with skip counting by 7s. They can use a number line or hundreds chart to help them.

Assess

Games

Play Around the World to practice dividing by 7. p. 317

Solve the following two problems. Draw pictures or arrays, or write the skip counts to show the division problem. Write the related multiplication equation.

35 ÷ 7 = [5, picture should show 35 total objects in 7 groups of 5 or skip count 7s to 35, 5 x 7 = 35]

56 ÷ 7 = [8, picture should show 56 total objects in 7 groups of 8 or skip count 7s to 56, 8 x 7 = 56]

Objective and Learning Goals

y Divide by 8 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Division - the act of dividing or splitting a total into equal groups

Materials

y Counters, beans or other small objects

y Small containers

y Division by 8 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplying by 8.

8 x 3 = [24]

8 x 6 = [48]

8 x 5 = [40]

8 x 9 = [72]

8 x 4 = [32]

8 x 7 = [56]

Guiding Questions

1. How can we divide by 8? [use the related x8 fact, make 8 equal groups out of the total or distribute the total into 8 rows in an array, skip count by 8s until you reach the total and keep track of how many skip counts]

1. Elijah received some new crayons as a present. He was so excited. There were 24 crayons arranged in 8 rows. If the same amount of crayons were in each row, how many crayons were in each row?

How many in all? How many groups? How many in each group?

Games

Play Around the World to practice dividing by 8. p. 317

Use an array to support your answer for

multiples does it take to get to 24?

Try it together!

List the multiples of eight below.

Use those multiples to help you solve the following problems.

3. Elijah lost 8 crayons and now only has 16 . If he still stores his crayons in sections of eight, how many sections will be full of crayons? sections

Elijah found some older crayons. Now he has 48 crayons. If he still stores the crayons in sections of eight, how many sections will be full? sections

Explain to students that when we divide by 8, we split a total into 8 equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into groups. Have a student suggest a way to make the array. Be sure to show students that they need to have 24 total objects in 8 rows and will end up having 3 objects in each row. Remind students that they can use skip counting to divide as well as multiply, and they need to make sure to keep track of how many times they skip count by 8. Remind them how to find the related multiplication equation by thinking “What times 8 equals 24?” Go through the Try it Together problems with the students. Have students help you list the multiples of 8. Tell them that they can use the pattern to skip count, or they can go through the x8 facts in order (1 x 8, 2 x 8, 3 x 8, etc.) to come up with the next multiple of 8. Go through the rest of the problems similar to the example in Let’s Learn.

Activities

Practice dividing a group of counters by 8. Have students share sets of counters equally among 8 small containers. Write the division equation to match each equal sharing situation.

Share 32 counters. [32 ÷ 8 = 4]

Share 16 counters. [16 ÷ 8 = 2]

Share 8 counters. [8 ÷ 8 = 1]

Share 48 counters. [48 ÷ 8 = 6]

Share 40 counters. [40 ÷ 8 = 5]

Share 56 counters. [56 ÷ 8 = 7]

Share 24 counters. [24 ÷ 8 = 3] Introduce the Lesson (Try

Find out what color each crayon is! Solve the division equation on each crayon. Then use the color key to ﬁnd out what color it should be. Color the crayon that color.

Struggling Learners

Consider allowing students to use a “cheat sheet” that lists the multiples of 8. Also, provide counters and grid paper for making equal groups and arrays more concrete for students.

Early Finishers

Choose 2 equations from numbers 19 - 27. Write and illustrate a story problem to go with each equation.

Solve each division equation. Complete the supporting multiplication equation.

Challenge and Explore

Present the following problem to students. Allow students to use counters or other objects to help them.

Solve

112 ÷ 8 = [14]

1. How did you solve this problem? [answers will vary. Students may have counted out 112 counters and then put them into eight equal rows of 14, or they may have skip counted by 8s to 112 and kept track of their 14 counts]

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students, and do the first division problem on the top row of crayons with the students. Ask students: “What is 48 divided by 8?” [6] If students struggle to come up with the answer, suggest a strategy. Tell students: “The answer is 6. Find 6 in the list on the left. It says purple, so color this crayon purple.” Read the directions for 11 - 16. Point out that number 11 is done for

Common Errors

Some students will struggle to keep track of their skip counts when using that strategy. Have them write down the counts or count on their fingers. Students may still struggle with skip counting by 8s. They can use a number line or hundreds chart to help them.

Assess

them. Say: “In this example, knowing 8 x 10 = 80 helps us know 80 ÷ 8 = 10.”

Review how the tables in numbers 17 and 18 and show students where the answers to the first division problems were written. Remind the students to use any strategy they want to solve division facts that they don’t have memorized yet.

Solve the following two problems. Draw pictures or arrays, or write the skip counts to show the division problem. Write the related multiplication equation.

48 ÷ 8 = [6, picture should show 48 total objects in 8 groups of 6 or skip count 8s to 48, 6 x 8 = 48]

56 ÷ 8 = [7, picture should show 56 total objects in 8 groups of 7 or skip count 8s to 56, 7 x 8 = 56]

Objective and Learning Goals

y Divide by 9 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Division - the act of dividing or splitting a total into equal groups

Materials

y Counters, beans or other small objects

y Small containers

y Division by 9 flashcards (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplying by 9.

9 x 3 = [27]

9 x 6 = [54]

9 x 5 = [45]

9 x 9 = [81]

9 x 4 = [36]

9 x 7 = [63]

Guiding Questions

1. How can we divide by 9? [use the related x9 fact, make 9 equal groups out of the total or distribute the total into 9 rows in an array, skip count by 9s until you reach the total and keep track of how many skip counts]

1. There are 45 boys playing ball in the park. If there are 9 teams, how many boys will be on each team?

How many in all? How many groups? How many in each group?

Games

Play Around the World to practice dividing by 9. p. 317

Use an array to support your answer for

List out the multiples of 9 , , , , How many

9)45 9)45 9)45

We can use our multiples to make dividing by 9 feel just ﬁne! List the multiples of nine below. Start with 9 .

Now use those multiples to help you solve the following problems.

3. The boys want to play a ball game with 9 boys on each team. If there are 27 boys that want to play ball, how many teams can there be? teams

4. If there are 18 balls and 9 players, how many balls will each player have to practice with? balls because × 9 = 18 Try it together!

Explain to students that when we divide by 9, we split a total into 9 equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into groups. Have a student suggest a way to make the array. Be sure to show students that they need to have 45 total objects in 9 rows and will end up having 5 objects in each row. Remind students that they can use skip counting to divide as well as multiply, and they need to make sure to keep track of how many times they skip count by 9. Remind them how to find the related multiplication equation by thinking “What times 9 equals 45?” Go through the Try it Together problems with the students. Have students help you list the multiples of 9. Tell them that they can use the pattern to skip count, or they can go through the x9 facts in order (1 x 9, 2 x 9, 3 x 9, etc.) to come up with the next multiple of 9. Go through the rest of the problems similar to the example in Let’s Learn.

Activities

Practice dividing a group of counters by 9. Have students share sets of counters equally among 9 small containers. Write the division equation to match each equal sharing situation.

Share 36 counters. [36 ÷ 9 = 4]

Share 18 counters. [18 ÷ 9 = 2]

Share 9 counters. [9 ÷ 9 = 1]

Share 54 counters. [54 ÷ 9 = 6]

Share 45 counters. [45 ÷ 9 = 5]

Share 63 counters. [63 ÷ 9 = 7]

Share 27 counters. [27 ÷ 9 = 3]

Who wins the race? You can ﬁgure out who wins the race. Solve the division equation for each racer. Then, look at the ﬁnish line to see which quotient is the winner. Circle that division problem.

Struggling Learners

Consider allowing students to use a “cheat sheet” that lists the multiples of 9. Also, provide counters and grid paper for making equal groups and arrays more concrete for students.

Early Finishers

Write related multiplication equations for the division equations on this page.

Challenge and Explore

Present the following problem to students. Allow students to use counters or other objects to help them.

Solve

117 ÷ 9 = [13]

Divide.

Solve each story problem below.

11. There are 45 boys that are racing for the 100 meter dash. If there are nine di erent races, how many boys will race at one time?

12. For the hurdles there are 36 boys signed up to race. If there are 9 boys that can race at a time, how many di erent hurdle races will there be?

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Show them how the table works using the example that was done for them. They should divide the number in the top row (81) by 9, and write the quotient (9) underneath in the bottom row.

1. How did you solve this problem? [answers will vary. Students may have counted out 117 counters and then put them into nine equal rows of 13, or they may have skip counted by 9s to 117 and kept track of their 13 counts]

Read the directions for numbers 2-4. Explain to students that they should solve all of the division equations first, and then circle the

Common Errors

Some students will struggle to keep track of their skip counts when using that strategy. Have them write down the counts or count on their fingers. Students may still struggle with skip counting by 9s. They can use a number line or hundreds chart to help them.

Assess

one where the quotient matches the number at the end of the row. So, even though number 2 already has the correct racer circled, they need to solve the rest of the division equations. Tell students that it’s great if they have the facts memorized already, but encourage them to use a strategy to check their work or to solve problems they aren’t sure about.

Solve the following two problems. Draw pictures or arrays, or write the skip counts to show the division problem. Write the related multiplication equation.

54 ÷ 9 = [6, picture should show 54 total objects in 9 groups of 6 or skip count 9s to 54, 6 x 9 = 54]

63 ÷ 9 = [7, picture should show 63 total objects in 9 groups of 7 or skip count 9s to 63, 7 x 9 = 63]

Objective and Learning Goals

y Divide by 6, 7, 8 and 9 using equal groups, arrays, skip counting and related multiplication equations

Vocabulary

y Divide - to split a number into equal groups

y Division - the act of dividing or splitting a total into equal groups

y Dividend - the number that you start with in a division equation

y Divisor - the number of equal groups you divide the dividend into in a division equation

y Quotient - the answer to a division equation

Materials

y Hundreds charts

y Colored pencils or crayons

Pre-Lesson Warm-up

Guiding Questions

Practice dividing by 1-5.

25 ÷ 5 = [5]

12 ÷ 4 = [3]

9 ÷ 3 = [3]

14 ÷ 2 = [7]

18 ÷ 3 = [6]

16 ÷ 4 = [4]

15 ÷ 5 = [3]

8 ÷ 4 = [2]

Guiding Questions

1. How can we figure out a division fact we do not know?

[use the related multiplication fact, make equal groups out of the total or distribute the total into rows in an array, skip count until you reach the total, and keep track of how many skip counts]

Read the problem in Let’s Learn to the students. Review the parts of a division equation and where each is located in the two different notations. Read the directions for Try it Together, and have the students help you fill in the chart. Ask students to write each equation in both notations, and then skip count together as a class to fill in the multiples. To find the multiplication equation, tell students to think (for the first problem) “What times 6 equals 24?”

Activities

Students will list and color code the skip counts for multiples of 6 through 9 on a hundreds chart. First have students make a list of all the multiples of 6, 7, 8 and 9 up through x12.

6 [6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72]

7 [7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84]

8 [8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96]

9 [9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108]

Next, have students circle all of the multiples in their lists that appear in more than 1 list. For example, 72 is a multiple of 6, 8 and 9, so they will circle it in each of those lists. Then students should choose a different color for multiples of 6, 7, 8 and 9. They will color on a hundreds chart all of the multiples of 6 one color, 7 another color, and so on. For each number that is a multiple of more than one of the numbers, they should divide the square up and color it in stripes. For example, on the hundreds chart, they will color 72 striped with the 3 colors they chose for 6, 8 and 9. Another example is that 42 will be colored half the color they chose for 6 and

the color they chose for 7.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Tell students that for number 1, they should write the quotient in the box for each equation. Remind students that while it is great if they have some of the facts memorized, they should always use a strategy to check their work if they are not sure.

Struggling Learners

Consider allowing students to use the “cheat sheet” that they made by coloring in the multiples of 6-9 on the hundreds chart in the activity portion of the lesson. Also, provide counters and grid paper for making equal groups and arrays more concrete for students.

Early Finishers

Write the related multiplication equations to go with the division problems on this page.

Challenge and Explore

Read the Challenge problem. Explain that they should use the given equation to make up their own party story problem. Have students brainstorm for things that may need to be divided up at a party to get them thinking of ideas. Discuss how many people will attend the party. Will they need to sit at tables? What kind of snacks or treats might they have? Are there favors or decorations that need to be split up somehow? Make sure they solve their equation for the correct quotient.

Students may think they have problems memorized but get quotients confused. Have them use a strategy to check their work. Common Errors

Assess

Check work for numbers 2 - 13.

Objective and Learning Goals

y Review

y Division using equal groups, arrays, skip counting and related multiplication facts

Vocabulary

y Divide - to split a number into equal groups

y Division - the act of dividing or splitting a total into equal groups

y Dividend - the number that you start with in a division equation

y Divisor - the number of equal groups you divide the dividend into in a division equation

y Quotient - the answer to a division equation

y Long division - a division notation where the dividend is inside the division symbol, allowing students to handle larger quantities

y Division notations - different ways of writing a division equation

Materials

y Grid paper

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up Guiding Questions

Practice multiplication facts.

8 x 3 = [24]

7 x 6 = [42]

6 x 5 = [30]

4 x 9 = [36]

9 x 8 = [72]

8 x 7 = [56]

Guiding Questions

1. How can we figure out a division fact we do not know?

[use the related multiplication fact, make equal groups out of the total or distribute the total into rows in an array, skip count until you reach the total, and keep track of how many skip counts]

Let’s

Try it together!

Introduce the Lesson (Try it Together)

Remind students that when we divide, we split a total into equal groups. Read the example problems in Let’s Learn to the students. Act out the problems by sorting counters or other small objects into groups. Point out that the carrots are shown in an array with 32 total carrots in 4 rows. There are 8 carrots in each row. Remind students that they can use skip counting to divide as well as multiply, and they need to make sure to keep track of how many times they skip count by 4. Remind them how to find the related multiplication equation by thinking “What times 4 equals 32?” When doing the Try it Together problems with the students, call on students to give the quotient. Ask other students to say if they agree or disagree. If they agree, periodically have them use a strategy such as drawing equal groups, making an array, skip counting or using the related multiplication fact to prove it. If they disagree, have them use a strategy to show why they disagree.

Activities

Practice making arrays to demonstrate division. Give students grid paper and a list of division facts without the quotients. Have them make arrays on the grid paper, write the equations underneath the corresponding arrays and solve for the quotient. Make arrays for the following division equations:

24 ÷ 3 = [8, array will have 3 rows of 8]

42 ÷ 7 = [6, array will have 7 rows of 6]

45 ÷ 5 = [9, array will have 5 rows of 9]

33 ÷ 3 = [11, array will have 3 rows of 11]

28 ÷ 4 = [7, array will have 4 rows of 7]

56 ÷ 7 = [8, array will have 7 rows of 8]

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Provide students with grid paper to make arrays or small objects to make equal groups. Also have available hundreds charts (perhaps one with multiples color-coded) and number lines. Consider providing a multiplication chart or table for some students.

Early Finishers

Write a related multiplication fact for numbers 11 - 28.

Challenge and Explore

Present the following Division Square problem to the students. Each row and column is a division equation. Fill in the missing squares. First show them how it works using this example. Remind students to think about related multiplication equations to help them.

Remind students how fact triangles work and that they can use the missing factor in a multiplication equation to solve a division equation. For example, in number one, they can think “What times 9 equals 45?” to solve 45 divided by 9. Briefly review how the tables work, and fill in the first box together with the students in numbers 9 and 10. Encourage students to use a strategy to solve division equations they are unsure of and to check their work.

Students may think they have problems memorized but get quotients confused. Have them use a strategy to check their work. Common Errors

Assess

Play Heads Up to practice finding missing factors and relate multiplication to division.

Check work for numbers 23 - 28.

Chapter 8

In Chapter 8, we will learn strategies for solving two-step story problems. We will also recognize and explain patterns in the hundreds chart and multiplication chart.

• Look for clues and information in the story problem

• Identify what we know and what we need to ﬁnd out

• Write equations using letters for the unknowns

• Check our answers with estimation

• Go back to the story problem and check to see if the answer makes sense

• Use steps and strategies to solve two-step story problems involving measurement

• Recognize and explain patterns in the hundreds chart

• Look for and use patterns in the multiplication chart

• Explain the di erence between factors and multiples

• Identify prime and composite numbers

Vocabulary Words

Objective and Learning Goals

y Solve 2-step word problems using all 4 operations

Vocabulary

y Addition - the act of adding or putting numbers together

y Subtraction - the act of subtracting or taking a number away from another number

y Multiplication - the act of multiplying or finding the total of a certain number of equal groups

y Division - the act of dividing or splitting a total into equal groups

Materials

y Dry-erase boards and markers

y Index cards

Pre-Lesson Warm-up Guiding Questions

Present the following problem to students:

Step 1 - Multiply 3 x 5 [15]

Step 2 - Add 6 to the answer from step 1 [21]

Have students write their answers on their dryerase boards. Discuss how students found the answer and tell students that today they will be solving word problems where they must do two steps like this to find the answers.

Guiding Questions

1. How can we solve 2-step word problems? [visualize the problem, choose the operations needed, write equations and solve for the unknowns]

2. How can we represent unknowns in an equation? [use a different letter for each unknown when writing equations]

The teacher has 7 boxes of crayons. There are 8 crayons inside each box. Noah lost 17 crayons. How many crayons are left?

Two-Step Story Problem: What do we know?

Visualize: There are 7 boxes of 8 crayons 17 crayons were lost What do we need to know and how can we ﬁnd out?

Step 1 : How many total crayons are there?

Use T to represent Total crayons.

Try it together!

Step 2 : How many crayons are left? Use L to represents crayons Left Noah had 56 crayons and lost 17

Solve the 2 -step problems. Write equations with a letter for the unknowns.

1. Mom put 30 fruit chews and 18 candy bars in a bowl. Then she made 8 goodie bags with the same number of candies per bag. How many pieces were in each bag?

C = total pieces of Candy

B = pieces of candy in each Bag

2. Joe collects stu ed bears. He has 4 brown bears and 5 black bears. Each bear cost him $5 , so how much did he spend on the bears?

= number of bears Joe has = total cost of the bears

Look at Let’s Learn and walk students through the steps of solving the example problem. First have students visualize what is happening in the problem. Remind students that they can always draw a picture to help them solve a word problem. Ask: “What do we know?” Then tell them to think about what they need to find out and which operations they need to perform on the numbers to solve the problem. Point out the underlined words “groups of” and “lost” that tell them they need to multiply and then subtract. Tell students that they can choose any letter to use in place of the unknown. Help students solve number 1 in Try it Together and for number 2, have students suggest the letters to use in place of the unknowns and the equations to use.

Activities

On index cards, write 2-step word problems like the ones in this lesson. On the back of the cards, write the equations used to solve them and the answers. Spread the problems out throughout the room, taping the cards to tables, counters, the wall, or other surfaces. Have students walk around the room, solving each problem and then checking their answer by looking at the back of the card. Students can do this activity independently, with a partner, or in small groups.

Fill in the equations to solve the 2 -step problem.

1. Dave had one box of connecting blocks with 147 blocks and another box with 232 blocks. He combined the two boxes. If he uses 98 blocks to build something, how many blocks does he have left?

Step 1 : How many Total blocks?

T = total blocks + = T

Step 2 : How many blocks are Left?

L = blocks left T = L

Answer:

Choose letters to represent the unknowns. Then write equations to solve the 2 -step problem.

2. Tim put his stu ed animals in 3 rows of 6 . Then he picked them all back up and put them in 2 rows. How many were in each row then?

Step 1 : How many total stu ed animals?

= total stu ed animals

Step 2: How many animals in each row?

R 281 blocks 98 9

= animals per row

Answer:

Solve the 2 -step problems. Write equations with a letter for the unknowns.

3. At the beginning of the school year the class had 9 packages of glue sticks with 6 in each package. They have used 37 glue sticks. How many glue sticks does the class have left?

Step 1 :

9 x 6 = E

Step 2 : Answer:

Challenge

A student solved this problem and wrote the following equations. Explain and ﬁx the mistake.

We bought 7 cartons of eggs with 6 eggs in each carton. When we got home, we found that 8 eggs were broken. How many eggs do we have?

Step 1 : 7 + 6 = A

Step 2 : A - 8 = B Answer: 5 eggs

4. Mom made one batch of 12 cookies and another batch of 24 cookies. If we split the cookies evenly among 6 people, how many cookies will each person get?

1 :

: Answer:

The student added 7 + 6. They should have multiplied because there are 7 groups of 6 eggs.

Step 1 :

Step 2 : Answer:

7 x 6 = A A - 8 = B 34 eggs

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Read problem number 1 and have students suggest the equations that can be used to solve the problem. After the class has agreed on which equations to use, have the students complete this problem and the rest of the page independently. Remind them that they can use any letter they want to represent the unknowns in their equations.

Struggling Learners

Have students draw pictures to represent the problems to help them understand what is going on in the problem. Ask questions to help them figure out which operation to use in each step like “Are we adding to something or putting two things together?”(addition) “Are we taking something away?”(subtraction) “Are we making a certain number of equal groups?” (multiplication) “Are we splitting something into equal groups?” (division)

If needed, provide students with manipulatives to help them add, subtract, multiply, and divide.

Early Finishers

Students can write their own 2-step word problems and trade with a classmate who is also finished to solve each other’s problems.

Challenge and Explore

Read the Challenge problem to the students. Have the students first talk about the mistake that was made before writing their explanation in their book. Then have all students try to solve the problem correctly, and go over the answer.

When students are finished have them choose a problem from this page to illustrate. Students should try to make an illustration that helps them make sense of the problem and know how to solve it. Remind students to set up equations and write a letter to stand for the value they are solving for in each step.

Students may choose the wrong operations to use when writing their equations and solving the problems. Some students may struggle with the computation itself. Common Errors

Play Brain vs Hand to practice basic multiplication and division facts.

Check work for numbers 3 and 4.

Solving

Objective and Learning Goals

y Solve 2-step word problems

y Use rounding and estimation to check to see if the answers to word problems make sense

Vocabulary

y Estimate to check - check if the answer is reasonable by rounding to close numbers

y Round - find a close but easier to work with number to a given number

Materials

y Dry-erase boards and markers

Pre-Lesson Warm-up

Guiding Questions

Practice rounding numbers to the nearest 10 and 100. Call out a number and tell students which place to round to. Have students write the answer on their dry-erase board and hold it up to show you.

Round 43 to the nearest 10 [40]

Round 568 to the nearest 100 [600]

Round 79 to the nearest 10 [80]

Round 802 to the nearest 100 [800]

Continue with more like this if more practice is needed.

Guiding Questions

1. How can we check our answers to 2-step word problems? [round the numbers to the nearest 10 or 100 and estimate. If the answer is close to the estimate, it is probably correct]

The teacher has 89 glue sticks. He gives each table 3 glue sticks. There are 9 tables. How many glue sticks does he have left?

How many glue sticks does he have left: Does the answer make sense? Yes No

2. At snack time the teacher put 8 crackers on each of 6 tables. She had another box of crackers that had 36 crackers in it. How many total crackers were in the classroom? Write

1. There were 76 red counters and 58 blue counters. When the teacher combined them, she spilled them and lost 22 counters under the sink. How many counters were left?

Does the answer make sense? Yes No

Look at Let’s Learn and remind students how to solve 2-step word problems. Walk through the steps in the example problem. Then tell the students that they can round numbers to close, but easier numbers to estimate. If their estimate is close to their answer, then they can be pretty sure that their answer makes sense. Point out that rounding numbers to the nearest 10 or 100 makes them easy to quickly add or subtract. Tell students that if they do not have their multiplication facts memorized yet, they can change the multiplication equation to something close, but easier for them as well. For example, they might multiply by 5 instead of by 4 or 6 or they might multiply by 10 instead of 9. However, if they do know the multiplication fact or can figure it out quickly, they should round the answer then add or subtract.

Activities

Write multi-digit addition and subtraction problems on the board. Have students solve the problems. Then have them work with partners to round the numbers and add or subtract to estimate. Have them then compare the estimates to their exact answers and discuss with their partner if their answers make sense. If they have some answers that don’t seem to make sense, tell them to try to solve the problem again.

1. There were 9 boxes of crayons with 7 crayons in each box. The students broke 24 crayons. How many crayons were left?

Step 1 :

Step 2 : Answer:

Estimate:

Does the answer make sense?

Yes No

3. At the carnival, dad spent $12 on each ticket and bought 4 tickets. Then he spent $33 on snacks. How much did he spend in all?

Step 1 :

Step 2 : Answer:

Estimate:

Does the answer make sense?

Yes No

Challenge

A student solved the following problem this way.

The food bank had 337 cans of beans and 588 cans of vegetables. They gave away 416 cans of food. How many cans of food do they have left?

Step 1 : 337 + 588 = A

Step 2 : A - 416 = B Answer: 321 cans

2. There were 46 apples and 83 oranges in the cafeteria. Students ate 61 pieces of fruit. How many pieces of fruit were left?

Struggling Learners

Estimate:

Does the answer make sense?

Yes No

4. The flower shop had 321 tulips and 287 roses. They sold 132 flowers this weekend. How many flowers are left?

Estimate:

Does the answer make sense?

Yes No

Estimate. Does the answer make sense? If not, ﬁnd the exact answer.

Estimate:

Does the answer make sense? Yes No

Exact answer:

Apply and Develop Skills (Practice / Exercise page)

Ask questions to help them figure out which operation to use in each step like “Are we adding to something or putting two things together?”(addition) “Are we taking something away?”(subtraction) “Are we making a certain number of equal groups?” (multiplication) “Are we splitting something into equal groups?” (division)

If needed, provide students with manipulatives to help them add, subtract, multiply, and divide. Consider providing a multiplication chart for those who struggle with multiplication facts.

Early Finishers

Students can go back to the previous lesson and use estimation to check if their answers to the problems on those pages make sense.

Challenge and Explore

Read the Challenge problem to the students.

1. Have students round the numbers and estimate the answer.

2. Ask: “Does the answer make sense?” [no] Why not? [the answer is almost 200 less than the estimate]

3. Have the students solve to find the exact answer.

Read the directions to the students. Then read problem number 1 and have the students suggest equations to use to solve the problem. After they have agreed on which equations to use, have the students solve the problem. Go over the answer and then ask students for ideas on how to round the numbers and what equation to use to estimate. Have students finish solving this problem and the other problems on the page independently.

When students are finished, have them go over their answers with partners. If they do not agree with each other’s answers, have them try to find each other’s mistakes and fix them.

Common Errors

Students may have forgotten how to round numbers to the nearest 10 and 100. Students may not have multiplication facts memorized yet. Students may still struggle to choose the correct operations to solve the problems and with the computation itself.

Play Draw and Round to practice rounding to the nearest 10 and 100. p. 310

Check work for numbers 3 and 4.

Objective and Learning Goals

y Measure to the nearest inch and centimeter

y Solve two-step word problems involving length

Vocabulary

y Addition - the act of adding or putting numbers together

y Subtraction - the act of subtracting or taking a number away from another number

y Multiplication - the act of multiplying or finding the total of a certain number of equal groups

y Division - the act of dividing or splitting a total into equal groups

y Inch - a unit of measurement that is onetwelfth of a foot

y Centimeter - a unit of measurement; there are 100 centimeters in a meter

Materials

y Rulers

y Blank paper

Let’s learn!

Measure by Length: Tim planted a flower. It was inches tall. It grew 2 inches the first week. It grew 1 more inch the last week. How tall is the flower now?

This rose grew 4 more inches. Then the ﬂorist cut 5 inches o of the stem. How long is the rose now? Step 1 :

Pre-Lesson Warm-up

Guiding Questions

Show students how to measure an object to the nearest inch and nearest centimeter. Have students use a ruler to measure their pencil to the nearest inch and to the nearest centimeter. Then have a student come up to show and describe to the class how they measured their pencil.

Guiding Questions

1. How can we measure to the nearest inch or centimeter? [line the object up at the 0 mark on the ruler, then find the inch or centimeter mark that the other end of the object is closest to]

2. How can we solve 2-step word problems? [visualize the problem, choose the operations needed, write equations and solve for the unknowns]

Solve the story problem.

2. There were 4 shelves that were 8 feet long each in the ﬂower shop. Then the owner added a 12 foot shelf. How many feet of shelving is there now?

it Together)

Look at Let’s Learn and tell students that they will continue to solve 2-step word problems, but today, the problems will all involve measurements of length. Remind students how to line objects up with the 0 mark on the ruler and then read the nearest inch or centimeter to find the length. Then go over the 2-steps needed to solve the example problem. Have students help you with the Try it Together problems by telling you how to measure and, in number 2, suggesting equations to use to solve the problem. Emphasize with the students that they can choose any letter they want to represent the unknowns in the problem.

Activities

Have students measure their pencils to the nearest inch. Then have them use that length to solve the following problem:

Imagine you had 4 pencils all the same length as your pencil lined up end to end. Then you sharpened one of the pencils until it was 2 inches shorter and put it back in the line. How long is the line of pencils now?

Have students share their strategies, equations, and answers to this problem with a partner. Partners should check each other’s work. Then have some students share with the class.

Measure the objects to the nearest centimeter. Then solve the story problems.

1. Ben built a wall that was 9 blocks long. Then while he was at school, his little brother added 16 more centimeters onto the wall. How long is the block wall now?

Struggling Learners

Provide students with an index card or other straight edge to line up at the end of the objects for help with measuring accurately.

2. The seedling grew 3 centimeters everyday for 7 days. How tall was the seedling after 7 days?

Solve the 2 -step problems. Write equations with a letter for the unknowns.

3. Each student’s paper chain was 8 cm long. 9 students connected their paper chains. Then 24 cm fell o How long is the paper chain now?

4. Mom needs 25 feet of wrapping paper to wrap 5 gifts. How many feet of wrapping paper does she need to wrap 8 gifts?

Challenge

Solve the story problem. (Hint: How many centimeters are in 1 meter?)

The teacher has 2 lengths of string. One is 1 meter long and the other is 2 meters long. If she cuts the string into 10 equal sized pieces of string, how many centimeters long is each piece of string?

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Read problem 1 and have all students measure the block. Then check to see that they measured correctly. Have students suggest equations to use to solve the problem. Once the class has agreed on equations that will work, have the students finish this problem and the rest of the page independently.

Early Finishers

Students can make an illustration and/or diagram on blank paper to show some of the problems. For example, for number 1, they could draw the correct number of blocks and label who built which part of the block wall.

Challenge and Explore

Read the Challenge problem to the students. Have students draw a picture or diagram to help them make sense of the problem if necessary and make sure they pay attention to the hint.

Have students try to write their own two-step word problems involving length. They could work independently or with a partner to do this and then trade problems with another person or group.

Common Errors

Students may not read the rulers carefully when determining the length of the objects. Students may still struggle to know which operations to use and how to set up the equations to use to solve the problems.

Assess

This problem is challenging because there is actually a 3rd step in this problem - students will need to convert meters to centimeters. For the first equation, students may write 1 m + 2 m = 3 m and then convert 3m to 300cm before dividing, or they may convert meters to centimeters before adding.

Games

Play The Measurement is Right to practice measuring to the nearest inch and/or centimeter. p. 314

Check work for number 2.

Objective and Learning Goals

y Solve 2-step word problems involving weight and volume

Vocabulary

y Weight - the measure of the force of gravity on an object; pounds and ounces are units of weight

y Liquid volume - the amount of space a liquid takes up

Materials

y Containers that show different amounts of liquid - cups, pints, gallons, etc, or pictures of these containers

y Blank paper

y Colored pencils, markers, or crayons

Pre-Lesson Warm-up

Guiding Questions

Show students containers that hold different liquid amounts such as a cup measure, an empty ice cream pint, an empty gallon milk jug, etc. If you don’t have access to the containers, you can show them pictures of these things. Remind students that these are all units that we can measure liquid amounts with. Ask questions like “If each pint container holds 2 cups of ice cream and I have 4 of them, how many cups of ice cream do I have?” [8] to warm up for today’s problem solving.

Guiding Questions

1. How can we solve 2-step word problems? [visualize the problem, choose the operations needed, write equations and solve for the unknowns]

Let’s learn!

A pencil weighs 4 ounces. There are 8 pencils in a box. The box weighs 2 ounces. What is the total weight of the box of pencils?

Try it together!

1. There were 8 pints of ice cream on each of the 3 shelves in the freezer at the store. Customers bought 15 pints of ice cream. How much ice cream was left in the freezer?

2. Three math books weigh 9 pounds. How much do 7 math books weigh?

Introduce the Lesson (Try it Together)

Look at Let’s Learn and read the example problem to the students. Explain to students that ounces are a unit of measuring weight and there are 16 ounces in a pound. Have students help you solve the problem. Remind students that they can choose any letter they want to represent the unknowns in the problems. Since students have been solving a lot of 2-step problems, have them take the lead in solving the Try it Together problems as much as possible.

Activities

Have students choose one of the Try it Together problems to illustrate. They should draw a picture or diagram to make sense of the problem. They should include the equations used to solve the problem and be sure to label all important parts of their drawing.

When students are finished, they can share their drawings with partners, small groups, or the whole class and explain how their drawing shows the problem.

Solve the 2 -step problems. Write equations with a letter for the

1. There were 4 cups of juice in each bottle. There were 6 bottles in the refrigerator. Then Dad brought home another bottle that had 5 cups of juice in it. How many cups of juice are there now?

Step 1 :

Step 2 : Answer:

3. The teacher had 6 math books in a tub. Each book weighs 5 pounds and the tub weighs 2 pounds. How much does the tub full of books weigh?

Step 1 :

Step 2 :

5. The carpenter is hauling 2 boards. One board weighs 139 ounces and the other weighs 146 ounces. He cuts o part of a board to ﬁt it in his truck. The part he cut o weighs 36 ounces. How much do the two boards weigh now?

2. Dad poured 34 ounces of milk into a jug. Then Dad poured 28 more ounces into the jug. Tim drank 4 ounces of the milk. How much milk was left in the jug?

A student solved this problem and wrote the following equations. Explain and ﬁx their mistake 4 x 6 = C

Challenge

The baker had 8 bags of flour. Each bag of flour weighs 5 pounds. She used 12 pounds of flour. How many pounds of flour does she have left?

Step 1: 8 x 5 = B

Step 2: B + 12 = F Answer: 52 pounds

4. 3 bottles hold 27 ounces. How many ounces do 7 bottles hold?

Struggling Learners

Have students draw a picture or diagram to show what is happening in the problem and underline any key words in the problem that can help them know which operation to use.

Provide manipulatives or other tools such as counters, base-10 blocks, hundreds charts, and multiplication charts to help students who struggle with computation.

Early Finishers

6. David had one barrel with 17 gallons of water and another barrel with 19 gallons of water. He divides the water equally among 9 buckets. How many gallons of water are in each bucket?

The student added 12. They should have subtracted because the baker used that much ﬂour.

8 x 5 = B

B - 12 = F 28 lbs

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Read problem number 1 to the students and have students suggest equations to use to solve the problem. Once the students have agreed, have them finish this problem and the rest of the problems independently.

Students can choose some problems to go back and use estimation to check to see if their answers make sense.

Challenge and Explore

Read the Challenge problem to the students. Then:

1. Have a class discussion about the equations the student chose to use and why they do or do not make sense.

2. Give students time to solve the problem on their own.

3. Share solutions and discuss the actual answer to the problem.

When all students are finished, have students try to write their own 2-step word problems involving weight and volume. Choose at least one of the students’ problems to have the class try solve together.

Students may struggle to make sense of the problems and decide which operations to use when writing equations to solve the problems. Some students may make mistakes in computation. Common Errors

Play Brain vs Hand to practice basic multiplication and division facts.

Check work for numbers 5 and 6.

Objective and Learning Goals

y Find and explain patterns on the hundreds chart

y Add and Subtract using the hundreds chart

Vocabulary

y Skip counting - counting by multiples of a certain number

y Addition - the act of adding or putting numbers together

y Subtraction - the act of subtracting or taking a number away from another number

Materials

y Paper copies of hundreds charts

y Counters or other small objects

y Sticky notes

Pre-Lesson Warm-up Guiding Questions

Display a hundreds chart. Ask students to recall what happens to the numbers in the chart as you go up and down [10 less and 10 more] and left and right [1 less and 1 more]. Have students count with you as you point to numbers on the chart. Practice counting forward and backward by 1s and also forward and backward by 10s starting at different numbers. For example:

Start at 6 and count up by 10s [6, 16, 26, 36, etc]

What pattern do you see? [ones digit is always 6]

Start at 27 and count up by 1s [27, 28, 29, 30, etc]

What we do when we get to the end of a row? [go to the first number in the next row]

Start at 93 and count backward by 10s [93, 83, etc]

Guiding Questions

1. How is the hundreds chart organized? [10 numbers per row, 10 rows. Numbers 1-10 in first row, 11-20 in next row, etc.]

2. What happens to the numbers in the hundreds chart as you move left, right, up and down? [decrease by 1, increase by 1, decrease by 10, increase by 10]

Let’s look for patterns in the 100s Chart!

Which numbers are shaded in purple?

Every other column is colored, numbers all have 2, 4, 6, 8, or 0 in ones place

Start at 10 , Count by 10 s, Circle each number on the hundreds chart above. 1. Which numbers did you circle? What pattern do you notice? Use the hundreds chart to add. Explain your strategy.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100 55

1 column at the end, on the right is circled, numbers all end in 0

Point to 21. Go down 3 for the 3 tens in 34. Then go over to the right 4 for the 4 ones in 34.

Direct students attention to the hundreds chart in Let’s Learn. Have students help you describe how the chart is organized [10 numbers per row, 10 rows. Numbers 1-10 in first row, 11-20 in next row, etc.] and different patterns they notice on the chart. Remind students that when you go left to right and top to bottom, the numbers increase by 1 and 10 respectively. Have the students help you fill in the number grid puzzle. Then ask them to identify which numbers are shaded on the chart and describe the patterns they see. Remind students how to break numbers into 10s and 1s and explain to them how to use the hundreds chart to add or subtract 10s and 1s. Tell them, when adding, to hop forward (down) by the 10s and over (right) by the 1s in the number they are adding. Do the opposite (up and left) for subtraction.

Activities

Pass out a paper hundreds chart and a counter to each student. Then give them a number to start with and a number to add or subtract from the start number. Have students place their counters on the start number and describe how to move the counter to add or subtract. They may count up or back by 1s, but encourage students to make hops forward and backward by the tens and ones in the number they are adding or subtracting. For example, if you tell students to start at 37 and add 42, they could move their counter down 4 to add 4 tens and then to the right 2 to add 2 ones.

Start at 5 . Count by 5 s. Circle each number.

1. What pattern do you notice?

1 column in the middle circled and 1 column at end circled, numbers all have a

Use the hundreds chart to add or subtract. Explain your strategy.

Start at 78. Go up 5 for the 5 tens in 51 and you get to 28. Then go backward 1 for the 1 one in 27.

Start at 24. Go down 4 for the 4 tens in 48 and you get to 64. Then go forward 8 for the 8 ones in 48. You have to move down to the next row when you get to 70. Once at 71 move one more over to 72.

Use the 100 s above. Start at 1 , add 9 and color in the number. Continue to add 9 and color in each number until you reach 100 . What pattern do you notice?

1 and 100 are colored and a diagonal from top left to bottom right. The number in the ones place decreases by 1 starting at 19.

Use the patterns you saw. Explain how to use the hundreds chart to add: 17 + 9 =

Go down diagonally left, or go to the next 10 and the ones place is 1 less

Subtract: 54 - 9 =

Go up diagonally right, or go to the previous 10 and the ones place is 1 more

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Explain to the students that number grid puzzles are like a chunk of the number grid cut out. Have a student remind the class of the pattern they can use to help them determine which numbers go in the blanks [up it 10 less, left is 1 less, right is 1 more, and down is 10 more]. Have students complete the page independently.

Struggling Learners

Prompt students to find patterns by asking “What happens to the numbers in the tens and ones places?” or “Do you see a certain design, or line on the chart?”

Provide a counter or other small object for students to actually move along as they are adding, subtracting and skip counting on the hundreds chart.

Early Finishers

Give students blank hundreds charts to find and mark their own patterns on. If time, they can share with another student who is finished early or even with the class.

Challenge and Explore

Read the Challenge problem to the students. Have them use their pencil first to lightly shade in case they make a mistake, then they can color in the chart darker or with a colored pencil or crayon when they are sure they have the correct numbers shaded in.

Have a class discussion about the patterns that they notice and how they can use that pattern to help them solve a problem adding or subtracting 9. Then have them solve the problems and write their explanations.

When students are finished, go over the answers and have a few students share their explanations. Then continue looking at other patterns on the hundreds chart and how they can use the hundreds chart to help with multiplication. Have students start at 4, skip count by 4s, and put a triangle on every number they count. Ask students to describe the patterns they see. Repeat this for other multiples, using a different shape or color to mark each number as time allows.

Common Errors

Some students may struggle to find patterns. When adding and subtracting, some students may skip numbers, forget which way to go when they get to the end of a row, or count the start number as their first move on the grid.

Have students solve the following problem on a sticky note: Use the hundreds chart to solve 65 + 23 = _____. [88] Explain your strategy.[Start at 65 and go down 2 to add 20 and over to the right 3 to add 3] Assess Games

Play Race to 500 to practice adding 2-digit numbers. p. 312

Objective and Learning Goals

y Use and fill in a multiplication chart

y Recognize and explain patterns in a multiplication chart

Vocabulary

y Skip counting - counting by multiples of a certain number

y Multiplication - the act of multiplying or finding the total of a certain number of equal groups.

Materials

y Printed multiplication charts

y Crayons

y Sticky notes

Let’s learn!

Let’s look for patterns in the Multiplication Chart!

Circle all of the numbers in the x1 row and column. What pattern(s) do you notice?

They are all the same as the number they are being multiplied by. They increase by 1 going down and across

Shade in all of the numbers in the x2 column. What pattern(s) do you notice?

They are skip counting by 2s. They are all even numbers. The ones place repeats 2, 4, 6, 8, 0, 2, 4, 6, 8, 0

Pre-Lesson Warm-up

Guiding Questions

Teach or review with students how to use the multiplication chart to find the answer to a multiplication fact by going down to the first factor and over to the second factor. Have students practice finding and pointing to the answers to several facts in the chart.

Guiding Questions

1. How do we use a multiplication chart to find products? [find the factors along the top and left side. The product is where that row and column intersect]

2. How can finding patterns in the multiplication chart help us with multiplication facts? [you can check to make sure the product you come up with fits the pattern or use the patterns to come up with the products]

1. Shade in the x5 column on the chart.

2. What pattern(s) do you notice?

Skip counting by 5s, ones place is alternating 5, 0, 5, 0, the tens place is the same for 2 numbers and then increases by 1 - 1, 1, 2, 2, 3, 3, etc.

3. Write the product of 5 x 11 and explain how it continues the pattern.

55. Skip counting by 5s, you’d say 55 next. The ones place is 5 and was 0 in the last number. The tens place is 5 - same as last number.

Introduce the Lesson (Try it Together)

Walk students through the Let’s Learn problems and discuss patterns that they notice. They may notice patterns not listed in the answer key! Have students explain how they know which numbers to shade in the Try it Together problem, and then have them explain the patterns out loud before writing what they notice in their books.

Activities

Give students a printed copy of a multiplication chart. Have them take a crayon and shade in all of the products that are odd numbers. Then discuss with the students the pattern they notice [every other number is colored in the rows and columns of odd factors, but no numbers are colored in the rows and columns of even factors] and what this tells them about odd and even factors and products [if either factor is even, the product will be even. Both factors have to be odd in order for the product to be odd]

1. Fill in the multiplication chart.

1 2 3 4 5 6 7 8 9 10

2 4 6 8 10 12 14 16 18 20

3 6 9 12 15 18 21 24 27 30

4 8 12 16 20 24 28 32 36 40

5 10 15 20 25 30 35 40 45

6 12 18 24 30 36 42 48

7 14 21 28 35 42 49 56

8 16 24 32 40 48 56 64 72 80

9 18 27 36 45 54 63 72 81 90

10 20 30 40 50 60 70 80 90 100

2. Circle the numbers in the ×4 row. What pattern(s) do you notice?

Skip counting by 4s. The numbers in the ones place repeat - 4, 8, 2, 6, 0, 4, 8, 2, 6, 0. All products are even numbers.

Struggling Learners

Provide paper, index cards, or other straight edges for students to line up with the rows and columns to read the chart.

Allow students to share the patterns they notice with each other. Ask students to describe the pattern that a classmate noticed if they didn’t notice one on their own.

Early Finishers

Students can find and describe other patterns in the multiplication chart that have not already been discussed. Students can share what they find with other students who are also finished early.

Skip counting by 9s. The numbers in the ones place decrease by each time and the numbers in the tens place increase by 1 each time. Products alternate - even, odd, even, odd.

3. Shade in the numbers in the ×9 column. What pattern(s) do you notice? Challenge

Extend the chart for ×4 :

× 11 12 13 14 15

4 44 48 52 56 60

Explain how the pattern continues and any new patterns you notice.

The products skip count by 4s and are all even, the numbers in the ones place continue the pattern - 4, 8, 2, 6, 0

Challenge and Explore

Read the Challenge problem to the students. Make sure they understand how to fill in the extended chart for x4. Then give them time to look for and explain the patterns they see. Call on some students to share their findings with the class.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Get them started filling in the multiplication chart by asking “Which facts to do you know for sure right away?” “Can you use some patterns to help you fill in some of the rows and columns?” Encourage them to fill in the chart without looking at the completed charts on the previous page. However, they can check their work by looking back at that page. Have students finish the page independently.

Go over the patterns that students found and then have students look at other rows and columns in the chart and describe other patterns that they see to partners or small groups. Share some of the patterns they found with the class.

Common Errors

Some students will have trouble recognizing patterns that aren’t pointed out to them explicitly. Students may have trouble staying in a row or column to read the chart accurately.

Assess

Games

Play Times Table War to practice multiplying by a given factor. p. 315

On a sticky note, have students describe one pattern they see in the multiplication chart. It can be a pattern that was discussed in class, or a new one.

Objective and Learning Goals

y Define prime and composite numbers

y List factors of a given number

y List multiples of a given number

Vocabulary

y Prime number - a number that has exactly 2 factors - 1 and itself

y Composite number - a number that has more than 2 factors

y Factors - the numbers being multiplied in a multiplication equation

y Multiples - the product of multiplying one whole number by another

Materials

y Counters or other small objects

y Printed hundreds charts

Pre-Lesson Warm-up

Guiding Questions

Ask students “What are all the pairs of numbers we can multiply to get 18?” and list them on the board as the students list them. [1 x 18, 2 x 9, 3 x 6, 6 x 3, 9 x 2, 18 x 1] You may need to remind the students of the identity property - any number times itself is that same number.

Point out to the students that all of the numbers that can be multiplied to get a certain product are called factors. Then have them list the factors of 18 with you:

1, 2, 3, 6, 9, 18

Guiding Questions

1. How can we find the factors of a given number? [find all of the numbers that the number can be divided evenly by - you could make arrays]

2. How can list multiples of a given number? [multiply that number by any other whole numbers]

Factors

Try it together!

List four multiples

Read through the information in Let’s Learn and explain to students that factors are the numbers you can multiply together to get a certain number and multiples are the products of multiplying by a certain number. Go through the examples to practice finding factors and multiples of numbers. When thinking about factors students should ask themselves “What can I multiply together to get this number?” or “What numbers can I evenly divide this number by?” Remind them that all numbers will have the factor 1 and the number itself. Explain that prime numbers are numbers that have ONLY 1 and the number itself as factors. When finding multiples of a number, students can simply multiply the given number by 2, 3, 4, 5, and so on. These products are the multiples of that number.

Activities

Demonstrate prime and composite numbers by having students use counters or other small objects to make arrays. For a prime number, they will only be able to make 1 array that is 1 row of that number of counters. For example, 2 is a prime number. The only array you can make is 1 row of 2 counters. 3 is also a prime number, you can only make one array that is 1 row of 3 counters. 4 is a composite number, so students can make more than 1 array. They can make 1 row of 4 counters, or 2 rows of 2 counters. Continue having students count out a certain number of counters and make as many arrays as they can with those counters. Then ask them to tell whether the number is prime or composite. Also relate the arrays to factors. For example, with 8 counters, they can make a 1 x 8 array and a 2 x 4 array, so the factors of 8 are 1, 2, 4, and 8.

List 4 prime numbers. Explain how you know these numbers are

Possible answer: 7 11 13 23

They only have the factors 1 and themselves, or you can only divide them equally by 1 or themselves.

List all of the factors for each number. Then circle whether the number is prime or composite.

List four multiples of each number.

possible answer: 12,18, 24, 30

possible answer: 4, 6, 8, 10

Challenge

The number 60 has 12 factors. Can you list them all?

possible answer: 14, 21, 28, 35

possible answer: 18,27, 36, 45

possible answer: 16, 24, 32, 40

possible answer: 22, 33, 44, 55

Struggling Learners

Give students counters to make arrays with to find the factors. Remind students that if a number is even, 2 will always be a factor. They can start by dividing the counters into 2 equal rows.

Early Finishers

Give early finishers a hundreds chart and have them color in as many prime numbers as they can. Have them check each number to see if it has more than 2 factors, and if not, color it in. They can work together with other students who are also done early.

Challenge and Explore

Explain how you found the factors.

Read the Challenge problem to the students. Ask students for ideas of strategies they can use to find all of the factors of a number. Then give the students time to find as many as they can and write their explanations. Then bring the class together and have students share the factors of 60 until all students have all 12 factors listed.

Apply and Develop Skills (Practice / Exercise page)

Read number 1 and have students give you numbers that they think are prime numbers. Each time, ask “How do you know?” Then have students write 4 numbers of their choosing and their explanations. Read the rest of the directions on the page to the students and ask a student to remind the class what factors and multiples are. Then have students finish the rest of the page independently.

Have students make a T-chart with prime numbers on one side and composite numbers on the other. The composite number column will need to be much wider than the prime number side. Next to each number, the students should draw arrays. For prime numbers, there will be just one array and for composite numbers, they will be able to make at least 2 arrays. Students can make the charts in partners or small groups.

Common Errors

Students may struggle to list all of the factors of a number, especially when some of the factors are greater than 10 or 12. For example they may struggle to find that 18 is a factor of 36 because 2 x 18 is not a fact they have learned.

Assess

Games

Play Times Table War to practice multiplying by a given factor. p. 315

On a sticky note, have students list all of the factors of 12 and also list at least 4 multiples of 12.

Objective and Learning Goals

y Review

y Solve 2-step word problems

y Recognize and describe patterns on the hundreds chart and multiplication chart

y Find factors and multiples of a given number

Vocabulary

y Factors - the numbers being multiplied in a multiplication equation

y Multiples - the product of multiplying one whole number by another

y Addition - the act of adding or putting numbers together

y Subtraction - the act of subtracting or taking a number away from another number

y Multiplication - the act of multiplying or finding the total of a certain number of equal groups

y Division - the act of dividing or splitting a total into equal groups

Materials

y Hundreds chart to display

y Grid paper

y Scissors

Two-Step Story Problem

The teacher put 8 glue sticks on each table. There are 6 tables. She has a tub with 23 more glues sticks. How many total glue sticks are there?

Pre-Lesson Warm-up Guiding Questions

Display a hundreds chart. Ask students to describe how the chart is organized [rows of 10 starting with 1-10, 10 rows] and patterns they see on the chart. Then ask students to come up and show how to use the chart to add or subtract. Remind them to think about tens and ones. 34 + 26 [60; start at 34, go down 2 rows and forward 6 columns]

57 - 34 [23; start at 57, go up 3 rows and backward 4 columns]

Repeat with other problems as necessary.

Guiding Questions

1. How can we solve 2-step word problems? [visualize the problem, choose the operations needed, write equations and solve for the unknowns]

3. How can we find the factors of a given number? [find all of the numbers that the number can be divided evenly by - you could make arrays]

4. How can we list multiples of a given number? [multiply that number by any other whole numbers]

Review how to solve 2-step word problems, the definitions and how to find factors and multiples, and how to solve number grid puzzles. Have students take the lead in working through the problems in both Let’s Learn and Try it Together since this is review.

Activities

Have students make their own number grid puzzles. They can outline and cut out pieces from grid paper and then fill in one or two numbers in the boxes. Students can make 2 copies of the puzzle, one to solve themselves as an answer key and one have a classmate try to solve. Have students solve each other’s puzzles and discuss the solutions.

Complete the number grid puzzles.

Solve. Describe how you can use the 100 s chart. 63 - 47 = ____

Circle the numbers in the x3 and x6 rows. Draw arrows from the x3 row to the corresponding product in the x6 row. Describe the pattern:

The product in the x6 column is double the product in the x3 column.

How can you use the pattern to solve x6 facts?

Possible answer: If you know the x3 fact, you can double the product to ﬁnd the x6 product. So, if you know 3 x7 is 21, you know 6 x 7 is double 21 or 42.

Solve the two-step story problem.

8. Tom’s blocks are 3 centimeters long. He built a wall 9 blocks long. Then his brother knocked down 12 centimeters of the wall. How long is the wall now?

Step 1 :

Step 2 : Answer:

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Have the students complete the page independently to review.

Struggling Learners

Provide students with a hundreds chart to refer to when solving number grid puzzles and an index card to help them move up and down the rows when adding and subtracting Help students make sense of word problems by drawing pictures or diagrams and underline key words to help them choose the correct operations.

If students struggle to find factors, give them counters or grid paper to use to make arrays.

Early Finishers

Students can list as many multiples as they can for the numbers in problems 11 and 12. Challenge them to continue past the multiples that are in the multiplication chart.

Challenge and Explore

Present the following story problem for students to solve and then have them use estimation to check that their answer makes sense.

The store had 62 pints of vanilla ice cream and 87 pints of chocolate ice cream. They sold 73 pints of ice cream. How many pints of ice cream were left?

When students are finished, have them partner up to compare and check answers. Then bring the class together to discuss any disagreements that the students had when comparing answers.

Common Errors

Students may struggle to solve number grid puzzles when there are blanks between numbers. They may also have trouble using the hundreds chart to add or subtract when adding or subtracting the ones requires them to move up or down a row.

1. Solution: [62 +87 = 149 149 - 73 = 76]

2. Estimate: [60 + 90 = 150 150 - 70 = 80]

Games

Play Times Table War to practice multiplying by a given factor. p. 315

Assess

Check work for numbers 4, 5, 6, 8, 9, and 11.

Some students may choose the wrong operations to use when writing their equations and solving the word problems.

Some students will have trouble coming up with ALL of the factors of a number.

Chapter 9

In Chapter 9, we will learn about fractions and how to represent and use them.

• Understand that fractions are values that represent parts of a whole or group

• Name fractions by the number of parts they have

• Find fractions on a number line

• Use fraction bars to visualize and name fractions

• Identify and write fractions

• The numerator tells us how many parts we have

• The denominator tells us how many parts the whole is divided into

Vocabulary Words

Objective and Learning Goals

y Understand fractions as equal parts of a whole

y Name fractions using fraction words

Vocabulary

y Fraction - a number that represents a part of a whole

y Parts - the equal size sections or groups that something is divided into when talking about fractions

y Whole - the entire thing or group of things that is divided into fractional parts

Materials

y Dry-erase boards and markers

y Index cards

y Sticky notes

Pre-Lesson Warm-up

Guiding Questions

Tell students that you have one cookie and draw a circle on the board to represent a cookie. Have the students draw a circle on their dry-erase boards to represent a cookie as well. Tell students that you want to share the cookie with with your friend. Ask them what to do. [cut it in half] Then have students draw a line to show you how to cut the cookie on their dryerase boards in half. Then draw a line on your cookie that cuts the cookie into one large piece and one much smaller piece. Ask the students if this is a fair way to cut the cookie [no] and have them help you fix it. Tell students that when we divide one whole thing into equal parts we are talking about fractions and we name them with words like halves, thirds, fourths, etc.

Guiding Questions

1. What is a fraction? [equal parts of a whole]

2. How do we name fractions? [by the number of equal parts; halves for 2 equal parts, thirds for 3 equal parts, etc.]

Look at Let’s Learn and emphasize with students that fractional parts must be equal in size. Show them how to partition a shape into equal size pieces and go over the fraction names for different numbers of parts (halves, thirds, fourths, fifths, etc.). Teach students that one part is called one-half, one-third, onefourth, one-fifth, etc.

Activities

Have students make a chart with 3 columns. In the first column they should write the words for fractional parts, starting with whole, then halves, thirds, etc. In the second column, they should write the number of parts that each fraction word means (whole - 1, halves - 2, thirds - 3, etc.). In the third column they should draw a picture of a shape divided into that number of equal parts. Students can fill in the chart as high as they would like, but they should try to go up to tenths at least.

Finish ﬁlling in the chart.

Partition the shapes into the correct number of parts.

How

or Why not?

Struggling Learners

Create an anchor chart like the chart that the students made in the Activities section of the lesson. Hang the chart on the wall for students to refer to as they work.

Early Finishers

Students can make “Fraction Flash Cards” by drawing shapes on index cards and dividing them into equal parts. On the back of the cards, they should write the word for the fraction shown. For example if they draw a rectangle divided into 5 equal pieces, they should write “fifths” on the back of the card. They can use their cards to quiz other students who are also finished early.

Challenge and Explore

Write the following on the board:

Zero-fourths

One-fourth

Two-fourths

Three-fourths

Four-fourths

Then:

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Point out that in numbers 1-4 the shapes are divided into equal parts with one part colored in. Ask students how many equal parts number 1 is divided into [4]. Ask: “What is the word for 4 equal parts?” [fourths] and “How many fourths are colored in?” [1] Have students fill in the blank with the word “fourths.” Have students complete the rest of the practice page independently. After students are finished, go over their answers to number 12. Help students to understand that fractional parts must all be equal in size. Have students draw 2 rectangles on their dry-erase boards or on paper. Tell students to cut each rectangle into 4 parts - one rectangle should have equal sized parts and the other should have unequal sized parts. Tell them to circle the rectangle that shows fourths [the one with equal sized parts]. If time, repeat this with other fractions.

Common Errors

Students may have trouble dividing a shape into equal size pieces. Some students may not understand how to name a fractional part (for example, they may say fours instead of fourths).

Assess

1. Have students copy these onto paper and next to each one, draw a rectangle or circle that is divided into fourths.

2. Then have students color in the amount shown. Ask: “How many parts will you color in to show Zero- fourths?” [none], “One-fourth?” [1], “Two-fourths?” [2] etc.

3. Ask: students “How many fourths is the whole thing?” [4]

Play Go Fishing to practice making equal groups. p. 314

Draw or show students a picture of a circle divided into 3 equal parts. Have students write on a sticky note the name for the fraction shown. [thirds]

12. David drew these red lines on the circle to show thirds.

many parts did he cut the circle into? Does David’s circle show thirds? Why

Objective and Learning Goals

y Understand what the numerator and denominator of a fraction represent

y Find missing numerators and denominators

y Partition shapes, shade in parts and write a fraction for the shaded parts

Vocabulary

y Fraction - a number that represents a part of a whole

y Parts - the equal size sections or groups that something is divided into when talking about fractions

y Whole - the entire thing or group of things that is divided into fractional parts

y Numerator - the top number in a fraction; represents the number of pieces shaded or being talked about

y Denominator - the bottom number in a fraction; represents how many equal parts are in the whole

Materials

y Pictures of fractions to display

y Number cards

y Dry-erase boards and markers

Pre-Lesson Warm-up

Guiding Questions

Show students pictures of fractions. Ask questions like “How many pieces is this shape divided into?” and “How many pieces are shaded?”

Guiding Questions

1. What is the numerator of a fraction? [the top number that tells how many parts are shaded or are being talked about]

2. What is the denominator in a fraction? [the bottom number that tells how many parts the whole is divided into]

Look at the Let’s Learn and explain to students that the top number in a fraction tells how many parts are shaded or are being talked about and the bottom number tells how many total parts the shape is divided into. Tell students to read the top number of the fraction first. They can think of the words “out of” when they see the bar between the numerator and denominator. For example, in the fraction one-fourth, 1 out of 4 pieces are shaded. Help students fill in the missing numerators and denominators by asking “How many parts are shaded?” and “How many total parts are in the whole?”

Activities

Have students pull two cards from a stack of number cards. Tell them to put the smaller number on top of the larger number, using their pencil as the horizontal bar to make a fraction. Then have students draw a shape on their dry-erase board or on paper, partition it into the correct number of total parts and shade in the correct number of parts. For example, a student who draws a 3 and an 8 should make the fraction 3⁄8, draw a shape divided into 8 parts, and shade in 3 of the parts. Then students can check each other’s work.

in and write the fraction indicated.

Fill in the missing numerators and denominators.

the shapes and shade in the correct number of

Struggling Learners

Have students point to the top number first and then the bottom number as they read a fraction. Have them say “out of” in between the two numbers. They can check their work by making sure that the top number out of the bottom number are shaded.

Early Finishers

Students can draw the fractions on the practice page in different shapes. For example, if the problem shows a rectangle, they can draw the same fraction of a circle instead.

Challenge and Explore

Draw two large circles on the board. Tell the students that these are pizzas. Then draw a line through each circle to cut it in half. Shade ½ of each circle. Tell students that the shaded part represents how much pizza someone ate. Say the person thinks they ate 2/4 of a pizza because there are 4 parts and they ate two of them.

Ask:

1. Is this correct? [no]

2. Why or Why not? [because the pizzas are divided in halves, not fourths. The whole is 1 pizza and there are 2 wholes]

3. How much pizza did the person eat? [2/2 or a whole pizza]

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Have a student describe how they know which number is which in a fraction (numerator and denominator) and what each number means. Do number 8 with the students. Say: “If we want to show two-thirds, first we need to partition the shape into thirds. How many parts is that?” [3] Show students how to divide the circle into 3 equal parts. Then ask “How many pieces should we shade in?” [2] and “How do we write the fraction?” [2 on the top and 3 on the bottom] On grid paper, have students draw rectangles and then shade in part of the rectangle. Have students write fractions to show how many parts of the rectangle they shaded in. For example, if a student draws a rectangle around 6 squares on the grid paper and colors in 2 squares, they should write the fraction 2/6.

Common Errors

Students may confuse the numerator and denominator. Students may also have trouble partitioning shapes into equal sized pieces.

Assess

Check work for numbers 11 - 13.

Objective and Learning Goals

y Identify fractions using fraction bars and fraction circles

Vocabulary

y Whole - the entire thing or group of things that is divided into fractional parts

y Parts - the equal-sized sections or groups that something is divided into when talking about fractions

y Fractional part - each individual section or group that can be represented by a unit fraction, such as 1 2

y Equivalent - the same, as in fractions that are the same size

Materials

y Plain white paper

y Printable fraction cards (for game)

Pre-Lesson Warm-up

Guiding Questions

Have students draw shapes and practice drawing a line to cut their shapes in half.

Draw a circle on your paper. Draw a line to split your circle in half.

Draw a rectangle on your paper. Draw a line that splits your rectangle in half.

Draw a triangle on your paper. Draw a line that splits your triangle in half.

Guiding Questions

1. How can we represent fractions of a whole? [we can use fraction bars and circles, among other things. We must divide the whole into equal size pieces. Each piece represents a different fractional part depending on how many pieces we divided the whole into. For example, if we divide the whole into 4 pieces, each piece is one-fourth]

Draw a circle on the board. Tell the students that it is a cookie you are going to share with a student. Draw a line to show where you cut the cookie, but make one piece very small and the other very large. Tell the students that you are going to take the large piece and give the other “half” to the student. Ask what they think. [students should recognize that’s not fair and that you didn’t really cut the cookie in half] Say to students: “But I cut the cookie in 2 pieces, so each piece is 1-half, right?” They should come to the conclusion that each piece needs to be the same size. Tell them whenever we are talking about fractions of a whole, each piece needs to be the same size. Read and go over the examples at the top of the page, starting with the apples.Tell students the whole is the group of apples. Ask: How many apples are there? [4] Are all of the apples the same size? [yes] So each apple is 1-fourth of the apples. How many apples are circled? [2] So, 2-fourths of the apples are circled. Point out the fraction 2 4 . Go through each example in a similar way, gradually asking the students to name the fractional parts. For the cake say: The whole is the cake. How many pieces is the cake cut into? [3] So each piece of cake is what fraction of the cake? [one-third] How many pieces are circled? [1] So what fraction of the cake is circled? [one-third] Go through the Try it Together problems with students. For number 1, say: This fraction is one-fourth. How many pieces is the whole divided into? [4] How many pieces do we color in? [1] Point out to students that the bottom number tells us how many pieces the whole is divided into, and the top number tells us how many pieces we are talking about or how many to shade in. Finish numbers 2 - 9 in the same way, and then tell students that equivalent fractions are different fractions that are the same size. For number ten, say: This fraction bar shows us two-halves. How many fourths is the same as two-halves? [four-fourths]

Activities

Have students fold a piece of plain white paper into fourths lengthwise and make and finish filling out a chart like this:

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Make and hang an anchor chart in the room like the one the students made in the activity portion of the lesson, or let them keep and use their chart to help them with their work.

Early Finishers

Look at the fractions in numbers 9 - 13. Draw pictures to show the fractions in another way.

Challenge and Explore

Have students answer and discuss the following questions:

Would you rather have 1 2 of a delicious pie or 2 4 of the same pie? [it doesn’t matter because both are the same amount of pie]

Would you rather have 1 5 of a delicious pie or 1 3 of the same pie? [ 1 3 because if you cut the pie in 3 pieces, the pieces are bigger than if you cut the pie into 5 pieces]

Read the directions and do number 1 with the students by saying: “This bar is divided into 3 equal pieces, or thirds. Two of those pieces are shaded in, so the fraction is twothirds. The circle is divided into 3 equal pieces as well. To shade two-thirds, we shade in 2 of the 3 pieces.” Have students look at number 2. Ask: How many pieces is the circle divided into? [4] How many pieces are shaded in? [3] What is the fraction that is shaded in? [three-fourths] How many pieces is the fraction bar divided into? [4] How many pieces should we shade to show three-fourths?[3] Color it in as students do the same. For numbers 9-13, tell students to match the fraction on the left with the picture on the right. Number 9 has been done for them. Point out that the fraction 2 2 tells us that the whole should be divided into 2 pieces, and 2 pieces should be shaded. Ask: Is that what the picture shows? [yes]

Common Errors

Students may not be used to reading and writing fraction notation. When they hear one-third, they may write 1 1 3 . Some students may see the fraction 3 4 and say “three fours” or “four thirds.” Practice fraction words aloud with students and remind them to think of a fraction as the top number “out of” the bottom number. For example, 3 4 means 3 out of 4.

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Check work for numbers 5 - 8. Assess

Objective and Learning Goals

y Identify fractions of a group

Vocabulary

y Whole - the entire thing or group of things that is divided into fractional parts

y Parts - the equal-sized sections or groups that something is divided into when talking about fractions

y Fractional part - each individual section or group that can be represented by a unit fraction, such as 1/2

Materials

y Counters

y Dry-erase board or blank paper

y Printable fraction cards (for game)

Pre-Lesson Warm-up

Guiding Questions

Fraction practice. Have students draw and divide shapes into equal parts, then shade a fraction of each part.

Draw a square. Divide it into 4 equal parts.

Shade 1 4

Draw a triangle. Divide it into 2 equal parts.

Shade 1 2 .

Draw a circle. Divide it into 4 equal parts.

Shade 3 4

Guiding Questions

1. How can we name fractions of a group? [the bottom number tells how many total in the group, and the top number tells how many we are talking about, so 3 4 is 3 out of 4]

Remind students that in the last lesson, they learned that the bottom number of a fraction tells them how many parts the whole is divided into, and the top number is how many we are talking about or are shaded. In today’s lesson, we will talk about fractions of a group of objects. The bottom number is still the whole, or the total number of objects. The top number is still the number we are talking about, or the number circled. Read the directions for the example, and ask: “How many total people?” [4] “How many are circled?” [2] “So that is 2 out of 4, or two-fourths.” Go through examples 1-8 in Try it Together in the same manner.

In numbers 9 - 12, have students first draw the total number of circles and then circle the number we are talking about. For number 9, say: “The fraction is three-fifths. How many total circles should we draw?” [5] “How many should we circle?” [3]

Activities

Students will demonstrate fractions with groups of counters with a partner. Write fractions on index cards, or use the printable fraction cards from the game (take out the cards with pictures on them). Have partners take turns drawing a card. They will get counters to represent the whole and place them on a dryerase board or blank paper. Then they will circle the fraction on the dry-erase board or paper. For example, if a student draws 2 3 , they will get 3 counters out and lay them on their paper. Then they will circle 2 of the counters. Partners should

each

and then switch roles.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Hang an anchor chart in the room that shows students that fractions can be read as “__ out of __.” The first blank is the top number, and the second is the bottom number.

Early Finishers

Choose some of the fractions on this page. For each fraction, draw a shape, divide it into parts and shade in parts to show the same fraction.

Challenge and Explore

Draw 4 shapes. Circle 2 of them. Write the fraction that you circled. [ 2 4 ] Now draw a pizza, divide it into pieces and color in pieces to show that same fraction. [students should draw a circle, divide it into 4 equal pieces and color in two of them] Can you divide your pizza into a different number of pieces and show an equivalent fraction? [divide it into 8 pieces and color 4

, or 2 pieces and color 1 2 , etc.]

Read the directions and explain to students that number 1 has been done for them. The fraction is 3 6 , so 6 shapes were drawn, and 3 were circled. Ask students how many shapes they will draw for number 2. [3] Have them do this. Then ask: How many of your shapes will you circle? [2] Tell students that in numbers 9-20, the shapes are already drawn and circled. They need to write the fraction. Ask: How many total apples are there in number 9? [7] How many are circled? [3] What fraction does this show? [three-sevenths]

Common Errors

Students often mix up the numerator and denominator. Some students will write the fraction for the group that is NOT circled.

Assess

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Check work for numbers 6, 8, 10 and 12.

Objective and Learning Goals

y Identify fractions on a number line

Vocabulary

y Fraction - a number that represents a part of a whole

y Parts - the equal size sections or groups that something is divided into when talking about fractions

y Whole - the entire thing or group of things that is divided into fractional parts

Materials

y Linking cubes, base 10 cubes, or other same-sized small blocks

y Counters or other small objects.

y Grid paper

y Printable fraction cards (for game)

Pre-Lesson Warm-up

Guiding Questions

Give students each a handful of linking cubes, or other small same-sized blocks. Have them connect the cubes or lie them next to each other in a straight line on a piece of paper. Instruct students to draw a straight line under the cubes and then make a vertical mark at the beginning of the cubes, end of the cubes, and at the end of each cube in between. Have students remove the cubes and tell them that they have made a number line. Have them start at 0 and label the marks on their number lines. Students will most likely label each mark after that with a whole number (1, 2, 3, 4, etc.) Tell students that today they will learn about fractions on a number line.

Guiding Questions

1. How can we use cubes to represent fractions on a number line? [line the cubes up and draw a vertical mark at the end of each cube. The line of cubes represent 1 whole. The total number of cubes tells us what fractional part to label each line; 2- halves, 3-thirds, etc.]

1. Make a fraction with cubes. This is a whole or 1 on the number line.

2. Make a mark after each cube on the number line.

There are parts in all. Each part of the number line is one-

3. Count the number of green cubes or the number of hops the frog makes. Write the fraction on the number line.

2. How can we represent fractions on a number line by making hops on the line? [the number of total hops from 0 to 1 tells what fractional part each hop is]

Look at Let’s Learn and show students how cubes can be used to section a number line into equal parts. We can think of a frog hopping from 1 cube to the next on the number line. Show them how to make a mark after each cube and remind them that the total number of parts, or hops, tells them what fraction each part is. Help students to count the parts and label the number lines. For number 4 in Try it Together, walk them through the steps. Ask, “How many sections is this number line divided into?” [5] “How many hops does the frog make to get from 0 to 1?” [5] “What fraction is each section?” [one-fifth] Say: “Each cube is one-fifth. Label the end of the first cube 1/5, the end of the second cube 2/5, and so on.” Check to make sure students label the fractions on the number line correctly.

Activities

Similar to the warm-up activity, give students each a handful of linking cubes, or other small same-sized blocks. Have them connect the cubes or lie them next to each other in a straight line on a piece of paper. Instruct students to draw a straight line under the cubes and then make a vertical mark at the beginning of the cubes, end of the cubes, and at the end of each cube in between. Have students remove the cubes to reveal their number line. Have them label the first mark “0” and the last mark at the end of the number line “1.” Now have students count their cubes, tell how many parts are in their number line and label each part with the correct fraction. For example, if a student had 6 cubes, their number line is divided into sixths. They should label 1/6, 2/6, 3/6, 4/6, and 5/6 on their number line. Point out that the end of their number line is the whole thing or 6/6.

Answers will vary. Possible answer: There are 4 sections or hops from 0 to 1 so the fractions should be fourths, not thirds. 1 is four-fourths

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Give students actual cubes to make the number lines with. Also, provide students with a counter or other small object to use to represent a frog. They can have the object hop from 0 to 1 and count how many times it hops before reaching 1. At the number 1 on the number lines, have students write in the fraction that represents one whole on that number line (2/2, 3/3, 4/4, 5/5, etc.)

Early Finishers

On a piece of paper students can use cubes to build and draw their own number lines. Students should label their number lines with fractions from 0 to 1.

Challenge and Explore

Guide students to find the mistake in the Challenge section by reminding students to count the number of sections or hops from 0 to 1. Allow students to use cubes or an object to “hop” with.

Have students share their explanations and work with students to construct coherent explanations and arguments to defend their answers. Have students revise their explanations as necessary.

Read the directions to the students. Explain that students can either count the number of blocks or the number of hops from 0 to 1 to find out how many fractional parts each number line is divided into. Emphasize to students that the whole, or 1 on the number line, could be written as a fraction with the same number on top as on bottom. For example, in number 1 there are 4 parts so 1 on the number line is 4 out of 4 or 4/4. Using grid paper, students can darken lines to make a number line with evenly spaced vertical marks. Have students count the total number of sections in the number lines they made and label each vertical mark with a fraction. Then trade with a partner to check their work.

Common Errors

Students may count the number of vertical lines on the number line instead of the actual number of sections that the line is divided into when deciding how many fractional parts the line is divided into. Students may get confused by the number of blank fractions to fill in between 0 and 1 since 1 would be the last fraction : 3/3, 4/4, etc.

Assess

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Check work for numbers 4 - 6.

Level C Chapter 9-6

Objective and Learning Goals

y Identify fractions on a number line

Vocabulary

y Fraction - a number that represents a part of a whole

y Parts - the equal size sections or groups that something is divided into when talking about fractions

y Whole - the entire thing or group of things that is divided into fractional parts

Materials

y Linking cubes, base-10 cubes, or other same-sized small blocks

y Pre-cut strips of paper

y Counters or other small objects.

y Printable fraction cards (for game)

y Sticky notes

Pre-Lesson Warm-up

Guiding Questions

As in the last lesson, give students each a handful of connecting cubes, or other small same-sized blocks and have them draw a number line under the cubes. Instruct them to section their number line by drawing vertical lines at the end of each cube. Tell them their number line should start at 0 and end at 1. Have them remove the cubes and label the fractions on their number lines. Remind students to first count the total number of sections on the line. Have them share their work with partners and help each other correct any mistakes.

Guiding Questions

1. How can we represent fractions on a number line? [count the total number of sections the line is divided into to find what fraction part each section is, then label the fractions in order on the line]

Let’s learn!

Fractions can be plotted and shown with a number line. Count the total amount of hops it takes to get to 1 whole. This is your denominator, or the amount of pieces in the

Introduce the Lesson (Try it Together)

Look at Let’s Learn and remind students that they can lay cubes over the top of a number line to divide it into sections and can think of a frog hopping from section to section to get from 0 to 1. Help students to count the number of sections in each number line and name the fraction that describes each section. Then have them fill in the fractions on the number lines in Try it Together.

Activities

Give each student a strip of paper. Have them fold the strip in half lengthwise and then in half again as many times as they want. After they unfold the paper, have them make tick marks on the folds and determine how many sections they divided their strip, or line, into. Then have them label the fractions on their strip of paper, starting with 0 on the left side and ending with 1 on the right side of the strip of paper.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Early Finishers

Students can create their own number line problems like in practice problems 4-7. Then trade their problems with a classmate, solve, and discuss their answers.

Challenge and Explore

Read the Challenge problem to the students:

The number lines in problems 6 and 7 are the same length. Explain why 3/4 is so much further along the line than 3/8.

Help students to understand and explain that the more sections the line is divided into, the shorter the sections will be. Therefore, fourths are longer than eighths.

Extend the problem by asking students “If we put three-tenths on the same line as threeeighths, would it come before or after threeeighths? Why?” [before because tenths would be shorter sections since there are more of them to fit on the line]

Read the directions to the students. Look at number 4 together. Tell students to start by counting the number of sections or hops between 0 and 1 so they can figure out what fractional part each section is. Tell them to label the fractions on the line if it helps them or to check their answers. Have students finish number 4 and clear up any misconceptions before having the students work on the practice page independently. When students are finished, allow time for them to check their work with a partner and discuss any disagreements that they have.

Common Errors

Assess

Draw a number line on the board and divide it into 5 sections. Label 0 and 1 on the number line like in practice problems 4 - 7. Circle the third line after 0. Ask students to write the fraction that you circled on a sticky note.

[3/5 ]

Objective and Learning Goals

y Identify and represent fractions in multiple ways

Vocabulary

y Fraction - a number that represents a part of a whole

y Parts - the equal size sections or groups that something is divided into when talking about fractions

y Whole - the entire thing or group of things that is divided into fractional parts

Materials

y Dry-erase boards and markers

y Number cards

y Sticky notes

Pre-Lesson Warm-up

Guiding Questions

Write the fraction 4/5 on the board. Ask the students which number is the numerator [4] and which number is the denominator [5]. Then have students describe what each number means. Remind students that they have learned multiple ways to represent fractions (circles, bars, part of a group, number lines) and have them draw one way to represent 4/5 on their dry-erase boards.

Guiding Questions

1. How can we represent the same fraction in different ways? [we can show the fraction on a number line, the part of a group of objects, or part of a shape or fraction bar shaded in]

2. How do we know if two different representations show the same fraction? [If the picture has the same number of parts in the whole and the shaded part, or part being talked about, is the same amount also]

Look at Let’s Learn and discuss each representation of fractions with the students, making sure they understand how each picture shows the given fraction. In each Try it Together problem, have the students tell what fraction each picture represents before deciding which picture to circle. You might have them write the fractions below each picture. Remind the students that the numerator tells how many parts are shaded or are being talked about and the denominator tells how many total parts are in the whole. Remind them to think numerator “out of” denominator. Also, remind them to think about blocks lined up above the number lines or making hops on the number line.

Activities

Have students draw two number cards. Have them make a fraction with the two numbers by putting the smaller number on top and the larger number on bottom with a line in between. Then have students draw 2 different ways to show the fraction that they made. For example, if they draw a 6 and a 2, they would make 2/6. They could show 2/6 in a fraction circle, fraction bar, fraction of a group of objects, fraction of a shape shaded in, or on a number line between 0 and 1. If time, challenge students to show their fraction in more than 2 ways or have them draw more cards to make another fraction to represent in multiple ways.

Draw two di erent ways to show the fraction.

Struggling Learners

Have students identify and write the fractions for all of the pictures before deciding which ones match correctly. If they find more than one that they think match, have them go back and count the number of parts in the whole and the number of parts shaded or circled again.

Circle the picture that shows the same fraction.

Do these two pictures show the same fraction? Explain how you know?

Possible answer: Yes, because both the circle and the number line are divided into 4 equal parts or fourths. 1 part is shaded in the circle so that is 1 /4 . The ﬁrst mark after 0 on the number line is circled, so that is 1 /4 also.

Apply and Develop Skills (Practice / Exercise page)

Early Finishers

Students can go through and “fix” the incorrect pictures to make them match the fractions or the other pictures shown. For example, in number 1, they could change the first picture to show just two triangles with one of them circled, so that the picture now shows ½.

Challenge and Explore

Present the following problem to the students:

There are 24 students in the 3rd grade class. They sit in 4 rows of 6 students each. If ¾ of the students eat school lunch on Tuesday, how many students eat school lunch? [18]

Have students suggest strategies for solving the problem. If students don’t suggest it, guide them to draw the 4 rows of 6 students and realize that each row is ¼ of the class, so 3 rows of students is ¾ of the class.

Read the directions to the students and do number 1 together. First ask a student to describe what the numerator and denominator in ½ tell us [there are 2 total parts and 1 should be shaded or circled]. Then have students finish the page independently. When students are finished, have them share their answers to number 7. After all students understand how these two pictures both show the same fraction, draw 2 pictures on the board that do not show the same fraction and have students discuss the same question as in number 7 with a partner. Then have some students share their answers with the class.

Common Errors

Students may struggle to pick out which pictures correctly represent the fractions and which pictures show the same fractions as other pictures. They may count sections on a number line incorrectly or look at the unshaded part of a shape instead of the shaded part.

Assess

On the board, write the fraction 1/5 . Have students draw 2 ways to represent this fraction on a sticky note.

Objective and Learning Goals

y Identify and represent fractions in multiple ways

Vocabulary

y Fraction - a number that represents a part of a whole

y Parts - the equal size sections or groups that something is divided into when talking about fractions

y Whole - the entire thing or group of things that is divided into fractional parts

Materials

y Poster board or large construction paper

y Crayons, markers, or colored pencils

Pre-Lesson Warm-up

Guiding Questions

Play a game of Around the World with the students using the printable fraction cards. Show two students a card and the first student who calls out the name of the fraction correctly moves on to the next student. Then show those two students a card. The goal is for a student to make it all the way around the classroom.

Guiding Questions

1. How can we represent the same fraction in different ways? [we can show the fraction on a number line, the part of a group of objects, or part of a shape or fraction bar shaded in]

Introduce

Look at Let’s Learn and review the different ways to represent fractions. Ask students to suggest other ways to represent fractions that are not pictured in Let’s Learn (fraction bars, fractions of a group). When working through the Try it Together problems, emphasize the meaning of the numerator and denominator by asking questions like “How many pieces are in the whole?” and “How many pieces should be shaded, circled, or hopped over?” If time, have students come up with more than 2 ways to show the fractions in numbers 4 and 5.

Activities

Have students work in partners or small groups to make posters to hang in the room that show fractions represented in multiple ways. Assign each group a fraction (1/2, 1/3, 2/3, 1/4, 3/4, etc). Have them show the fraction on their poster with a fraction circle, a fraction bar or fraction of a shape, a number line, and a fraction of a group of objects. Students can present their posters to the class before hanging them up in the room.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Call on students to remind the class of the meaning of the numerator and denominator and of all the different ways they have learned to represent fractions for numbers 6 and 7. Have the students complete the page independently.

Struggling Learners

Have students go back and count the number of parts in the whole and the number of parts shaded or circled to double check their work. Remind them to think “out of” when they see the fraction bar separating the numerator and denominator.

Early Finishers

Students can go back through the practice page and draw different ways to show each fraction on a piece of paper.

Challenge and Explore

Present the following problem to students.

Dad ordered two pizzas that were the exact same size. He cut the first pizza into 4 equal pieces and gave Mom 3 pieces. He cut the second pizza into 10 equal size pieces and gave Brother 3 pieces. Who got more pizza? [Mom]

Have students draw a picture to help them solve this problem and ask them to explain to a partner how they know their answer is correct. [the first pizza only has 4 pieces so the pieces are very large, 2 pieces is half of the pizza. The second pizza is cut into much smaller pieces. It would take 5 of them to make ½ of the pizza]

When students are finished, have them share their answers with a partner and check each other’s work.

Common Errors

Students may count sections on a number line incorrectly or look at the unshaded part of a shape instead of the shaded part.

Assess

Play Fraction Card Memory to practice identifying fractions. p. 318

Check work for numbers 6 and 7.

In Chapter 10, we will learn about equivalent fractions, comparing fractions and benchmark fractions.

• Understand that equivalent fractions show the same value

• Represent equivalent fractions using di erent numerators and denominators

• Compare fractions using fraction bars, shapes, groups and number lines

• Utilize benchmark fractions to help us identify and compare fractions

• Use symbols <, >, = to compare fractions

• Identify and explain fractions greater than 1

Vocabulary Words

Level C Chapter 10-1

Objective and Learning Goals

y Identify equivalent fractions

y Explain why a fraction is equivalent or not equivalent

Vocabulary

y Equivalent fractions - Fractions that are the same size and cover the same area of a whole or are on the same point on a number line

Materials

y Chart paper

y Small green paper (1 per student)

y Small red paper (1 per student)

y Fraction tiles

y Index cards

Pre-Lesson Warm-up Guiding Questions

On chart paper, draw various equivalent fractions with shapes. For example, draw two circles. Split one circle into 8 equal parts with 2 parts shaded. Split the other circle into 4 parts with 1 part shaded. Point to a shape and ask students: What fraction does this shape show? [answers vary based on the fraction] Repeat with the corresponding equivalent fraction. Guide students to notice how the fractions are similar.

Guiding Questions

1. How can you tell that the fractions are equal? [they have the same portion of the shape shaded]

2. Do any of these shapes have similar amounts shaded? [answers may vary; example answers may be 2/8 and ¼ have the same amount of the circle shaded]

Look at Let’s Learn and remind students that a fraction is a part of a whole. Explain that equivalent fractions are two or more fractions that cover the same area of a whole. Direct students to point to each example of equivalent fractions and explain that the amount of parts may be different, but the amount shaded is the same. Then, have students point to the non examples. Emphasize that equivalent fractions must cover the same amount of the same size whole. While looking at non examples, ask students: Why are these fractions not equivalent? [answers may vary based on the fraction]

Activities

Pass out a small green piece of paper and a small red piece of paper to each student. Draw two examples of fractions on the board or paper. For example, draw a square showing ¼ and a square showing ½. Direct students to hold up their green paper if the two fractions are equivalent and their red piece of paper if they are not equivalent. Repeat for more fractions.

Answers may vary. Example answer: both circles have the same amount of the whole shaded.

Look at the 2 pies. The chocolate pie plate is larger and has 1 2 the pie left. The berry pie is in a smaller plate, but has two-fourths left. Is there the same amount of pie left in each plate? Why or why not?

The chocolate pie has more because it is 1 /2 of a larger circle

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice have students correct the nonequivalent fractions shown in independent practice, numbers 5 and 6.

Struggling Learners

Allow students to explore equivalent fractions with fraction tiles. Direct students to match up fraction tiles to see how different fractions can cover the same amount of the whole. For example, direct students to place a ½ fraction tile down. Then, tell students to make an equivalent fraction with ¼ tiles. Tell them to place ¼ tiles on top of the ½ tile until they match. Repeat with other fraction values.

Early Finishers

Pass out 10 index cards to students. Have them draw various fractions on the 10 index cards. Then, tell students to flip over and spread out their fraction cards on the floor. Then, direct students to flip over two cards at a time to see if they find an equivalent fraction match. If they find a match, they keep the cards. If they do not find a match, they flip the cards back over.

Challenge and Explore

Present the problem. Have students draw the fractions and explain if the fractions are equivalent or not.

A large pizza is divided into 8 equal slices. 2 of the slices have been eaten.

A small pizza is divided into 4 equal slices. 1 out of the 4 slices have been eaten.

Are these slices of pizza eaten equivalent?

Discuss the results by asking the following questions:

1. What fraction of the large pizza was eaten? [2/8]

2. What fraction of the small pizza was eaten? [1/2]

3. Are these fractions equivalent? Why or why not? [these fractions are not equivalent because one pizza is large and the other pizza is small]

Common Errors

Students may think that fractions are not equivalent if the fraction numbers are not the same. Students may think a fraction is not equivalent because the denominator is bigger.

Assess

Draw two fractions on the board or on paper. Provide students with an index card. Direct students to write down if the fractions are equivalent or not and to explain their reasoning.

Objective and Learning Goals

y Shade in equivalent fractions on fraction bars or shapes

y Write equivalent fractions

y Mark equivalent fractions on a number line

Vocabulary

y Equivalent fractions - Fractions that are the same size and cover the same area of a whole or are on the same point on a number line

Materials

y Index cards

y Strips of white paper (all the same size)

y Fraction tiles

y Sticky notes

Pre-Lesson Warm-up

Guiding Questions

Pass out an index card to each student with a fraction drawn on it. Have students walk around to music. When the music stops, tell students to find a partner closest to them. Direct students to show their fraction cards to their partner. Then, tell students to discuss if their fractions are equivalent or not. After discussing, play the music again and direct students to find new partners.

Guiding Questions

1. Are your fractions equivalent or not? How do you know? [answers may vary. Example answer may be: Yes because they are shaded the same amount]

2. Do equivalent fractions have to have the same amount of parts? Why or why not? [No because they can still have the same amount of the whole shaded in]

Look at Let’s Learn and remind students that a fraction is a part of a whole. Direct students to point to the first set of fraction bars representing 1/2 and 2/4. Ask students: How many fourths are equivalent to 1/2? [2/4] Explain to students that these fractions are equivalent because they are shading the same amount of the whole. Ask students: Why does it take 2 parts out of the 4 to be equivalent to 1/2? [because the fourths are smaller] Emphasize to students that the numerator and denominator do not have to be the same in order for fractions to be equivalent. Next, direct students to shade in the sixths to make an equivalent fraction to 2/4. Ask students: What are the equivalent fractions shaded in this example? [2/4 and 3/6] Tell students to write the equivalent fractions.

Activities

Games

Play Fraction Card Memory to practice identifying fractions.

Pass out 3 strips of white paper (cut to the same size). Begin by directing students to fold one strip of paper in half. Tell students to shade in 1 out of 2 parts of the strip of paper. Next, direct students to grab a second strip of paper and to fold it into 4 equal parts. Direct students to shade in 2 out of 4 parts. Ask students: Why are these fractions equivalent? [because they have the same amount of the whole shaded in]. Then, direct students to grab the third strip of paper and to fold the paper into 8 equal parts. Direct students to shade in parts to make an equivalent fraction to 1/2 and 2/4. Ask students: How many parts did you shade in out of 8? [4]

Have students line the 3 strips of paper in a column. Tell students that each of these fractions are divided into different parts but they are equivalent because they have the same amount of the whole shaded.

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can draw an additional equivalent fraction for each problem in independent practice.

Struggling Learners

Early Finishers

Pass out more blank strips of paper to each student. Direct them to fold each strip of paper into equal parts. Remind them that each paper should have a different amount of parts. Then, tell students to shade in equivalent fractions for each strip.

Challenge and Explore

Present the problem. Direct students to draw and write their solution.

Jim and Mark each had a rectangle cake. Their cakes were the same size.

Jim cut his cake into 4 equal parts. 2 people ate pieces of Jim’s cake.

Mark cut his cake into 8 equal parts. 4 people ate pieces of Mark’s cake.

Mark thinks more of his cake was eaten.

Is Mark correct? Why or Why not?

Discuss the results by asking the following questions:

1. What fraction of Jim’s cake was eaten? [2/4] What fraction of Mark’s cake was eaten? [4/8]

2. Are these fractions equivalent? [Yes]

3. Is Mark correct? Why or why not? [No; the same amount of the cakes were eaten since they are equivalent fractions]

Common Errors

Students may think that fractions are not equivalent if the fraction numbers are not the same. Students may think a fraction is not equivalent because the denominator is bigger. Students may think equivalent fractions means shading the same amount of parts. For example, students may think shading in 1 out of 4 parts is equivalent to shading 1 out of 2 parts because 1 part is shaded in both cases.

Assess

Tell students to draw two equivalent fractions on a sticky note and to hang it on the equivalent fraction chart from the previous lesson.

Objective and Learning Goals

y Identify fractions that are greater using fraction tiles or images of fractions

y Draw and write fractions that are greater

y Identify equivalent fractions

Vocabulary

y Equivalent - the same, as in fractions that are the same size

y Whole - the entire thing or group of things that is divided into fractional parts.

Materials

y Fraction tiles

y Dominoes

y Paper

y Pencil

Pre-Lesson Warm-up

Guiding Questions

Pass out fraction tiles to students. Tell students to find the ½ fraction tile and the ¼ fraction tile. Guide students to match up the fraction tiles. Ask students: Which fraction tile is bigger? Repeat with other fraction tiles to compare.

Guiding Questions

1. What do we say if the fraction tiles are the same size? [they are equivalent]

2. If a fraction tile is bigger, is it greater than or less than the other fraction? [greater than]

We can decide which fractions are equivalent or greater.

• Shade in the fractions.

• Determine which fraction has more of the whole shaded.

Try it together!

Look at Let’s Learn and tell students that we can compare fractions to find which are equivalent and which are greater. Explain to students that the greater fraction has more of the whole shaded. Tell students to look at the first example with the fractions 1/2 and 2/3. Show students how 2/3 has more of the whole shaded in. Explain that 2/3 is greater than 1/2. Next, move to the fractions 2/4 and 2/8. Ask students: Which fraction has more of the whole shaded? [2/4] Circle 2/4 and explain that 2/4 is greater than 2/8. Finally, tell students to shade in the fraction for 1/2 and 1/4. Ask students: Which fraction has more of the whole shaded? [½] Which fraction is greater? [½] Direct students to circle 1/2.

Activities

Pass out dominoes and fraction tiles to students. Students get in pairs. Each student places their dominoes face down on the floor. Students flip over a domino at the same time. Then, students use their fraction tiles to make the fraction pictured on the domino. For example, if a student flips over a domino with 3 dots on top and 4 dots on bottom, students use their fraction tiles to make 3/4. Students then compare their fraction tiles to see which domino fraction is greater (covers more of the whole). The student with the greater fraction keeps both dominos. If fractions are equivalent, students return each dominos back into their group.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Allow struggling students to build each fraction from Try it Together and independent practice with fraction tiles. Let them line-up or stack the fractions in order to compare. This will allow them to see which one is bigger or covers more of the whole.

Early Finishers

Students can continue playing the domino comparing game with a partner. If playing independently, students can flip over two dominos, compare them with fraction tiles, and place the greater fraction domino in a “winner's” pile.

Challenge and Explore

Ask students to find two fractions that are greater than ½. Allow students to draw or use fraction tiles to find the two fractions.

Discuss the results by asking the following questions:

1. How did you find which fractions are greater than ½ [answers may vary; example answer is: I used fraction tiles to compare to ½. The tiles combined that are bigger are greater than ½.]

2. Are your two fractions equivalent? Is one greater than the other? [answers may vary]

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can explain their independent practice answers to a friend. When explaining, students can compare their answers to their partner’s answers. Students should find out that there are different solutions. More than 1 fraction can be greater than the fractions listed. Have students discuss if their fraction is greater than or equal to their partners fraction for each problem.

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Common Errors

Assess

Tell students to draw two fractions on paper (fraction bars or circles) and to circle the greater fraction.

Objective and Learning Goals

y Draw to compare fractions using multiple models including fraction bars, shapes, number lines and groups of objects

y Compare fractions using <, > and = symbols

Vocabulary

y Equivalent - the same, as in fractions that are the same size

y Whole - the entire thing or group of things that is divided into fractional parts

Materials

y Chart paper

y Sticky notes

y Fraction tiles

y Index cards

y Dry-erase boards

y Dry-erase markers

Pre-Lesson Warm-up

Guiding Questions

Create a t-chart with the titles “less than ½,” “equal to ½” and “greater than ½.” On a sticky note, write a fraction. Tell students to use their fraction tiles to compare the fraction to ½. Ask students if it is less than (smaller), equal to (the same size) or greater than (bigger) ½. Sort the sticky notes on the anchor chart accordingly. For example, hold up the fraction ¼ on a sticky note. Students take out a ½ fraction tile and a ¼ fraction tile. Students compare the tiles and determine that ¼ is less than ½.

Guiding Questions

1. How do you know if a fraction is greater than ½? [it is bigger or is more of the whole]

2. How do you know if a fraction is equivalent or equal to ½? [they are the same size]

Same Numerator

If the numerator is the same, the fraction with the smaller denominator is greater.

Same Denominator

If the denominator is the same, the fraction with the larger numerator is greater.

Teacher Notes

Introduce the Lesson (Try it Together)

Look at Let’s Learn and tell students that we can compare fractions by using various models. We can also use symbols, <, > and =, to compare fractions. Have students point to the first fraction comparison example. Ask students: Are the fractions equivalent? [no] Which fraction is greater? [¾] Remind students that 3/4 is greater because more of the whole is shaded. Show students how the symbol faces the greater fraction. Describe the symbol as opening its mouth to eat the greater number. Continue on with the other 3 examples. For each example, ask students if the fractions are equivalent. If not, ask students which fraction is greater.

Activities

Write two fractions on the board. Direct students to use their fraction tiles to compare the two fractions.Then, direct students to hold up their arms in the shape and direction of the correct comparison symbol (<,> or =). For example, write 2/3 and 1/4 on the board. Direct students to use their fraction tiles to compare 2/3 and 1/4. Then, tell students to hold up their arms to show their symbol. Student arms should match the > symbol. Repeat with other fraction pairs.

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can work on putting groups of 3 fractions, from independent practice, in order from least to greatest. Students can write their fractions in order on a dry-erase board. Students can use fraction tiles to help order the fractions.

Struggling Learners

Early Finishers

Pass out 10 index cards to students. Students write 10 different fractions on each index card. Students place their 10 cards face down and spread out on a table or the ground. Then, students flip over two cards at a time. Students compare the two fractions. The greater fraction goes in the "winner's" pile. The other fraction gets flipped back over. Students keep playing until they have the last card left - the “losing” card.

Challenge and Explore

Put these fractions in order from least to greatest on a dry-erase board. Use fraction tiles to help compare.

1/2, 3/4, 1/3, 4/6 [1/3, 1/2, 4/6, 3/4]

Discuss the results by asking the following questions:

1. Which fraction was worth the least amount? How do you know? [1/3 because it covered the least amount of the whole]

2. Which fraction could 2/4 replace in this order? Why? [1/2 because they are equivalent]

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Common Errors

Students may assume that the fraction with the greater denominator is the greater fraction. For example, students may assume that ¼ is greater than ½ because 4 is greater than 2. Students may also assume that fractions can not be compared with different denominators. Students may draw their symbols incorrectly. Remind students that the “mouth” of the symbol opens to “eat” the greater number or fraction.

Assess

Have students draw the symbol (<, > or =) for each fraction pair. Direct students to use fraction tiles to help solve.

1. 1/2 < 3/4

2. 1/3 > 1/8

Objective and Learning Goals

y Draw to compare if fractions are greater than or less than 1

y Write how many whole amounts and parts are left over in fractions greater than 1

y Write <, > or = for fractions when compared to 1

Vocabulary

y Parts - the equal size sections or groups that something is divided into when talking about fractions

y Whole - the entire thing or group of things that is divided into fractional parts.

Materials

y Popsicle sticks

y Modeling clay

y Fraction tiles

y Dry-erase boards

y Dry-erase markers

Pre-Lesson Warm-up

Guiding Questions

Pass out a popsicle stick and modeling clay to each student. Direct students to make a “cookie” out of the clay. Direct students to use the popsicle stick to cut their cookie in half. Ask students: How many pieces are there in the whole? [2] Show students the fraction 2/2. Remind students that this shows a whole. Then direct students to cut their cookies into fourths. Ask students: What is the fraction for this whole? [4/4]

Guiding Questions

1. If I took a 1 out of the 4 parts away, what is the fraction? [¾]

2. Is this fraction greater than 1 or less than 1? [less] How do you know? [because a part of the cookie is gone]

Look at Let’s Learn and explain to students that they can shade fraction parts to determine if a fraction is greater than or less than 1. Show students the fraction 6/4. Explain that this fraction has a whole and 2 out of 4 parts left over, so it is greater than 1. Direct students to look at the fraction 5/2 and to shade in 5 parts. Ask students: How many whole circles did you shade? [2] How many left over parts are there? [1 out of 2] Is this fraction greater or less than 1? [greater]. Move to the fraction 2/4. Explain to students that this fraction does not have a whole shaded in, so this fraction is less than 1. Direct students to look at the fraction 1/3 and to shade in 1 part. Ask students: How many whole circles did you shade? [none] Is this fraction greater than or less than 1? [less]

Activities

Pass out a popsicle stick and modeling clay to each student. Direct students to make 2 circles or “cookies” out of their clay. Tell students that their “cookies” should be the same size and shape (or as close as possible). Tell students that they have 2 whole cookies. Next, direct

students to cut their “cookies” into fourths. Ask students: How many parts did we cut each whole into? [4] How many parts do we have in all? [8] Write this fraction on the board (8/4). Explain to students that fractions can be written to be greater than 1. 8/4 is greater than 1 because it fills up 2 whole cookies.

Next, write the fraction 6/4 on the board. Direct students to count 6 pieces of their “cookies” and to move the extra (2) pieces away. Next, direct students to see how many whole cookies they can make with their 6 pieces. Ask students: How many wholes can you make with the 6 parts? [1] How many are left over? [2]. Tell students this fraction is also greater than 1 because you made 1 whole and have some parts, or a fraction, left over. Repeat with more fractions like 5/4 and 7/4 for students to see fractions greater than 1.

Conclude with a fraction less than 1 like ¾. Ask students: Were you able to make a whole cookie? [no] Explain that this means the fraction is less than 1.

Solve the riddle. Write the fraction. Draw to explain.

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can write their own fractions on a dry-erase board. Students can share their fractions with a partner and ask their partner to circle the fractions that are greater than 1. Students can use fraction tiles to help determine which fractions are greater than 1.

Struggling Learners

Allow struggling students to build each fraction from Try it Together and independent practice with fraction tiles. Let them line-up or stack the fractions onto a whole bar in order to compare. This will allow them to see if it is greater or less than a whole.

Early Finishers

Allow students to build their own fractions with modeling clay. Tell students to make 2 cookies. Then, tell students to cut their cookies into equal parts. Finally, direct students to move away parts of the cookies to see what fractions they can make. For example, students may cut their two cookies into eighths. Then, students may take away 5 parts. Students can discover they made 1 whole and 3/8 left over.

Challenge and Explore

Jim wrote these two fractions down and said they were the same. Is Jim correct? Draw fraction circles to explain.

1 ¼ is the same as 5/4.

Discuss the results by asking the following questions:

1. How many circles can you shade in for the fraction 5/4? [1 whole circle]

2. How many parts are left over? [1 out of 4]

3. Are these fractions the same? [yes]

Games

Play Fraction Card Memory to practice identifying fractions.

Common Errors

Students may assume that the denominator of a fraction greater than 1 should be the total amount of parts combined. For example, if two circles are divided into 4 equal parts and 7 parts are shaded, students may think the denominator is 8 (2 circles with 4 parts each, is 8 in all).

Have students write <,> or = for the the following fractions. They may use fraction tiles or draw pictures to help them solve.

Objective and Learning Goals

y Identify the benchmark fraction (0, ½ or 1) that is closest to a given fraction

y Compare benchmark fractions to a given fraction using symbols (<, > or =)

Vocabulary

y Benchmark fraction - commonly used fractions that are easy to visualize and identify

Materials

y Paper

y Fraction tiles

y Dominos

y Index cards

Compare Fractions to Benchmark Fractions

• Benchmark fractions are commonly used fractions that are easy to visualize and identify.

• Is the fraction less than <, greater than > or equivalent = to the benchmark fraction?

Pre-Lesson Warm-up Guiding Questions

Review the meaning of equivalent fractions with students. Tell students they will play a matching game to find equivalent fractions to ½ and 1 whole. On 10 sheets of paper write the fractions below. Then, place the papers face down and spread them out on the ground. Students will take turns flipping over 2 papers at a time. Students must find a fraction and its equivalent benchmark. If they match a fraction and a benchmark, they put the papers in the winner pile. If the two papers do not have equivalent fractions, students flip them back over.

Introduce the Lesson (Try it Together)

Guiding Questions

1. Why is 5/5 the same as 1? [They both represent a whole]

2. Are 2/4 and 3/6 equivalent? How do you know? [Yes because they are both equivalent to ½]

Look at Let’s Learn and explain to students that we can compare fractions to a benchmark fraction. Benchmark fractions are fractions that are easy to visualize and identify. To compare, align fractions on a number line or use fraction bars or tiles to see if the fraction is greater than, less than or equal to the benchmark. Direct students to look at ¾ compared to ½. Explain to students that ¾ is past ½ on the number line. This means it is greater than ½. Trace the symbol. Direct students to look at 5/6 compared to 1 whole (or 3/3). Ask students: Is 5/6 greater than or less than 1 whole? [less] How do you know? [less of the bar is shaded] Trace the symbol.

Activities

Pass out fraction tiles to each student. Direct students to line up a whole fraction tile and a half fraction tile. Write a fraction on the board. Then, tell students use their fraction tiles to build this fraction and compare it to the benchmark. Ask students if the fraction is closer to 0, ½ or 1.

For example, write the fraction 1/8 on the board. Direct students to build 1/8 with their fraction tiles. Then, ask students: How many tiles away is 1/8 from 0? [1 tile] How many more 1/8 tiles would you need to get to ½? [3] How many more would you need to get to 1? [7] So, is 1/8 closer to 0 ½ or 1? [0]

Repeat with other fractions like 5/6, 2/4, and 2/6.

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can write 10 fractions on index cards. Then students can work with a partner to shuffle their fraction cards together and sort them into 2 piles - closer to 0 or closer to 1.

Struggling Learners

Early Finishers

Pass out dominos to students. Students pick a domino and compare it to the benchmark fractions ½ and 1. Students may use fraction tiles to help compare. Students sort the dominos into closer to ½ or closer to 1 piles.

Challenge and Explore

Present the following problem to students:

Rob checked his cat’s food bag. The bag has 7/8 left in it. Rob’s mom said to go buy more cat food when there was ½ left in the bag. Does Rob need to go buy more food?

Discuss the results by asking the following questions:

1. What benchmark is 7/8 closest to? [1]

2. So if 7/8 is closest to 1, does Rob need to buy more food? [no]

3. Would Rob need to get food when the bag is at 4/8? Why or Why not? [Yes because 4/8 is equivalent to ½]

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Common Errors

Students may assume that fractions are closer to ½ if they are not a whole (like 3/3). Students may assume that fractions are closer to 1 if their denominator is a large number.

Assess

Write different fractions on sticky notes and pass them out to each student. On a piece of chart paper, draw a number line with 0, ½ and 1 marked on it. Direct students to place their fraction on the benchmark it is closest to.

Objective and Learning Goals

y Read and draw fractions from a word problem

y Compare fractions from a word problem

y Write to explain a fraction comparison word problem

Vocabulary

y Equivalent - the same, as in fractions that are the same size

y Whole - the entire thing or group of things that is divided into fractional parts

y Parts - the equal size sections or groups that something is divided into when talking about fractions

Materials

y Beach ball

y Fraction tiles

y Dry-erase boards

y Dry-erase markers

y Paper

y Crayons

y Sticky notes

Pre-Lesson Warm-up

Guiding Questions

Write different fractions all over a beach ball. Tell students to sit in a circle on the ground. Pass out fraction tiles to each student. Toss the beach ball to a student. Ask the student to share the fraction their left hand is closest to or touching. Write this fraction on the board. Then ask the student to share the fraction their right hand is closest to or touching. Write this fraction on the board. Ask students to use their fraction tiles to determine which fraction is greater. Call on a student to share which fraction is greater. After solving, direct the student with the ball to pass it to another student.

Guiding Questions

1. How do you know which fraction is greater? [the one that is more of the whole]

2. How could you solve for which fraction is greater without using fraction tiles? [compare it to benchmark fractions]

Look at Let’s Learn and explain to students that they will read fraction comparison word problems. Read the word problem to students. Ask students: What is the fraction of pizza that Tim ate? [2/6] What is the fraction of pizza that John ate? [2/4]. Direct students to look at the fraction circles. Who’s pizza has more of the whole shaded? [John’s pizza] Direct students to circle John.

Activities

Read a fraction comparison story problem to students. Direct students to use fraction tiles to solve the word problems. Then, tell students to write their answers on a dry-erase board. Walk around to check student answers and fraction tiles.

Story problems:

Jeb completed 2/3 of his painting. Tom completed 2/8 of his painting. Who completed more of their painting? [Jeb]

Tim read 1/2 of his book. Sam read 3/4 of his book. Who has more book left to read? [Tim]

Larry shared 2/8 of his pizza. Dan shared 4/5 of his pizza. Who shared more pizza? [Dan]

Sam Joe Jim Tony

Read the story problem. Shade in the fraction bars. Circle the answer.

1 Larry went to the grocery store. 1 5 of the food Larry bought were fruits. 3 5 of the food he bought were vegetables. Did he buy more fruit or vegetables?

2 Joshua ate 2 5 of apple pie. Tom ate 6 7 of pumpkin pie. Whose pie has more left?

3 Sam was at a zoo. 3 6 of the animals he saw were zebras. 1 6 of the animals he saw were gira es. Which animal did he see more of?

4 Ezra completed 1 3 of his homework. Greg ﬁnished 1 4 of his homework. Who has more homework left?

Struggling Learners

Early Finishers

Pass out a piece of paper and crayons to each student. Direct students to draw a picture and to write a story problem to match their picture. Tell students that their story problem must be a fraction comparison problem. Then, students can switch their story problem with a partner. Students can solve their partner’s word problem.

Challenge and Explore

Present the following problem to students:

5 Henry cut his brownies into 8 pieces. He gave away 2 pieces. Patrick cut his brownies into 3 pieces. He gave away 2 pieces. Who has more brownies left? How do you know?

Read the story problem. Use the fraction bars to help solve. Write to explain your answer. Henry

Explanations will vary. Example explanation - Henry has more brownies left because the pieces he gave away were smaller.

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can explain their solutions for each story problem to a partner. Students can also explain how they can use benchmark fractions (0, ½ and 1) to check their solutions.

Tim ate 4/6 of his cookie. Ezra ate 2/3 of his cookie. Who ate more of their cookie?

Discuss the results by asking the following questions:

1. What do you notice about the fractions when you use fraction tiles? [they are both the same amount of the whole]

2. So, who ate more of the cookie? [They ate the same amount]

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Common Errors

Assess

Read the story problem to students. Direct students to draw fraction circles or bars on a sticky note to solve.

William ate 6/8 of his sandwich. Saul ate 4/8 of his sandwich. Who ate more of their sandwich? [William]

Objective and Learning Goals

y Identify equivalent fractions

y Put fractions in order from least to greatest

y Identify and write fractions that are greater than 1

y Use symbols, <, > and =, to compare fractions

Vocabulary

y Benchmark fraction - commonly used fractions that are easy to visualize and identify

y Equivalent - the same, as in fractions that are the same size

y Whole - the entire thing or group of things that is divided into fractional parts

Materials

y Fraction tiles

y Index cards

y Playing cards

y Dry-erase boards

y Dry-erase markers

Pre-Lesson Warm-up

Guiding Questions

Write a fraction on the board. Tell students to make the fraction with their fraction tiles. Tell students to give a thumbs up if the fraction is greater than 1/2 and a thumbs down if it is less than 1/2.

Guiding Questions

1. How do you know if the fraction is greater than 1/2? [compare it to the ½ fraction tile]

2. Why is it helpful to compare to ½? [½ is easy to remember and identify]

Introduce the Lesson (Try it Together)

Look at Let’s Learn and emphasize to students that fractions can be represented with different visual models. Ask students: What are some ways we can show a fraction? [fraction tiles, fraction bars, shapes, number line, groups, etc.] Tell students that these visual models help us to compare fractions. We can compare fractions to each other to find the greater fraction or to find equivalent fractions. Ask students: How do you know which fraction is greater than another? [the fraction that is more of the whole] What does it mean to be equivalent fractions? [fractions that are the same size] Finally, remind students that fractions can be compared to benchmark fractions, or fractions that are easy to visualize. Ask students: What are some benchmark fractions? [0, ½ and 1]

Write fractions (less than or greater than 1) on index cards. On the back, draw the corresponding fraction bar. Put only one fraction and drawing on a card. Pass out 1 card to each student. Tell students to stand up and walk around to music. When the music stops, students must find a partner closest to them. Provide a fraction discussion topic for students to discuss with their partner. Walk around to listen to student discussions. Then, play the music again and have students find a new partner. Provide students with a new discussion topic

Fraction Discussion Topics:. Whose fraction is closer to the

Whose fraction is greater? Are your fractions equivalent? Why or why not?

Whose fraction is less?

Are your fractions greater than 1? How do you know?

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can create their own fraction review questions on a dry-erase board. Students can switch their boards with a partner and solve. Remind students to include an equivalent fraction question, benchmark question, and a fraction greater than 1 question.

Struggling Learners

Early Finishers

Pass out a stack of playing cards to each student. Students work with a partner. Students put their cards in a pile face down. Both students flip over two cards. Students use their two cards to make a fraction. For example, a student may flip a 2 and a 5. Students can make the fraction 2/5 or 5/2. Students compare their fractions. The student with the larger fraction keeps all 4 cards. Students keep playing until one student collects all of the cards.

Challenge and Explore

Present the following problem:

Paul has 2 candy bars. He split each candy bar into parts. He ate 6/4 of the candy bars. Did he eat more than 1 whole candy bar?

Discuss the results by asking the following questions:

1. What parts did Paul split his candy into? [fourths]

2. Is 6/4 more than 1 whole? [yes]

3. How do you know? [answers may vary. Example answers - 1 whole is 4/4 and 6/4 is more; 6/4 fills a whole fraction bar and 2 left over]

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Common Errors

Students may assume that the fraction with the greater denominator is the greater fraction. For example, students may assume that ¼ is greater than ½ because 4 is greater than 2. Students may also assume that fractions can not be compared with different denominators. Students may draw their comparison symbols incorrectly. Remind students that the “mouth” of the symbol opens to “eat” the greater number or fraction.

Assess

Have students write the answers on a sticky note. They can use fraction tiles for help.

1. Write a fraction greater than 1.

2. Write a fraction less than ½.

3. Write an equivalent fraction to ½.

Chapter 11

In Chapter 11, we will practice how to measure to the nearest inch, half inch and quarter inch. We will also practice ﬁnding perimeter and area, and learn about measuring volume and mass.

• Measure more accurately by measuring to the nearest inch, 1 2 inch and 1 4 inch

• Use ruler lines to help us measure more accurately

• Perimeter is a measurement of the distance around the outside of a shape

• Area is the space inside a shape

• Calculate the area in terms of square units

• Liquid volume can be measured with mL

• Capacity is how much a container can hold

• Measure mass by comparing objects on a balance scale

Objective and Learning Goals

y Measure objects to the nearest 1 4 inch

Vocabulary

y Inch - a unit of measurement that is onetwelfth of a foot

Materials

y Rulers

y Several small objects such as paper clips, glue sticks, erasers and base-10 rods

Pre-Lesson Warm-up

Guiding Questions

Practice counting out loud by 1 2 inches [0 in, 1 2 in, 1 in, 1 1 2 in, 2 in, 2 1 2 in, 3 in, 3 1 2 in, …..]

Practice counting out loud by 1 4 inches [0 in, 1 4 in, 1 2 in, 3 4 in, 1 in, 1 1 4 in, 1 1 2 in, 1 3 4 in, 2 in …..]

Guiding Questions

1. How can we measure things accurately? [use the little lines in between whole inches to measure to the nearest 1 2 and 1 4 inches to get a more accurate measurement]

learn!

Hand out rulers to students. Before measuring anything, spend some time looking closely at the rulers with students. Ask them to point to the line on the ruler that shows 1 inch. Then ask them to point to the line that shows 1 2 an inch. Ask: “How do you know which line shows 1 2 an inch?” [it is halfway between 0 and 1 inch, and it is longer than the other lines] Next, have students point to the line that shows 1 4 of an inch. Ask: “How do you know which line shows 1 4 of an inch?” [it is halfway between 0 and 1 2 inch, and it is slightly longer than the other lines around it] Demonstrate for students how to measure objects to the nearest quarter inch by using the lines on the ruler to help them decide which measurement the object is closest to. Work through problems 1-10 together with the students. Make sure that students know how to correctly write the fractional parts of an inch.

Activities

Students will practice measuring small objects. Students will each need a ruler. Hand out a set of small objects to each small group. Be sure that each group has the same objects and they are the same length. You could give each small group a large paperclip, an unused eraser, a glue stick and a base-10 rod. Have each student in the group take turns measuring and recording the length of each object to the nearest 1 4 inch, passing the objects around the group. When everyone in their group has measured each object, they should compare their measurements and spend some time clearing up any disagreements about the length of the objects. Go over the correct measurement for each object and ask students to measure again if they did not get the correct answer. Discuss any difficulties they had agreeing on the correct measurement.

Circle all the objects that measure half an inch (2 in)

Struggling Learners

Write or have students write the 1 4 inch and 1 2 inch labels on the rulers before measuring the objects.

Early Finishers

Measure other small objects around the room or in your desk. Make a T-chart with the names of the objects on one side and the measurement to the nearest 1 4 inch on the other.

Challenge and Explore

Review the Challenge problem with students. Guide students to set up a t-chart for the days and length of caterpillar.

Day 1 3 cm

Day 2 [5 cm]

Day 3 [7 cm]

Day 4 [9 cm]

Samuel is watching a caterpillar grow before it becomes a butterﬂy. The ﬁrst day he measured the caterpillar it was 3 cm. The caterpillar grew 2 cm each day. How long was the caterpillar on the fourth day?

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, direct students to use their rulers to measure the objects from the activities section in centimeters.

Discuss the results by asking the following questions:

1. What equation could we use to solve this problem? [3 cm + (2 cm x 3) = 9 cm]

Games

Play The Measurement is Right to practice estimating and measuring lengths. p. 314

Common Errors

Students may not know how to write fractions correctly and may only write 1 2 when they mean 1 1 2 . Students may not take their time and measure carefully or may not line up the edge of the object with the zero on the ruler.

Assess

Provide 2 objects for students to measure and record the length to the nearest 1 4 inch.

Level C Chapter 11-2

Objective and Learning Goals

y Measure objects to the nearest inch, ½ inch, and ¼ inch

Vocabulary

y Inch - a unit of measurement that is onetwelfth of a foot; there are 12 inches in 1 foot

Materials

y Inch rulers

y 2 objects that are not the same exact length, but measure the same to the nearest inch

y Small objects to measure

Pre-Lesson Warm-up

Guiding Questions

Show students two objects that both measure the same when measured to the nearest inch, but one is visibly, slightly longer than the other. Ask students which object is longer and then show them how you measure the two objects to the nearest inch. Ask: “If one object is longer, how come we get the same answer when we measure them?” [you need to measure using a smaller unit because they are close to the same length]

Guiding Questions

1. How can we measure more accurately when measuring in inches? [use the lines in between the inch marks on the ruler to measure to the nearest ½ inch or ¼ inch]

2. Why do we sometimes get the same answers when measuring to the nearest inch, ½ inch or ¼ inch? [when measuring to the nearest ½ inch, the object could still be closest to a whole inch, and when measuring to the nearest ¼ inch, the object could still be closest to a whole or ½ inch mark]

Look at Let’s Learn and discuss with students how we can measure more accurately by measuring to the nearest ½ inch and even more accurately than that if we measure to the nearest ¼ inch. Show students how to use the lines on the ruler to determine which inch, ½ inch, or ¼ inch the object is closest to. Work through the Try it Together problems with the class. Point out that sometimes the answers will be the same like in number 1 where measuring to the nearest ½ and ¼ inch are both 2 ½ inches.

Activities

Have students practice measuring small objects from inside their desks or within the classroom. They should measure to the nearest inch, ½ inch, and ¼ inch and record the measurements. Then they can trade objects with a partner and see if they agree on the measurements. They should remeasure and discuss the results to settle any disagreements.

Measure your pencil to the nearest inch, 1 2 inch, and 4 inch.

Nearest inch = inches

Nearest 1 2 inch = inches

Nearest 1 4 inch = inches

Nearest inch = inches

Nearest

Measure another small object to the nearest inch, 1 2 inch, and 1 4 inch. Object:

Struggling Learners

Provide students with an index card or other straight edge to line up the end of the object they are measuring. Practice counting by ½ inches and ¼ inches. If possible, give students paper rulers and have them write in the counts at the correct marks on the ruler.

Early Finishers

Students can make a 3-column chart where they measure several objects to the nearest inch in column 1, then ½ inch in column 2, then ¼ inch in column 3. Have students compare and contrast the 3 measurements.

Challenge and Explore

Have students solve the following problem:

This object measures a di erent length each time when you measure ﬁrst to the nearest inch, then the nearest 1 2 inch and then nearest 4 inch.

an object ever measure the same length for all 3 measurements? Explain.

Answers will vary. Possible answer: Yes, if the object ends exactly at an inch mark, such as 4 inches, then all 3 measurements would still be 4 inches.

Sam drew a rectangle. The sides measured 2 ½ inches, 3 inches, 2 ½ inches, and 3 inches. What is the total of all 4 sides added together? [11 inches]

Have students sketch a rectangle and label the side lengths. Ask students how they added the side lengths. Students should realize that they can combine the ½ inches to make 1 whole inch when adding.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Allow them time to practice measuring carefully and double check their work. When students are finished, discuss their answers to number 8. If possible find an object that measures exactly a whole inch measurement to demonstrate for the students. Find an object that might round up to the nearest inch and and one that rounds down to that same inch. These objects will be different lengths, but they will be measured to the same inch. Remind students that an object that measures 2/4 of an inch is the same as an object that measures ½ inch. Look for patterns on the ruler to help students see fractions of an inch. Encourage students to work carefully and take their time to get the most precise measurement as possible. If students have different answers, have them explain their reasoning for which was the closest measurement.

Common Errors

Students may have trouble lining objects up and looking at the ruler carefully to determine which mark the object is closest to. Some students think that if you are measuring to the nearest ½ inch or ¼ inch, the answer has to have that fraction in it. For example, they may think the answer has to be 2 ½ inches or 3 ½ inches, and can’t be just 3 inches.

Games

Play The Measurement is Right to practice estimating and measuring lengths. p. 314

Assess

Objective and Learning Goals

y Find the perimeter of a shape

y When given the perimeter, find a missing side length

Vocabulary

y Perimeter - the distance around the outside; found by adding all of the side lengths

Materials

y Pattern blocks or shapes to trace

y Rulers

y Blank paper

learn!

• The measurement all the way around the outside of an object

• To ﬁnd the perimeter, add up the lengths of all the sides.

Pre-Lesson Warm-up

Guiding Questions

Draw a rectangle on the board.Tell students that it shows a map of the sidewalk around the park. Label the short sides of the rectangle 24 ft and the long sides 40 ft. Ask students how far they would walk if they walked all the way around the park once. [128 ft] Have students share their strategies. Tell students that this is called the perimeter.

Guiding Questions

1. How can we find the perimeter of a shape? [add up all of the side lengths]

2. How can we find a missing side length when given the perimeter and the other side lengths of the shape? [add the known side lengths and subtract them from the perimeter]

Look at the Let’s Learn and explain what perimeter is. Have students trace the perimeter of the shapes with their finger. Discuss different strategies for adding the side lengths to find the perimeter. Students might first add side lengths that make 10, for example. Have students help you do numbers 1 and 2 in Try it Together. Then explain that to find missing side lengths, they will need to add the known side lengths and subtract that from the perimeter. They could also add the known side lengths and count up to the perimeter, keeping track of how much they count, to find the missing side length.

Activities

Give students a few different pattern blocks. Have them trace the shapes onto a piece of blank paper. Then have them measure the sides of the shapes to the nearest centimeter and label the sides. Last, have them add the side lengths to find the perimeter of each shape.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Ask a student to remind the class what perimeter means and how to find the perimeter. Also ask a student to remind the class how we find a missing side length when we know the perimeter.

Struggling Learners

Have students write down the equations and record the answers as they add each side length. When helping students with missing side length problems, ask “How much do we need to add to ____(the known sides added together) to get ____” (the perimeter). For example, in number 5, ask “How much do we need to add to 7 to get to 9?” [2]

Early Finishers

Students can draw shapes on a blank piece of paper using a straight edge. Then measure the side lengths and find the perimeter. They can write their side lengths and perimeters on a separate sheet of paper or on the back. Then trade with a partner and find the perimeter of each other’s shapes.

Challenge and Explore

Read the word problem in the Challenge section to the students. Tell students to draw a picture to represent the problem and then solve. Discuss their strategies for adding the larger numbers to find the perimeter.

Tell students that a student in another class solved for the missing side length in number 6 and got 25 centimeters. Ask “Could that be right?” [no] “Why or why not?” [25 cm is only 1 less than the perimeter of the whole triangle so the other two sides together would have to add up to only 1] Then have them look back at their own answers to make sure they are reasonable.

Students may lose track of which numbers they have already added when adding multiple numbers to find the perimeter. Some students will struggle to find missing side lengths. Common Errors

Games Play The Measurement is Right to practice measuring. p. 314

Check work for numbers 3 and 5. Assess

Objective and Learning Goals

y Find the area of a rectangle using repeated addition and multiplication equations

y Partition rectangles in rows and columns

Vocabulary

y Area - the space inside an object or shape; measured in square units

y Square units - the units used to measure area; 1 square unit equals the area taken up by a square with all sides 1 unit in length

Materials

y Picture of a room with a square tile floor if the classroom floor is not made up of square tiles

y Grid paper

y Crayons, markers, or colored pencils

y Scissors

y Glue sticks

y Construction paper

y Sticky notes

Pre-Lesson Warm-up

Guiding Questions

If the classroom floor is made of square tiles, direct students’ attention to the tiles on the floor. If not, show a picture of a square tiled floor. Explain to students that each tile is, for example, 1 foot on all sides, so that tile is 1 square foot. Tell students that we can measure the area, or space inside, a room by calculating the number of square feet inside the room. Have children begin counting the tiles. Then ask for the student’s ideas for ways to find out how many square feet are in the room without having to count each individual square one by one.

Guiding Questions

1. How can we use repeated addition to find the area? [count how many squares are in one row and add that number as many times as there are rows]

2. How can we use multiplication to find the area? [multiply the number of rows, by the number of squares in each row]

Look at Let’s Learn and explain to students that area is the number of squares, or square units, inside a space. Show students that the squares are lined up in neat rows and columns, so we can use repeated addition or multiplication to find the total rather than simply count each square individually. Remind students how to partition the rectangle into rows and columns to find the area in number 2.

Activities

Students will make an art project and find the area. Give each student 2 pieces of 1 inch grid paper. Students should cut a rectangle of whatever size they wish out of the first piece of grid paper. On the other piece, students should color in squares in different colors. They need to color enough squares to fill the rectangle they cut out. Then students should carefully cut out each individual square that they colored and “tile” the rectangle they cut out, by spreading glue on it and carefully placing the colored squares in the squares of the rectangle in any order they want. When students are finished, have them find the area of their rectangle by counting how many squares they glued inside. They can write equations on the back of the rectangle as well as the area of the rectangle. Have students share their strategies for finding the area. Introduce

the Lesson (Try

Partition the rectangles. Find the

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Be sure to have students double check the number of rows and columns that are drawn for them and also go back and count how many they drew when they are partitioning their own rectangles.

Early Finishers

Students can cut rectangles of different sizes out of grid paper. They can then glue their rectangles on construction paper, label the side lengths, write equations, and calculate the area of each rectangle.

Challenge and Explore

Draw the shape below on the board with the sides labeled as shown.

Read the directions to the students. Tell students that they may use either a repeated addition equation or a multiplication equation to calculate the area of each rectangle and that they should write the equation that they used on the line. Point out that students will need to partition the rectangles themselves starting with number 5. Help students picture the floor of the closet by imagining that it is lined with square tiles. How many rows and columns will they make? [3 rows and 3 columns]

When students are finished have them go back and count the squares to make sure they calculated the area correctly. They can work with partners to fix any mistakes.

Common Errors

Some students may count the number of rows and columns wrong and use the wrong equation to calculate the area. Students often have trouble partitioning rectangles in the correct number of rows and columns.

Games

Play Go Fishing to practice multiplying equal groups. p. 314

Assess

Display a rectangle that has 3 rows of 8 squares. Have students write an equation and solve for the area [24 sq units] on a sticky note.

Objective and Learning Goals

y Distinguish between perimeter and area of a rectangle

y Find the perimeter and area of a rectangle

Vocabulary

y Perimeter - the distance around the outside; found by adding all of the side lengths

y Area - the space inside an object or shape; measured in square units

y Square units - the units used to measure area; 1 square unit equals the area taken up by a square with all sides 1 unit in length

Materials

y Blank rectangles pre-drawn on paper

y Grid paper

y Sticky notes

Pre-Lesson Warm-up

Guiding Questions

Give students some blank rectangles and have them partition them into different numbers of rows and columns. For example, you might have them partition a rectangle into 3 rows with 6 squares in each row. Then have them trace their finger along the outside edge of the rectangle, counting the squares as they go, to find the perimeter. Next have them count the number of squares inside to find the area. Then have students remind the class of equations that can be used to find area and perimeter.

Guiding Questions

1. How can we find the perimeter of a rectangle? [add all of the side lengths]

2. How can we find the area of a rectangle using multiplication? [multiply the number of rows of squares, by the number of squares in each row; or multiply length times width]

Introduce the Lesson (Try it Together)

Look at Let’s Learn and explain to students that each square in the rectangles is one unit in length on all sides. Show them how to count the squares to find the side lengths. Remind them how to add the side lengths to find the perimeter and how to use multiplication to find the area. Walk students through the steps in finding the area and perimeter of number 1 in Try it Together and then have the students take the lead on number 2. Have students do number 3 independently and then share their answers.

Activities

On grid paper have students outline rectangles of different sizes. Have students write the area and perimeter underneath each rectangle. Start by dictating rectangle dimensions for the students to draw such as “Draw a rectangle with 3 rows of 7 squares.” Then you can have the students make up their own and even have students dictate the size and have the rest of the class find the area and perimeter. The student who dictated the size of the rectangle can call on another student to answer and see if they agree.

Find the perimeter and the area of each rectangle. Record the equations you use to ﬁnd each.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Give students a way to remember which is area and which is perimeter. One way to remember is that peRIMeter has the word rim in it which is the outside edge of something.

Early Finishers

Have early finishers use grid paper and try to find other rectangles that have the same areas as the rectangles in numbers 1 - 4.

Challenge and Explore

Draw the shape below on the board with the sides labeled as shown.

Read the directions to the students. For numbers 3 and 4, ask students to fill in the opposite side lengths to make sure they know that opposite sides are equal in a rectangle. Allow them to partition the rectangles into rows and columns if it helps them. As students are working, emphasize that multiplication is the most efficient way to find the area, however accept the strategies of repeated addition and drawing/counting squares as well.

When students are finished, go over their answers to number 6 and have students share their strategies for finding other rectangles with the same area.

Common Errors

Students may confuse area and perimeter. They may not know how to find the side length from the grid squares, or may not count accurately, especially at the corners.

Assess

Ask students if they can find the area of this shape. Help students to realize that they can look at this as two rectangles put together and find the area of each rectangle and add the two together to find the total. They will need to find at least one missing side length though. They can see there is a 9 cm by 2 cm rectangle, but the other rectangle is not labeled. Since the left side of the figure is 6 cm total and the rectangle on top is 2 cm tall, they can subtract 6 - 2 to find that the bottom rectangle is 4 cm tall. Similarly, they can subtract 9 - 3 to find that the length of the bottom rectangle is 6 cm. So, the total area of the figure is (9 x 2 = 18) + (4 x 6 = 24) = 42 square cm

Games

Play Brain vs Hand to practice multiplication facts. p. 308

Draw a rectangle on the board. Label the short sides 3 cm and the long sides 7 cm. Have students calculate the perimeter [20 cm] and area [21 sq cm] and write it on a sticky note.

Objective and Learning Goals

y Determine the liquid capacity of a container by reading its scale

y Measure the volume of a liquid

y Solve problems involving liquid volume

Vocabulary

y Liquid volume - the amount of space a liquid takes up

y Capacity - the maximum amount a container can hold

Materials

y Containers for measuring liquid volume such as measuring cups, graduated cylinders, and beakers

y Grid or lined paper

Pre-Lesson Warm-up

Guiding Questions

Ask students for ideas of times when you would need to measure a certain amount of liquid. They may come up with ideas like measuring liquids like oil, milk, and water for recipes, or measuring how much gasoline or oil you put in your car or lawn mower. Ask students what units for measuring liquids they are familiar with. They may say cups, tablespoons, or gallons. If they don’t mention them, tell students that liquids can be measured in liters and milliliters as well. If possible, show them a container such as a water bottle that tells how many liters or milliliters the container can hold and point out the label.

Guiding Questions

1. How can we measure the volume of a liquid? [fill a container that has markings such as a graduated cylinder, measuring cup, or beaker with the liquid and read the mark that the liquid comes to]

Look at Let’s Learn and read the definitions of capacity and volume to the students. Have them look at the containers to determine the capacity of each. Then have them read the markings to figure out the liquid volume that is in the container. Point out that different containers will have different scales. They will need to count how many lines are in between each number on the container to figure out how many milliliters each line represents. Go through each container on the page and have the students figure out the scale with you. They can label some or all of the other lines on the containers if it helps. For example, in number 1, they can label the longer mark in between 10 and 20 with 15. Each little line represents 1 milliliter, so they could label each mark counting by ones if they have space. For number 3, count the number of lines from 250 to 500 with students. Say: “You count up 5 times from 250 to 500, so what do you need to count by?” [50] Students may struggle to come up with this number. They can guess and check to narrow it down. Have them try counting up by 100s and realize that is too much. Let them suggest other amounts to try. Point out to students that often each mark will represent a number they have learned to skip count by like 2s, 5s, 10s, 100s, etc.

Activities

Set up stations with containers that have some liquid in them. Have students rotate through the stations, writing down the capacity of the container as well as the volume of the liquid in the container at each station. Then bring the students back together and discuss their results. Clear up any confusion about reading the scale on each container.

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Have students guess and check to determine the scales on the containers. If students struggle to do this, give them a couple of choices. Say, for example, “Try 50 and 100, which one works?” Have students label the lines on the containers that are not labeled at least in between the two numbers where the liquid falls.

Early Finishers

Students can make their own liquid volume problems by drawing containers on grid or lined paper and using the lines as the scale. They can label some, but not all of the lines and color in some “liquid.” Then students can trade papers with each other to solve each other’s problems.

Challenge and Explore

Present the following problem for students to solve:

There were 450 milliliters in the beaker. A student knocked it over and spilled 200 milliliters. Then the teacher poured 500 more milliliters in. How much liquid is in the beaker now? [750 mL]

Read the directions to the students. Ask a student to remind the class what capacity and volume mean. Then have the students look at number 1 and determine how many milliliters each line represents on the measuring cup. [50 mL] Have students explain how they figured it out. Next read problems 7 and 8 to the students and point out that they will need to first figure out how much liquid is in the container shown and then add or subtract to get the answers. If possible, give students actual containers to “act out” the problems in numbers 7 and 8. They can pour liquid into another container to that also has markings to measure the liquid they are adding to or pouring out of the first container.

Students may have trouble determining how much liquid is in a container if the line that the liquid comes to is not labeled. They may have trouble determining the scale on the container. Common Errors

Have students write equations to show the 2-steps and solve the problem.

Games

Play The Biggest Difference to practice subtracting larger numbers.

Assess

Check work for numbers 5-8.

Objective and Learning Goals

y Determine the mass of an object by reading a balance scale

y Solve problems involving mass

Vocabulary

y Mass - the amount of matter an object has

y Grams - unit of measuring mass; a paperclip is about 1 gram

y Kilograms - unit of measuring mass equal to 1,000 grams; a dictionary is about 1 kilogram

Materials

y Balance scales

y Small objects place on scales

Pre-Lesson Warm-up

Guiding Questions

Show students a balance scale. Put an object, like a pencil, on one side, and heavier object, like a glue bottle, on the other side. Ask: “Which object has more mass?” [the glue bottle] and “How do you know?” [the glue bottle goes down and the pencil goes up] Ask students what would happen if both objects had exactly the same mass. [the scale would be balanced - both sides the same height] Then show students some masses and try to balance the scale with one of the objects on one side and masses on the other. Show students how to add up the masses to determine the mass of the object.

Guiding Questions

1. How can we determine the mass of an object? [put the object on one side of a balance scale and masses on the other side until the scale is balanced, then add up the masses]

Mass is the amount of matter that an object has.

Units of Measurement:

Grams: about the weight of a paper clip

gram = = 1 g

Kilograms: about the weight of one dictionary

,000 grams = 1 kilogram

4. One block has a mass of 78 grams and the other block has a mass 84 grams. What is the mass of the blocks altogether?

Introduce the Lesson (Try it Together)

Look at Let’s Learn and read the information about mass to the students. Help the students read the scales and find the mass of the marker and pumpkin by adding up the grams and kilograms. Point out in the Try it Together problems that sometimes the masses on the balance will be more than 1 gram or kilogram. Remind students to skip count by the amounts of mass (100 g, 5 g, 5 kg, etc.) and then count up by 1s if there are 1 g or kg masses on the scale. Help students determine which operation (add, subtract, multiply, divide) to use to solve the word problems.

Activities

Give students access to balance scales and masses and have them find the mass of objects around the classroom. Then have students partner up and measure each other’s objects to see if they agree. Let them measure again together if they disagree on the mass of an object.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Have students work independently to find the masses of the object in numbers 1-6. Read the word problems to the students.

Struggling Learners

Have students underline the labels on the masses that tell how much each is before they begin adding them up. Remind them that they may need to skip count.

To help students who struggle with word problems, have them draw a picture to represent the problem and/or underline key words in the problem.

Early Finishers

Students can use a balance scale to measure the mass of more objects in the room.

Challenge and Explore

Have students research the difference between mass and weight. Then have students explain in their own words the difference between mass and weight.

Explain to them that when we use a balance scale, we are comparing the mass of an object to objects of known mass and this will be the same no matter where you are (Earth, Moon, another planet). However, when you step on a scale to weigh yourself, you are measuring the pull of gravity, so you will weigh more here on Earth than you will on the Moon, since there is less gravity on the Moon.

After students have finished the practice page, challenge them to write their own word problems involving mass. Choose a few of the students’ problems to read aloud and have the rest of the class try to solve.

Common Errors

Students may not read the masses on the balance scales carefully. For example, if they see a mass of 2g, they may only count it as 1g when adding up the total mass.When solving word problems, some students may struggle to know which operation (addition, subtraction, multiplication, division) to use to solve the problem.

Games

Play The Biggest Difference to

Assess

Check work for numbers 5 - 8.

Objective and Learning Goals

y Review

y Measure to nearest ½ and ¼ inch

y Find the area and perimeter of a rectangle

y Measure liquid volume and mass

Vocabulary

y Inch - a unit of measurement that is onetwelfth of a foot; there are 12 inches in 1 foot

y Perimeter - the distance around the outside; found by adding all of the side lengths

y Area - the space inside an object or shape; measured in square units

y Square units - the units used to measure area; 1 square unit equals the area taken up by a square with all sides 1 unit in length

y Liquid volume - the amount of space a liquid takes up

y Capacity - the maximum amount a container can hold

y Mass - the amount of matter an object has

y Grams - unit of measuring mass; a paperclip is about 1 gram

y Kilograms - unit of measuring mass equal to 1,000 grams; a dictionary is about 1 kilogram

Materials

y Ruler

y Beakers or other containers with mL and L markings on them

y Balance scales

y Small objects to measure on balance scales

Pre-Lesson Warm-up

Guiding Questions

Draw a rectangle on the board. Have a student come up and measure the side lengths to the nearest inch. Write the side lengths on the rectangle. Then have all students calculate the area and perimeter of the rectangle. Discuss their strategies, the equations they used, and their answers.

Guiding Questions

Let’s learn!

1. How can we measure more accurately when measuring in inches? [use the lines in between the inch marks on the ruler to measure to the nearest ½ inch or ¼ inch]

2. How can we find the perimeter of a rectangle? [add all of the side lengths]

3. How can we find the area of a rectangle using multiplication? [multiply the number of rows of squares, by the number of squares in each row; or multiply length times width]

4. How can we measure the volume of a liquid? [fill a container that has markings such as a graduated cylinder, measuring cup, or beaker with the liquid and read the mark that the liquid comes to]

5. How can we determine the mass of an object? [put the object on one side of a balance scale and masses on the other side until the scale is balanced, then add up the masses]

Introduce the Lesson (Try it Together)

Look at Let’s Learn and review the measurement definitions with the students. Go through the examples in Try it Together with the students. Answer any questions they still have about these topics.

Activities

Give students beakers or other containers with mL and L measurements marked on the outside. Pour water into the containers and have students read the liquid volume measurement for each container. Have partners check each other’s measurements.

Find the area and perimeter.

Struggling Learners

Have students practice counting by ½ and ¼ inches.

Remind students that the word perimeter has the word rim in it.

Have students label the unmarked lines when measuring liquid volume and underline the numbers on the masses on the scales.

Early Finishers

Measure the volume. Then answer the questions.

Find

Solve the problem. Each glue stick has a mass of 8 g. There are 6 glue sticks. What is the mass of all of the glue sticks

Allow students who finish early to practice measuring the mass of small objects around the classroom on a balance scale.

Challenge and Explore

Present the following 2-step word problem for students to solve:

5 beakers each have 7 mL of water in them. The teacher pours them all into a jug and spills 15 mL. How much water is in the jug? [20 mL]

Have students write equations to show how they solve the problem. If students are struggling, encourage them to draw a picture to help them.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Have students finish the page independently.

When students are finished, get out the balance scales and have students practice putting masses on one side to balance objects on the other side. Be sure they add the masses and record the total mass of the objects.

Common Errors

Some students think that if you are measuring to the nearest ½ inch or ¼ inch, the answer has to have that fraction in it. For example, they may think the answer has to be 2 ½ inches or 3 ½ inches, and can’t be just 3 inches. Students may confuse area and perimeter. Students may have trouble determining the scale when measuring liquid volume and may not read masses on a balance scale carefully.

Games

Play The Measurement is Right to practice

Assess

Check work for numbers 1, 3, 5, 6, and 7.

the mass.

Chapter

In Chapter 12, we will learn about graphs and data. We will also learn the di erence between edges, vertices and faces of 3D shapes. We will name and classify quadrilaterals using attributes.

Graphs:

• Create bar graphs from tallies

• Interpret bar graphs, dot plots and pictographs

• Use scaled graphs to answer questions

• Create dot plots using measurement data

Edges, Vertices, Faces:

• Understand the concepts and parts of a 3 D shape

Quadrilaterals:

• Understand and learn the characteristics of the di erent types of quadrilaterals

• Trapezoid

• Trapezium

• Parallelogram

• Rhombus

• Rectangle

• Square

Vocabulary

Words

Objective and Learning Goals

y Create bar graphs from tallies

y Interpret and answer questions about bar graphs

Vocabulary

y Tally marks - a way of keeping count by drawing marks. Every fifth mark is drawn across the previous four marks

y Bar graph - a representation of data using rectangular bars to show how large each value is

y Data - a collection of facts such as numbers or measurements that can be represented in a graph

Materials

y Index cards

y Linking cubes, blocks or base-10 cubes

y Printed tally charts of different data such as favorite ice cream flavors (1 for each small group)

Pre-Lesson Warm-up

Guiding Questions

Show students sets of tally marks and ask them to write the number that the tally marks represent.

Show [5]

Show [10]

Show [12]

Show [19]

Show [23]

Guiding Questions

1. How can we represent data in a bar graph? [Color in each data point up to its corresponding number on the side of the graph]

Read the directions and the headings on the tally chart out loud to the students. Model counting the tally marks next to “roller coaster” and show students how that corresponds to the bar that is already colored in on the graph. Ask students: “How many minutes is the wait for the ferris wheel?” [20] How many boxes should I color in for “ferris wheel” on the bar graph? [2] Continue filling in the bar graph with the students’ help.

Work through the questions about the bar graph with the students. Ask: “How do you know which ride has the longest/shortest wait time?” [the tallest/ shortest bar] For number 3, ask students: “How do we find out how much longer the wait time is for the ferris wheel than for the go-carts?”

Activities

Students will work in small groups to make a “3D” bar graph from a tally chart of data. Give each group a tally chart of different data (for example favorite ice cream flavors). Then in small groups, students should fold the index cards in half so that they can stand them up and write one label (ice cream flavor) on each card. Then they should stack cubes or blocks behind each label to show how long each bar should be in their graph. Students can then trade tally charts with other groups to make more “3D” bar graphs. Students can also be directed to write and answer questions about the data in their graphs.

Use the tallies in the table to color in the

Struggling Learners

1. Who lives the closest to school?

2. Who lives the farthest from school?

3. Which two students live the same distance from school?

4. How many more blocks does Robert live from school than Nate?

Show the equation: - =

Use tallies in the table to make a bar graph. Properly label the bar graph parts.

For students who struggle to answer questions like “How much longer of a wait does the ferris wheel have than the go carts?” show them how they can count how many more boxes are colored in on the graph. To assist them with writing the correct subtraction equation, remind them that the largest number must always come first in subtraction.

Early Finishers

Write more questions about the data shown in the bar graph. Write the answers to the questions as well.

Challenge and Explore

Provide the following challenge questions about the last bar on the practice page:

1. How many total tickets were sold? [195]

2. How many fewer tickets did rooms 38 and 39 sell than rooms 35 and 36? [50]

6. Which room sold the most tickets so far?

7. Which room has sold the least tickets so far?

8. How many tickets did Rooms 38 and 39 sell all together?

9. How many more tickets has Room 37 sold than Room 35 ?

Show the equation: - =

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Color in the first bar for each of the two graphs on the page with the students. Point out in the second graph that only every other line (the multiples of 10) is labeled and help them to understand which numbers should go on the lines that are not labeled (5,15, 25, etc.). Remind students that in the second graph, they will need to put the labels in the correct places on the graph.

Common Errors

Students do sloppy work when coloring in the bar graph and it is not clear where their bar ends. Some students may count each group of 5 tally marks as 1 or 10 instead of 5.

Assess

Check work for problems 4, 5, 6, and 7.

Objective and Learning Goals

y Interpret and answer questions about dot plots and pictographs

Vocabulary

y Data - a collection of facts such as numbers or measurements that can be represented in a graph

y Dot graph - a representation of data using dots

y Pictograph - a representation of data using pictures or symbols

Materials

y Printed 0-10 number lines

y Counters, pennies or other round, flat objects

Pre-Lesson Warm-up

Guiding Questions

Practice skip counting aloud together as a class. Skip count by 2, 5, 3, 10, 100 and 1,000s.

Guiding Questions

1. How do graphs such as bar graphs, pictographs and dot graphs help us understand a set of data? [by giving us a visual representation of how the values compare to each other]

Let’s learn!

A graph shows information. Look at these two di erent graphs. Use the graphs to answer the questions.

1. What does this graph tell us?

Title:

2. How many apples were sold on Monday?

3. What does this graph tell us?

Title:

4. What is the highest score?

5. What is the lowest score?

6. Which kind of book was the most favorite?

7. Which kind of book was the least favorite?

8. How many students voted in all?

Introduce the Lesson (Try it Together)

Introduce the pictograph and dot graph. Discuss the similarities and differences between these two types of graphs. Point out the key and ask students: “In the pictograph, how many apples does a picture of an apple represent?” [5] Remind students to always look for the key before answering questions about a graph. Read through the directions and questions for each graph.

After you have gone through the questions on the page, ask other questions that can be answered by the graph such as “How many more students scored 95 than 80?”[5] Have students think of their own questions to ask a partner about the graph and allow time for partners to ask and answer questions. Call on a few students to share their questions with the class.

Activities

Students will make a dot graph on their desks showing the number of letters in the first names of the students in class. First, have students count the number of letters in their first name. Then, make a tally chart on the board of how many students have each number of letters. Have students raise their hand when you call out the number of letters in their name and put tally marks next to the number of letters to complete the chart. Next, pass out number lines that go from 0-10 and counters, pennies or other round objects that can represent dots. Ask students to make a dot graph on their desk or table showing the data in the tally chart. (This can be done individually, in partners or in small groups depending on the amount of materials available.)

Use the pictograph to answer the questions.

Trips Planned

Struggling Learners

= 2000 people = 5 ﬁsh

1. What does this graph show?

2. How many months does the graph cover?

3. Which month had the highest trips?

4. What does this graph show?

5. How many grades participated?

6. Which grade caught the most ﬁsh?

Students can cross out pictures or write the count above the picture as they skip count to find how many. Give students a number line or hundreds chart to circle the skip counts if needed.

Early Finishers

Write more questions about the data shown in the graphs. Write the answers to the questions as well. Share your questions with each other or the class.

Challenge and Explore

Have students look again at the pictograph of Trips Planned. Ask the following questions.

1. How many total people planned trips from November through January? [32,000]

2. How many more people planned trips in February than in March? [10,000]

7. How many children read 5 books?

8. How many children read 3 books?

9. How many books did most children read?

10. How many students got 7 hours of sleep?

11 How many students got either 11 or 12 hours of sleep?

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Draw students’ attention to the pictographs at the top of the page and to the keys. Ask the students: “How many people does one picture of a bus represent?” [2,000] and “How many fish does one picture of a fish represent?” [5]

Common Errors

Students do not read the titles and labels of the graph and misunderstand what the graph represents. Students forget to look at the key and simply count the pictures by ones.

Assess

Check work for numbers 4, 5, 6, 10 and 11.

Objective and Learning Goals

y Measure items using a ruler to the nearest ¼ inch.

y Use measurement data to create a dot plot.

y Answer questions based on a dot plot.

Vocabulary

y Dot plot - a representation of data using dots above a number line.

Materials

y Ruler

y School supplies (pencils, crayons, erasers, scissors etc.)

y Tape

y Paper

y Paper plates

y Dry-erase boards

y Dry-erase markers

y Index cards

Let’s learn!

Look at the data in the table. Collect the last piece of data by measuring the paper clip. Fill in the table. Then, complete the dot plot. A dot plot or line plot displays data above a number line.

Length of Supplies

Dot Plot

Length of Supplies

How long was the shortest object? How many objects were measured in all?

Pre-Lesson Warm-up

Guiding Questions

Gather a ruler and an item like a stapler. Line up the item on the ruler. Tell students to write down the measurement on their dry-erase boards to the nearest ½ inch. Walk around to see student work. Repeat with other items.

Guiding Questions

1. How do you measure an item? [line the item up with the zero and look what number the other end lines up with]

2. Why do we use ½ as a benchmark number when measuring? [½ is easy to identify and visualize]

Length of Bugs

Introduce the Lesson (Try it Together)

Look at Let’s Learn and explain to students that they will record measurements in a dot plot. Direct students to look at the table. Tell students that these are measurements of different supplies. First, the supply is measured and the measurement is written down in the table. Then, the measurement is recorded in the dot plot. Ask students: How long is the green crayon? [5 inches]. Tell students to find and trace the circle for the number 5. Next, tell students to measure the paperclip and record their measurements in the table. Ask students: How long is the paper clip? [1 inch] Tell students to draw their dot above 1 inch on the dot plot. Next, ask students the questions listed. Guide students to use the dot plot to answer each question. Remind students to count all of the dots in order to find the total amount of objects measured.

Activities

Gather tape, paper and plates. Place a strip of tape down on the ground to act as the dot plot line. Write down inches from 0 to

7 in increments of ½. (0, ½, 1, 1 ½, 2…etc.) on the pieces of paper and line them up on the dot plot line. Pass out a ruler to each student. Tell students to take out one tool from their supplies, like a pair of scissors, a crayon, a pencil or an eraser. Direct students to measure their supply to their nearest ½ inch. Call on students to use a paper plate to place on the dot plot to match their measurement. For example, if a student measures a crayon to be 3 inches, then they place a paper plate above the 3 inch line. After all students have put down their paper plates, ask questions about the plot.

Discussion questions: What was the longest measurement? What was the shortest measurement? How many objects did we measure in all? Which measurement was most often recorded?

How many pieces of fruit and vegetables measured 6 inches?

How many fruits and vegetables were measured?

How many more pieces of fruit and vegetables measured 6 inches than 2 inches?

How many fruits and vegetables measured 2 inches, 6 inches and 15 inches?

Struggling Learners

Provide struggling learners with small index cards to help align the end of the object with the ruler. This will help students to see where the object aligns with the measurement on the ruler. Additionally, provide students with support by reading and discussing the questions regarding the dot plot. Encourage students to describe how they would solve and answer each question.

Early Finishers

Provide students with a ruler, a pencil and a piece of paper. Tell students to create their own dot plot for measurements. Students can select 5 things around the classroom to measure.

Challenge and Explore

Tell students to create their own questions for the plots they created or for the plots in Try it Together. Provide students with a piece of paper and pencil to record their questions and answers. Students can then show their plot and questions to a partner to discuss.

Discussion Question:

1. Why is it important to ask questions about plots? [answers may vary; example answer is - to learn more about the data and to compare]

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice have students draw their own fruits and vegetables on a dry-erase board. Direct students to switch their drawings with a partner and to measure their partner’s drawings with a ruler. Then, tell students to add these measurements to the fruits and vegetables dot plot in independent practice.

Common Errors

Students may not line up the zero with the end of the object which will lead to false measurements and data. If there is already a dot for a measurement, students may not add an additional dot for objects with the same measurement. Remind students that each object needs to have a dot for it’s measurement.

Assess

Create a dot plot on an anchor chart for classroom shoe sizes. Direct each student to measure one of their shoes with their ruler and to draw a dot on the class dot plot.

Then ask students to answer the question below on a sticky note:

Which shoe size is the most common in our class?

Objective and Learning Goals

y Solve 2-step word problems using graphs for data

Vocabulary

y Addition - the act of adding or putting numbers together

y Subtraction - the act of subtracting or taking a number away from another number

y Multiplication - the act of multiplying or finding the total of a certain number of equal groups

y Division - the act of dividing or splitting a total into equal groups

Materials

y Chart paper

y Linking cubes

y Sticky notes

Scaled Bar Graphs: It is important to look at the scale on a bar graph to determine the amount of units it increases by.

Scaled Bar Graph

How many more students chose green and blue than pink?

Step 1 : How many chose green and blue in all? + = green blue total

Step 2 : How many more green and blue than pink? = green/blue pink

Use the bar graph above to solve the story problems. Write the equations and solve.

1. Green and red combined got how many fewer votes than pink?

Pre-Lesson Warm-up Guiding Questions

Read a story problem. Have students show fingers (1 or 2) to signify if it is a one-step or two-step word problem. Discuss the operations they would use.

Story Problems:

Tom had 4 batches of 12 cookies. How many does he have left if he shared 4 cookies? [two-step; operations: multiplication and subtraction]

Marty has 1 box of 24 markers and 1 box of 12 markers. If we split the markers evenly among 4 people, how many markers does each person get? [two-step; operations: addition and division]

There are 4 ducks in the pond. 18 more join. How many are there in all? [one step; operation: addition]

Guiding Questions

1. How do you know if it’s a two-step problem? [there is more than 1 operation]

Look at Let’s Learn and walk students through the steps of solving the example problem. First have students visualize what is happening in the problem. Guide students to look at the graph and to circle the parts they are using in the equation (blue, green and pink). Then tell them to think about the first operation in step 1. Tell students, since we are combining green and blue, we add. Ask students: What is the sum of the green and blue? [10+15=25] Next, tell students to think about the second operation for step 2. Tell students since we are comparing the amounts, we subtract. Ask students: What is the difference between green and blue and pink? [25-20=5] Help students solve number 1 in Try it Together

Activities

On 5 different pieces of blank chart paper, draw a graph and a two-step question. Graphs may include favorite animals, favorite food, favorite color, etc.

Leave enough room on each chart paper for student responses. Place the chart paper on the ground around the room. Play music and allow students to walk or dance around the room. When the music stops, students find the closest chart paper. Students work independently, in groups or with a partner to solve the two-step word problem on the chart paper. Students write their equations and solutions on the chart paper. Play music again and tell students to go to a different chart paper. Walk around to help students and to check their answers.

Possible two-step questions: fill in ______ with category from data

How many more ______ than ________ and_________combined?

How many fewer ________ than ________ and ________combined?

I added _______and _________. How many more do I need to count to get to the amount of ________?

Circle if the problem is one step or two steps. Then solve using the bar graph above.

1. How many more

Struggling Learners

Allow students to build the parts of the bar graph with linking cubes. This will allow them to manipulate the amounts and represent them in the equations. Ask questions to help them figure out which operation to use in each step like “Are we adding to something or putting two things together?”(addition) “Are we taking something away?”(subtraction) “Are we making a certain number of equal groups?” (multiplication) “Are we splitting something into equal groups?” (division)

Early Finishers

3. How

Early finishers can write their own two-step word problems for the chart paper graphs. Students can write their story problems on sticky notes and attach them to the chart paper.

Challenge and Explore

Read the Challenge problem to the students. Have the students share their question with a partner and solve each other’s questions.

Write

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can explain their solutions for each word problem to a partner.

Common Errors

Students may choose the wrong operations to use when writing their equations and solving the problems. Some students may struggle with the computation itself.

Assess

Create a class graph for student color shirts. Have students solve the two-step story problem on paper: How many more (color) and (color) than (color)?

Objective and Learning Goals

y Name 3D shapes

y Describe and count the number of faces, edges and vertices on 3D shapes

Vocabulary

y Edge -the line formed on a 3D shape where two faces meet

y Face - the flat sides on a 3D shape

y Vertex - the point formed at the corners where edges meet on a 3D shape

Materials

y Rectangular wooden blocks, boxes or other objects that are rectangular prisms

y Models of various 3D shapes

Pre-Lesson Warm-up

Guiding Questions

Practice describing attributes of shapes using 2D shapes. Draw or display shapes on the board one at a time and ask students to name the shape and its unique attributes.

Draw or display a square.

Ask: “What shape is this?” [square]

“How do you know?” [it has 4 sides that are all the same length and its opposite sides are parallel, 4 right angles]

Draw or display a triangle.

Ask: “What shape is this? [triangle] How do you know?” [it has 3 sides] Draw or display a rectangle.

Ask: “What shape is this? [rectangle] How do you know?” [it has 4 sides, opposite sides are parallel, it has a long side and a short side, 4 right angles]

Guiding Questions

(Try it Together)

1. How can we describe and differentiate 3D shapes from one another? [by the shape of their base and the number of faces, vertices and edges]

Draw students’ attention to the shapes at the top of the page. Tell them the names of each shape and ask them to describe what they notice about each shape. For example, all of the faces of the cube are squares, the triangular prism has two triangles whose sides are connected by rectangles.

Go over the definitions of face, edge and vertex with students. For the shapes pictured, have the students count each of these attributes out loud with you as you point to them.

Draw students’ attention to the collection of shapes in number 4. Ask: “What is the difference between a 2D shape and a 3D shape?” [2d shapes are flat and have only length and width, 3d shapes have length, width and depth]

Activities

Give students each a rectangular wooden block, rectangular box or other object that is a rectangular prism. Have students point to each vertex and count the number of vertices. [8] Then have students run their fingers along each edge and count the edges. [12] Lastly, have students run their fingers over each face and count the number of faces. [6]

Identify it.

1. How many faces, vertices and edges does this shape have?

Struggling Learners

2. Match the 3 D shapes with real life objects.

Provide students with blocks or other 3D models of the shapes they are describing in this lesson. In the pictures of the shapes, it may help for students to put some sort of mark or sticker on each face, edge, or vertex as they count it.

Early Finishers

Make a table with names of 3D shapes across the top. In each column, list as many everyday objects you can think of that are examples of that shape.

Challenge and Explore

Give students a 10-sided 3D figure such as a 10-sided die. Have students count the number of faces, edges and vertices on the figure.

1. How many faces? [10]

2. How many edges? [20]

3. How many vertices? [12]

Apply and Develop Skills (Practice / Exercise page)

Read the directions for all 3 sections to students. Remind students that sometimes there will be faces, edges and vertices that are not visible in the pictures of the shapes on the page. Let students know where to find models of the shapes if they need them to help determine the number of faces, edges or vertices on a shape.

Common Errors

Students lose track of which faces, edges and vertices they have already counted. Students do not count the faces, edges and vertices that are “hidden” in the picture of the 3D shape. Some students may confuse the terms and forget which is a face, which is an edge and which is a vertex.

Games

Play 2 Truths and a Lie to practice describing attributes and non-attributes of 3D shapes. p. 319

Assess

Display a model of a 3D shape for the students. Have them write the number of faces, number of edges and number of vertices that the shape has.

Lighthouse Math | Level C Chapter 12 Exercise 5

Objective and Learning Goals

y Identify types of quadrilaterals

y Describe the attributes of different types of quadrilaterals

Vocabulary

y Quadrilateral - a shape with 4 sides

y Parallel - side by side, always keeping the same distance apart

y Congruent - having the same size and shape

Materials

y Grid paper

y Ruler or other straightedge

Pre-Lesson Warm-up

Guiding Questions

Review the terms parallel and congruent. Ask students: “What are some examples of parallel lines in the classroom?” [possible answers: the sides of a desk or table, the top and bottom edge of the board, lines between tiles on the floor]

Guiding Questions

1. How can we identify different types of quadrilaterals?

[by the number of parallel and congruent sides and by the size of the angles]

These are the di erent types of quadrilaterals. Quadrilaterals are shapes with four sides. These lines are parallel.

This is a parallelogram: It has two pairs of parallel sides.

This is a rhombus: A rhombus is a parallelogram with four congruent sides.

This is a rectangle: It is a parallelogram with 4 right angles and opposite sides that are equal.

the name of each quadrilateral.

This is a trapezoid: It has one pair of parallel lines.

This is a square: It is a rectangle with 4 congruent sides. Circle the quadrilateral in the set of shapes.

Define quadrilateral for the students, emphasizing that a quadrilateral is any shape that has 4 sides, but there are some special types of quadrilaterals that they are going to learn about. Read through the definitions of each type of quadrilateral together. After each type, draw or display some other examples that meet the criteria, as well as non-examples. Ask students to identify whether the figures you show them are examples of that quadrilateral type.

Activities

Students will practice drawing quadrilaterals on graph paper. Give each student a piece of graph paper and a ruler or other straightedge. Have students fold the long sides of the paper together (hot dog style) and open it back up. Then have students fold the short edges of the paper together (hamburger style) and then fold it the same way again. When they open their paper up, they should have made 8 boxes to draw quadrilaterals in. Tell students to write small and label the top of 5 of the boxes each with a different type of quadrilateral: square, rectangle, parallelogram, rhombus and trapezoid. Guide students through the process of making four dots on the grid and connecting them with a straight edge to form each type of quadrilateral. Help them to understand that the dots will need to be the same number of squares apart in order for the lines to be congruent, and help them understand how to make right angles and parallel lines on the grid. After all 5 types have been drawn, tell students that in the last 3 boxes, they can choose any 4 dots to connect to make 3 more quadrilaterals. After some time, have a few students share what they drew. Discuss as a class if what they drew is in fact a quadrilateral and if it meets the criteria for any of the special types they learned.

Rectangle Parallelogram Square Trapezoid Rhombus

Circle it.

Circle

Struggling Learners

Show students how to line up two rulers, pencils or other straight objects along the opposite sides of a quadrilateral. If the rulers cross each other, then the sides are not parallel. They can also use a ruler to help them check whether sides are congruent or not by actually measuring the sides.

Early Finishers

Draw more quadrilaterals on the back of your graph paper. Try to make each type of quadrilateral but in a different way than you did on the front.

Match the characteristics.

Challenge and Explore

Have students go back through numbers 9-13 and name the type of quadrilateral. [9. Square, 10. Rhombus, 11. Trapezoid, 12. Rectangle, 13. Parallelogram]

Apply and Develop Skills (Practice / Exercise page)

Point out the examples of the types of quadrilaterals at the top of the page. To review, ask students to describe the criteria that each type of quadrilateral must meet. Remind students that shapes can meet those criteria while not looking exactly the same as the examples shown here.

Model for students how to think through number one and ask them to help you. Say: “Look at this shape. Could it be a trapezoid?” [no] “Why not?” [it has 2 sets of parallel sides, and trapezoids only have one set of parallel sides] Go through each type of quadrilateral in this manner. Be sure students don’t just say: “It looks like a rectangle.” Insist that they describe the attributes that make it a rectangle.

Common Errors

Students have difficulty visualizing if two lines will eventually intersect if they continued on forever. This causes them to have difficulty deciding if lines are parallel. Students can look at a shape and tell you which shape it looks like, but they cannot describe the attributes of the shape to prove it.

Assess

Games

Play 2 Truths and a Lie to practice describing attributes and non-attributes of 3D shapes. p. 319

Draw or display a quadrilateral on the board. Students should 1) name the type of quadrilateral and 2) describe the attributes of that type of quadrilateral.

Give students the following list of key words to use when describing the quadrilateral: parallel, congruent, angles.

6. Set 1

Set 3

Rectangle Parallelogram Square

Trapezoid Rhombus

Objective and Learning Goals

y Classify quadrilaterals based on characteristics

y Compare and contrast quadrilaterals based on characteristics

Vocabulary

y Quadrilateral - a shape with 4 sides

y Congruent - having the same size and shape

y Parallel - side by side, always keeping the same distance apart

Materials

y Quadrilateral shape manipulatives

y Bag

y 10 sticky notes per student group

y Chart paper

y Dry-erase boards

y Dry-erase markers

Pre-Lesson Warm-up

Guiding Questions

Place different quadrilateral shapes in a bag. Secretly pick a shape and hold it behind your back. Describe the quadrilateral with its characteristics. Direct students to guess your quadrilateral based on your descriptions. Call on one student at a time to come up to pick their own mystery quadrilateral from the bag and to give clues to their peers.

Guiding Questions

1. What clues helped you determine the shape was a rectangle and not a square? [answers may vary. Example answers - it had opposite sides that were equal in length]

2. If my shape is a square, what else could it be? Why? [A rhombus because it has 4 parallel and congruent sides; A rectangle because it has 4 parallel sides and right angles]

Let’s learn!

Classifying Quadrilaterals: Some quadrilaterals ﬁt into multiple categories based on their qualiﬁcations or rules.

All other quadrilaterals

Parallelogram rule: must have 2 pairs of parallel sides Rhombus

Circle true or false.

1. A trapezoid has 2 sets of parallel sides.

2. A square is a rectangle.

3. A rhombus is a type of parallelogram.

4. A rectangle is a rhombus.

Introduce the Lesson (Try it Together)

Look at Let’s Learn and explain to students that quadrilaterals can be classified into multiple categories based on their attributes. Read through each rule with students. Then give students mystery shape clues to practice classifying each quadrilateral.

Mystery Shape Clues:

• The mystery shape has 4 parallel sides. It is a rectangle and a rhombus. What is the shape? [square]

• The mystery shape has 4 parallel sides and 4 right angles. It is not a rhombus. What is the shape? [rectangle]

• The mystery is a parallelogram. It has 4 congruent sides but it is not a square. What is the shape? [rhombus]

Activities

Place students in groups of 2 to 3 students. On 10 sticky notes per student group, draw rectangles, squares, and rhombuses of different sizes. Pass out the sticky notes and a piece of chart paper to each student group. Direct the students to draw a big venn diagram on the chart paper. Tell students to label the left circle “rectangles,” the right circle “rhombuses” and the overlapping portion “squares.” Next, direct students to discuss and sort each sticky note shape into 1 of the 3 categories of quadrilaterals. Remind students to discuss the characteristics of each shape.

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice, students can create their own venn diagram on a dry-erase board. They can choose their 3 categories and sort shapes from independent practice.

Struggling Learners

Provide students with shape manipulatives to compare and sort each quadrilateral. Discuss the attributes that each of the quadrilaterals have in common. For example, when solving number 1 in Let’s Learn, compare the square to a rectangle. Ask students: Can a square also be a rectangle? Why or why not? [Yes because it has 4 parallel sides with right angles]

Early Finishers

Pass out a handful of quadrilaterals to students. On their dry-erase boards, direct students to create a tally graph for the amount of parallelograms, rectangles, rhombuses, squares and “other” shapes in their pile.

Challenge and Explore

Discuss the answer to question number 7. [A rectangle is different from a square because it does not have 4 congruent sides.] Ask students to further explain why a rectangle cannot be a rhombus. [It does not have 4 congruent sides]

Common Errors

Students may think that each shape has only 1 name or category it can belong to. For example, students may not understand that a square can also be considered a rectangle and a rhombus. Similarly, students may not understand why a rectangle and a rhombus cannot be considered a square.

Assess

Games

Play 2 Truths and a Lie to practice identifying shapes. p. 319

Hold up or draw a square. Have students write the different categories it belongs to on a piece of paper. [parallelogram, rectangle, rhombus]

Objective and Learning Goals

y Count and identify a three-dimensional shapes edges, vertices and faces

y Create a bar graph using data from a tally graph

y Answer one-step and two-step questions about a dot graph

y Identify quadrilaterals based on classifications

Vocabulary

y Dot plot - a representation of data using dots above a number line.

y Quadrilateral - a shape with 4 sides.

y Faces - the flat sides on a 3d shape

y Vertex - the point formed at the corner where edges meet

y Edges - the line formed on a 3d shape where two faces meet

Materials

y Chart paper

y Dry-erase boards

y Dry-erase markers

Pre-Lesson Warm-up

Guiding Questions

Make a class dot graph together based on student shoe color. After making the graph, allow students to discuss the results with various partners. Play music. When the music stops, direct students to find a partner close to them. Then, direct students to ask their partner a question about the graph. For example, students may ask “How many more students have black shoes than brown shoes?”

Guiding Questions

1. Why do we display data in a graph? [answers may vary. Example answer -to see data in an organized and easy to read manner]

Try it together!

1. How many students were asked their favorite fruit in all?

Three Dimensional: Quadrilaterals: shapes with 4

Favorite Fruits

2. Which fruit had the least amount of votes? How many votes did it have? Bananas Apples Oranges Grapes

Introduce the Lesson (Try it Together)

Look at Let’s Learn and tell students they will review graphing and shapes. Look at the bar graph. Remind students to check the scale for a graph, the title and the categories. What does the scale tell us about this bar graph? [it skip counts by 2] Ask students: How many more students chose dog than cats? [2]. Next, move on to the shapes review. Remind students that counting a shapes’ faces, vertices and edges can help identify a three-dimensional shape. Ask students to count the faces, vertices and edges for the cube. Ask students: How many faces? [6] How many vertices? [8] How many edges? [12]

Activities

Put students into pairs. Direct students to come up with a question and 3 choices to ask their peers. For example, students may ask their peers their favorite ice cream flavor, chocolate, vanilla, or strawberry. Student partners will walk around to ask their question and collect data. To collect data, students will create a tally chart. Then, on a piece of chart paper, direct student partners to create a graph of their own - bar graph, picture graph or dot graph. Next, direct students to write three questions about their graph. Encourage students to make 1 of their 3 questions a two-step question.

2. How many shells measured 8 inches?

Struggling Learners

Show students how to use a ruler to help them line up data to read the graph. Allow students to reference charts for 2D and 3D shapes.

Early Finishers

Have early finishers come up with 5 questions about the bar graph in number 1 of independent practice. Students can write questions on paper or dry-erase board.

Challenge and Explore

3. How many more shells measured 5 inches than 1 inch and 2 inches?

Circle the shape name based on the clues.

5. I have 4 congruent sides.

I have 4 right angles. I am a rectangle. I am a rhombus.

6. I have 1 vertex. I have 1 face. My face shape is a circle.

4. How many fewer shells measured 10 inches compared to 5 inches and 8 inches?

Direct students to create their own riddle about quadrilaterals. Make sure students include at least 2 qualifications for each shape.

I am a quadrilateral. I have 1 pair of parallel sides.

Apply and Develop Skills (Practice / Exercise page)

Continue working through the rest of the Try it Together problems and independent practice. For additional practice have students draw a shape on their dry-erase board. Students then give a partner clues about their shape. Partners must guess the name of the shape drawn based on the clues. Then students can switch roles.

Common Errors

Students may not check the graph's scale or key prior to comparing or answering questions about the data. Students may think that each shape has only 1 name or category it can belong to. For example, students may not understand that a square can also be considered a rectangle and a rhombus. Similarly, students may not understand why a rectangle and a rhombus cannot be considered a square. Students may miscount the faces, edges and vertices of a three-dimensional shape.

Assess

Games

Play 2 Truths and a Lie to practice identifying shapes. p. 319

Have students answer the following questions about the bar graph from Let’s Learn:

1. How many total students voted? [18 students]

2. How many fewer students chose fish than dogs and cats? [14 students]

In Chapter 13, we will

learn about elapsed time, counting money and making change.

Elapsed time

• Tell time to the minute

• Calculate elapsed time

• Connect elapsed time to multiples of 5 s

• Draw hands on a clock

Money

• Count and write money using dollar signs and decimals

• Learn how make change by counting on

• Determine di erent ways to group bills and coins to represent the same values

Vocabulary Words

Level C Chapter 13-1

Objective and Learning Goals

y Tell time to the nearest minute

Vocabulary

y Hour hand - the short hand on the clock that tells the hour

y Minute hand - the long hand on the clock that tells the minutes

y Skip counting - counting by multiples of a certain number

Materials

y Demonstration clock

y Play clocks or paper clocks

Pre-Lesson Warm-up

Guiding Questions

Using a demonstration clock, have the students tell times to the nearest 5 minutes. Have students explain how they find the time on the clock. Then give students a time and have them explain to you how to set the hands on the clock to make that time.

Guiding Questions

1. How can we tell time to the nearest minute? [First read the number that the hour hand is at or past, then count by 5s and then 1s to find the minutes]

2. How can we set the hands on a clock to show a time to the nearest minute? [put the hour hand at or past the hour depending on how close it is to the next hour, then count by 5s and 1s to set the minute hand on the correct mark]

Let’s learn!

• Look at the short hand (hour hand)

• Look at the last number the hour hand passed

• Do NOT pass the next hour 3

• Look at the long hand (minute hand)

• Start at the 12 (:00 ) and count by 5 s

• From there, count the small ticklines by

21, 22, 23

Introduce the Lesson (Try it Together)

Look at Let’s Learn and walk students through the steps of finding the hour and then the minutes when looking at a clock. Remind students that 12:00 is :00 minutes and then each number represents 5 minutes. Point out that there are 5 small marks from each number to the next. Remind students to count by 5s, and then have them count up by 1s to find the time. Have students explain how to do the examples in Try it Together

Activities

Give students play clocks or have them make paper clocks. Students can work in small groups or partners. One student should set the clock to any time they wish and the other student(s) should tell the time. Students can also practice by having one student name a time and the other student(s) set that time on the clock. Another option is to provide students with a sheet of blank clock faces. Students can draw the hands on the clock and trade papers. Each student can write or read the time on drawn on each clock.

Struggling Learners

Explain how you ﬁgured out the time in number 4

Possible answer: I saw the short hand is past the 10, but not to 11 yet, so the hour is 10. Then I started at 12 and counted by 5 until I got to 11. Then I counted 1 more minute since the long hand is 1 mark past the 11 and I got 56 minutes.

Draw the hands on the clocks. Challenge Joe says the time on this clock is 8 :04 . Explain and ﬁx his mistake.

Have students label the hour hand and minute hand on the clocks, reminding them that the short hand comes before the long hand and the hour comes before the minutes when reading a clock. You can help students label the 5 minute increments around the outside of their clocks, starting with :00 at the 12, :05 at the 1, etc. If needed, provide students with an index card to line up with the minute hand to be sure they are counting the correct number of marks on the clocks.

Early Finishers

Explain how you decided where to draw the hands in number 9

Possible answer: I put the short hand in between the 6 and 7 because it’s almost 7:00. Then I started at 12 and counted by 5s until I got to 55 at the number 11 and counted the little marks by 1s until I got to 58.

Possible answer: Joe counted each number as 1 instead of 5 minutes. He should have counted the small lines between 12 and 1 and stopped when he got to 4.

Apply and Develop Skills (Practice / Exercise page)

Have students who finish early partner up and check each other’s work. Tell students that if they disagree on an answer, both students should double check their work. If they still disagree, they should explain to each other how they got their answer and see if they can find each other’s mistake.

Challenge and Explore

Read the Challenge problem to the students. Ask students to tell what time is actually on the clock. [8:20]

Then have students explain Joe’s mistake in their own words. Help students to construct clear, concise explanations and have them write their explanations in their books. Then have students draw the hands to show 8:04 on the clock. Have a student explain how they decided where to put the hands.

Read the directions to the students. Have a student remind the class which hand is the hour hand. Tell students to always start with the hour hand and write it first. Have a student explain in their own words how to tell time to the nearest minute and then have students complete the practice page independently. If you don’t already have it posted, write your daily schedule on the board. Next to each activity, write the time that it occurs. Try to include some times that are not multiples of 5 minutes. For example, if Art starts at 9:50, perhaps you line up to go to Art at 9:46. Have students make these times on play clocks or draw hands to show the times on a clock on paper.

Common Errors

Students may confuse the hour hand and minute hand. Some students may start counting by 5s saying “5” at 12 instead of 1. Some students may have a hard time keeping track and counting the small marks between the numbers on the clock.

Assess

Times Table War to practice multiples of 5. p. 315

Set a demonstration clock to 7:54. Have students write the time on a sticky note.

Objective and Learning Goals

y Tell time to the nearest minute

Vocabulary

y Skip count - counting by multiples of a certain number

Materials

y Play clocks or paper clocks

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice skip counting by 5s, and then count up by 1s.

Count by 5s four times. [5, 10, 15, 20] Now count up by 1s 3 times. [21, 22, 23]

Count by 5s 2 times. [5, 10] Now count up by 1s 4 times. [11, 12, 13, 14]

Count by 5s 8 times. [5, 10, 15, 20, 25, 30, 35, 40] Now count up by 1s 2 times [41, 42]

Count by 5s 10 times. [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] Now count up by 1s 3 times [51, 52, 53]

Guiding Questions

1. How can we tell time to the nearest minute? [the hour is the number the short hand is pointing to or past. To find the minutes, start at 12. Moving towards the 1, count each number by 5s, and then count each small mark by 1s]

Review telling time with students. Ask them which hand is the hour hand [short] and which is the minute hand. [long] Remind students that the hour is whichever number the hour hand is pointing to OR has passed. Then to find the minutes, they can count each number starting with 1 by fives and count on by ones for each small mark in between the numbers. For each of the examples, ask students which number the hour hand is on or has passed. Then have them count by 5s out loud with you. Review that 30 minutes past the hour is sometimes called “half past,” and 15 minutes past the hour is sometimes called “quarter past” because they are halfway and a quarter of the way around the clock. For the Try it Together examples, you will need to count the tick marks by ones after you get to the closest number counting by fives.

Activities

Students practice making and reading times on a clock with a partner. Partner 1 moves the hour and minute hand on the clock to make any time they want. Then they show the clock to Partner 2, and Partner 2 must read the time out loud. The students should settle any disagreements by counting the hours and minutes together. Then switch roles, and Partner 2 makes a time on the clock for Partner 1 to read.

Apply and Develop Skills (Practice / Exercise page)

Read the directions. Have the students help you read the time on the first clock the same way you did in the examples, and then have students point to where the line should be drawn to in their books. [9:07] Read the rest of the directions on the page and have students finish the page on their own.

Struggling Learners

Give students play clocks to move the hands and count the minutes on. Post an anchor chart of some type telling the students which hand is which on the clock.

Early Finishers

Draw your own clocks. Label them with important events in your day, such as what time you get up, when school starts, the time your favorite subject starts, lunchtime, when school lets out, dinner time, bedtime, etc. Draw the hands on the clock to show what time those events start.

Challenge and Explore

Read the Challenge problem and ask students to share their answers. Make sure that students know where and how to draw the colon in the times. Talk about a.m. and p.m. and make sure that students put the correct label on their times.

Common Errors

Students often confuse the hour and minute hands. Sometimes students simply read the number on the clock instead of counting by 5s. For example, if the hour hand is pointing to the 6 and the minute hand is pointing to the 2, they may say that it is 6:02 or 6:2 instead of 6:10.

Assess

Games

Play Times Table War practice multiples of 5. p. 315

Check work for numbers 9, 10, 14 and 15.

Objective and Learning Goals

y Calculate elapsed time using number lines and T-charts

y Determine end time of an activity given the start and elapsed time

Vocabulary

y Number line - a tool to help with counting

y T-chart - a tool used to separate and organize information

y Elapsed time - the amount of time that passed from one time to another

Materials

y Demonstration clock

y Chart paper with 3 columns labeled START TIME, 30 MINUTES LATER, 1 HOUR LATER

Pre-Lesson Warm-up

Guiding Questions

Set a demonstration clock to 1:00. Ask students where the hour hand is pointing and what that hand tells us. [to the 1. It tells us the hour is 1 o’clock] Where is the minute hand pointing and what does it tell us? [to the 12. The minutes are 00]. If I move the minute hand to 1, how many minutes have gone by? [5 minutes] How about if I move it to the 2? [10 minutes] Keep doing this around the clock, skip counting by fives. What happens when I get back to 12? How much time has gone by? [60 minutes or 1 hour]. When we look at how much time has gone by, we call this ELAPSED TIME. We can determine the elapsed time in different ways. One way is to count by fives on a clock. Set the clock to 1:15. Ask a student tell the time and write 1:15 on the board. Now move the clock to 1:35. How much time as passed? Let’s count together. Put your finger on the start time (on the 3). Move your finger to the 4 and count by 5s to the 7. 5, 10, 15, 20. Our elapsed time is 20 minutes.

Guiding Questions

Let’s learn!

Try it together!

1. How can we count elapsed time on a clock? [each number represents 5 minutes]

2. What happened when we get to 60 minutes? [60 minutes equals one hour]

3. Does one hour go by every time we get to 12? [No. It depends where you start. You have to go all the way around to where you started for 1 hour to go by]

the Lesson (Try it Together)

Tell students to look at the Let’s learn section. We can figure out how much time has passed by using number lines and T-charts. When using these strategies, we want to use numbers that are easy to add up, like 5s and multiples of 10. Look at the first clock. The start time is 2:05. Our end time is 2:50. How much time has passed? To use a number line, write the start time. Then think about what would be easy to add. Let’s add 30 minutes. Make the hop, and write the new time, 2:35. We can now add 10 more minutes and get 2:45. Then we just need to add 5 more minutes to get to 2:50. When we add all the minutes together we get an elapsed time of 45 minutes. We can also write this out in a T-chart. Look at the example. Discuss alternate ways to count and get the elapsed time of 45 minutes.

Now look at the Try it together. Have students fill in the time hops and arrows to match the times listed on the number line. In number 2, tell students sometimes it’s easier to make our minutes end in a 5 or 0. We can start by first adding 2 minutes to 2:03 to make it a nicer number of 2:05.

Activities

Post a piece of chart paper on the wall with three columns. Label columns START TIME, 30 MINUTES LATER, 1 HOUR LATER. Write the 5:00 in the first column. Have students talk with their neighbor about what the time will be in 30 minutes and then an hour. Have students share their answers and write them on the chart paper. Then choose another time, such as 6:15. Do the same. Write in the answers. Do this a few more times with start times of 3:20, 12:35, 10:50, and 7:12. Discuss patterns students notice when 30 minutes and 1 hour have passed. Introduce

Elapsed time: Elapsed time:

Write the end time. Use a number line, T-chart or a clock to help you solve.

Start time: 6 : 13 , Elapsed time: 37 minutes 4. Start time: 7 : 30 , Elapsed time: 48 minutes

Struggling Learners

Practice adding ten minutes to times. Start with 12:00, 12:10, 12:20 etc. Then start at 12:05, 12:15, 12:25 etc. Have students put their thumbs up and when you pass the time they are supposed to stop at, turn their thumbs down. For example if the start time is 12:40 and end time is 1:15, count up 12:50, 1:00, 1:10 and when you say 1:20, students should put their thumb down.

Early Finishers

time: End time: End time: End time:

Solve the story problems. Use a number line, T-chart or a clock to help you solve.

7. James woke up at 7:00 AM. He ate breakfast for 30 minutes. What time was he done? 7:30 AM 8. Jake left school at 2:45 . It took him 35 minutes to get home. What time did he get home?

9. Sam starts his music practice at 7 :40 . His practice ends at 9 :10 How long was his practice? 10. Jan started reading at 6 :07 . She stopped at 6 :45 . How long did she read for?

Nancy goes to sleep at 9 :15 pm. She wakes up at 6 :25 am. How long does she sleep for? 6:50 8:18

Apply and Develop Skills (Practice / Exercise page)

Students double check their work in 3-10 by solving the problem using a different strategy than they originally used. Find and fix any errors.

Challenge and Explore

How can we find elapsed time when we move from PM to AM? Look at the Challenge problem with a partner. Start by setting up a number line or a T-chart. How might you start solving this problem? Work with your partner to see if you can find how long Nancy was asleep for. Have students share out how they solved the problem.

Questions

1. How did you start this problem? What was the first increment of time you used? [answers will vary]

Read the directions to the students. In the first two problem, practice the strategy of a T-chart. The first problem is structured and students will fill in the blanks. Remind students that there is more than 1 way to arrive at an answer. Students can share counting strategies with each other. By explaining how they get to an answer, students will understand and check their work. They should however get the same elapsed time.

In problems 3-10 students may choose the strategy they like best. Encourage students to solve the problems using more than 1 strategy to see if they get the same answer. Discuss with students which strategy they prefer and why.

Common Errors

Students may think an hour (60 minutes) has gone by when a times cross over to a new hour. For example 11:45 to 12: 05 is 20 minutes, not an hour and 20 minutes. Remind students that for an hour to go by, the minute hand has to move a full circle from where it started.

Assess

Check work for numbers 2, 5 and 8.

Level C Chapter 13-4

Objective and Learning Goals

y Tell time to the nearest minute

y Find elapsed time using multiple strategies.

Vocabulary

y Hour hand - the short hand on the clock that tells the hour

y Minute hand - the long hand on the clock that tells the minutes

y Elapsed time - the amount of time that passed from one time to another

Materials

y Demonstration clock

Pre-Lesson Warm-up

Guiding Questions

Play a game of Around the World. Set a time on a demonstration clock. Two students stand up. The first of those two students to call out the correct time moves on to compete against the next student. The goal is for a student to make it around to all of their classmates.

Guiding Questions

1. How can we find elapsed time using an open number line? [hop by hours and minutes starting at the start time until you reach the end time. Add up how many hours and minutes you hopped]

2. How can we find elapsed time using a t-chart? [on side of the t-chart count up by hours and minutes from the start time to the end time. On the other side keep track of how many hours or minutes you added. Then add the total hours and minutes together to find the elapsed time]

Let’s learn!

Elapsed time: is the amount of time that passes between two events. On a Number Line

Try it together!

Write the time on each clock. Find the elapsed time. Check using a di erent strategy.

Introduce the Lesson (Try it Together)

Look at Let’s Learn and remind students that they have learned to find elapsed time by counting up hours and minutes on the clock. Show them how to find the elapsed time in the example using all 3 strategies. In the Try it Together problems, have a students suggest a strategy and go through the steps in finding the elapsed time using that strategy. Then have another students suggest a different strategy to solve the same problem. Go through the steps in the second strategy to check the answer. If time, demonstrate all 3 strategies for each example problem.

Activities

List some activities on the board and list start and end times for each activity. For example, you might write a that a concert started at 8:04 and ended at 10:32. Have students find out how long the activities lasted, or the elapsed time. Alternatively, for some activities, you can write the start time and the elapsed time and have the students fill in the end time. Students can work with partners or in small groups.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Point out to students that they must use the strategies indicated in numbers 1 and 2, but can choose any strategy they wish to solve the rest of the problems. Encourage students to solve the problems using more than 1 strategy to see if they get the same answer. Discuss with students which strategy they prefer and why.

Struggling Learners

Practice counting aloud by hours with students. Start with 12:00, 1:00, 2:00, etc. Then make it more challenging by changing the minutes. Have students start at 12:42 and count 1:42, 2:42, 3:42, etc. Have students put their thumbs up and when you pass the time they are supposed to stop at, turn their thumbs down. For example if the start time is 12:42 and end time is 3:25, count up 1:42, 2:42, and when you say 3:42, students should show thumbs down.

Early Finishers

Students can go back and check their work using a different strategy. For example, if they used a number line, they can use a t-chart or play clock to add up the hours and minutes again and see if they get the same answers. Then they can find and fix their errors.

Challenge and Explore

Challenge students to solve the following problem that requires them to find an elapsed time that is longer than 12 hours.

If the sun rises at 6:56 am and sets at 8:35 pm, how many hours and minutes of sunlight do we have today? [13 hours 39 minutes]

Have students share strategies for solving this problem including making hops on an open number line and using a t-chart.

Common Errors

When finding elapsed times that span more than 1 hour, students may struggle to count the hours correctly. Students may still have trouble when adding minutes that cross over into a new hour.

Assess

Check work for number 5.

Objective and Learning Goals

y Count dollars and cents

y Write money amounts with dollar signs and decimal points

Vocabulary

y Decimal point - the period that goes between dollars and cents or whole numbers and fractions of a whole number

y Dollar sign - the symbol that represents dollars; $

Materials

y Play money - bills and coins

y Dry-erase boards and markers or paper/ pencil

Pre-Lesson Warm-up

Guiding Questions

Practice skip counting by money amounts. Give students a starting point and have them practice counting up by money amount.

Start at 0, count by $20. [$20, $40, $60, etc.]

Start at $20, count by $5.

[$25, $30, $35, $40, etc.]

Start at $25, count up by $1.

[$26, $27, $28, etc.]

Start at $1, count up by 25 cents.

[$1.25, $1.50, $1.75, etc.]

Start at $1.25, count up by 10 cents.

[$1.35, $1.45, $1.55, etc.]

Start at $1.35, count up by 5 cents.

[$1.40, $1.45, $1.50, $1.55, etc.]

Start at $1.55, count up by 1 cent.

[$1.56, $1.57, $1.58, etc.]

Guiding Questions

1. How can we count money amounts with dollars and cents?

[start with the largest bills and count up by their values, then start with the largest coin and count up by their values until you have counted all of the bills and coins]

2. How can we write money amounts with a dollar sign and decimal point?

[write a dollar sign and then write the number of dollars. Next to that, write a decimal point and write the number of cents to the right of the decimal point]

Remind students that when we count money, we can skip count by the values of the bills and coins. Model for them counting the money in the two examples in Let’s Learn. Count the first example by pointing to each bill and coin and saying: “1 dollar, 1 dollar and 25 cents, 1 dollar and 35 cents.” Then explain to students how $1 and 35¢ can be written with a dollar sign and decimal point by writing the dollar sign, the dollar amount, the decimal point and then the number of cents. Count the second example for them: “5 dollars, 5 dollars and 10 cents, 5 dollars and 15 cents, 5 dollars and 16 cents, 5 dollars and 17 cents.” Have students write $5.17.

For the Try it Together problems, have students count the money amounts out loud and then tell you where to draw the line to match.

In number 5, students should trace the dollar sign and then write it on each of the lines that follow.

Activities

Students practice counting and writing money amounts with partners. Provide students with play bills and coins and a dry-erase board and marker or paper and pencil. Partner 1 counts out a money amount (not out loud) to give to Partner 2. Then Partner 2 counts the money out loud and writes the amount on the

board with a dollar

and decimal point. Partner 1 checks to see if they agree with the amount and how their partner wrote it, then the students switch roles.

Struggling Learners

Give students actual or play money to count the money amounts. Consider providing a “cheat sheet” or poster on the wall that tells students the values of each coin. Also, post examples of how money amounts are written with the dollar sign and decimal point.

Early Finishers

Draw bills and coins to make your own money amounts. Count them up and write the amounts with a dollar sign and decimal point.

Challenge and Explore

Show students a 5 dollar bill, a 1 dollar bill, 5 quarters, 4 dimes, 2 nickels and 3 pennies. Challenge them to count the money and write the amount using a dollar sign and decimal point.

[$7.78]

Discuss students’ strategies and what made this problem more challenging. [strategies will vary. The problem is more challenging because the coins add up to more than a dollar]

Apply and Develop Skills (Practice / Exercise page)

Read the directions and do the first problem with the students. Have the students help you count the money, then show them how to fill in the blanks with the dollars and cents and then write the money amount with the dollar sign and decimal point.

Point out to students that in numbers 5 - 12, they will just write the amount with the dollar sign and decimal point.

Common Errors

Some students write the dollar sign to the right of the number of dollars instead of to the left. Watch for students who struggle counting up by 25s, 10s and 5s, especially when they are not starting from 0.

Assess

Games

Check work for numbers 6, 8, 10 and 12.

Objective and Learning Goals

y Make change by counting on from the known cost

Vocabulary

y Decimal point - the period that goes between dollars and cents or whole numbers and fractions of a whole number

y Dollar sign - the symbol that represents dollars; $

y Change - the money you get back when you pay with more than the cost of the item

Materials

y Play money - bills and coins

Pre-Lesson Warm-up

Guiding Questions

Practice counting money. Show students different amounts of bills and coins and have them count up and write the amount using the dollar sign and decimal point on a dry-erase board or on paper.

1 dollar bill, 1 quarter, 2 dimes [$1.45]

5 dollar bill, 2 quarters, 2 pennies [$5.52]

2 dollar bills, 3 quarters, 1 dime, 1 nickel, 1 penny [$2.91]

1 dollar bill, 2 quarters, 3 dimes, 2 nickels, 3 pennies [$1.93]

Guiding Questions

1. How can we count the amount of change we should get back?

[start at the cost of the item and count up by coins and bills until you reach the amount you paid]

Read the example in Let’s Learn and show the students how to count up to make change. Say: “The toy costs $2.24 and we paid with a five-dollar bill. We need to count up from $2.24 to $5 to find out how much extra we paid. That is how much change we should get back. We can start by counting up pennies to get to a multiple of 5. So, 1 penny will get us to $2.25. Since a quarter is worth 25 cents, we can now count up by quarters to get to the next dollar. $2.50, $2.75, $3. That is 3 quarters. Now that we are at a nice round dollar amount, we can count up by dollars to get to the amount we paid. $4, $5. That was 2 dollars. We counted up 2 dollars, 3 quarters and 1 penny. That is $2.76, so that is how much change we should get back.”

Do the Try it Together problems with the students in a similar manner. Have the students do as much of the counting on their own as they can.

Activities

Games

Play Almost a Dollar to practice counting money. p. 309

Students act out purchasing items and making change with a partner. Give students play money - bills and coins. Have them use the chart at the top of the exercise page. Partner 1 pretends to be the cashier, and Partner 2 is the customer. Partner 2 will tell the cashier what they want to buy, and Partner 1 will tell Partner 2 how much it costs. Then Partner 2 will give Partner 1 a round dollar amount to pay for the item(s) and Partner 1 will make change. Have Partner 2 count the change to make sure it is correct as well. Then the two students switch roles.

John buys a chocolate and a water. How much does it cost?

Marissa orders an ice cream, a water and a candy. How much does it all cost?

Sydney asks for a lemonade and a pizza. How much will it cost?

Cooper buys a cupcake, lemonade and a candy. How much does it all cost?

5a. 6.

Logan orders a pretzel and a water. What is the total cost?

Cassidy wants to buy a pizza and a water. What will the total be of her order?

John has $10 . How much money will he have left?

Marissa has $7 in her purse. How much money will she have left?

Sydney has $9 00 How much money will she have left?

Cooper has $12 in his wallet. How much money will he have left?

Logan looks in his wallet and has $6 . Can he buy chocolate and lemonade instead? Yes or no?

Jennifer has $7 75 . If she buys 3 ice creams, how much will she have left?

Struggling Learners

Give students actual or play money to act out the making change situations with. This will help them keep track of the amount they are counting up. If needed, consider giving students a “cheat sheet” that shows the values of each coin.

Early Finishers

Imagine you have $10 to buy whatever you want from the snacks on the chart. What would you buy? How much would it cost? How much change would you get back? What if you only had $5? What if you only had $2?

Challenge and Explore

Challenge students to solve the following problem.

Ben buys an art set that costs $34.78. He pays with a $50 bill. How much change will Ben get back?

Count up with coins and bills to find the change.

2 pennies - $34.80

2 dimes - $35.00

$10 bill - $45.00

$5 bill - $50.00

Total change = $15.22

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Do the problems about John together. Tell students to find the costs of the chocolate and water in the chart and ask them: What is the total? [$4.25] Then say: “He has $10 to pay for his items with. How do we find out how

Common Errors

Students may not be careful to keep track of the coins and bills they are counting up when making change. Some students will choose odd combinations to count up. For example, when counting up from $2.24 to $5, they decide to count up nickels instead of starting with a penny to get to 25 cents where they can count up quarters.

Assess

much change he will have left?” [count up from $4.25 to $10] Have students suggest ways of counting up. Be sure that they record the coins and bills as they count them. [count up 3 quarters to get to $5 and then count up 5 dollars to get to $10]

A coffee costs $2.37. I pay with a $5 bill. How much change should I get back?

Draw the coins and bills to count up:

coin and bill combinations could vary slightly, but the amount of change should be the same. One possible solution:

3 pennies - $2.40

1 dime - $2.50

2 quarters - $3.00

2 $1 bills - $5.00

Total change - $2.63

Objective and Learning Goals

y Show the same money amount with different combinations of bills and coins

Vocabulary

y Decimal point - the period that goes between dollars and cents or whole numbers and fractions of a whole number

y Dollar sign - the symbol that represents dollars; $

Materials

y Play money - bills and coins

y Dry-erase boards and markers or paper/ pencil

Pre-Lesson Warm-up

Guiding Questions

Show students combinations of coins and/or bills and have them count the money amount and write it using a dollar sign and decimal point on a dry-erase board or paper.

1 dollar bill, 3 dimes, 2 pennies [$1.32]

1 dollar bill, 1 quarter, 1 nickel, 2 pennies [$1.32]

5 1-dollar bills, 2 quarters, 1 dime [$5.60]

1 5-dollar bill, 6 dimes [$5.60]

2 1-dollar bills, 5 nickels, 1 penny [$2.26]

2 1-dollar bills, 1 quarter, 1 penny [$2.26]

Guiding Questions

1. How can we show the same money amount using a different combination of bills and coins?

[use your knowledge of what each bill and coin is worth to break the values down into lesser-valued coins and bills, or put them together into greater-valued coins and bills]

Games

Play Almost a Dollar to practice counting coins. p. 309

Tell students that the same money amount can be made in different ways. Ask students the following questions and help them count up to find the answers if they struggle.

“How many pennies make a nickel?” (count up 1,2,3,4,5) [5] “How many nickels make a dime?” (5,10) [2] “How many nickels make a quarter?” (5,10,15,20,25) [5] “What is another way to make a quarter using different coins?” [2 dimes and 1 nickel] Continue asking questions like these as needed to help students get thinking about the different combinations of coins and bills.

Have the students help you count the money amounts in Let’s Learn to see that they are the same. Then have students count the money amounts and match them to the combination that is the same amount in Try it Together. Go over the answers and discuss how different combinations made the same amount. For example, in number 1, 2 $5 bills is the same as 1 $10 bill. 3 dimes is the same as 1 quarter and 1 nickel. Have students point out the other combinations that are the same.

Activities

Partners use play money to practice making the same amount of money with different combinations of bills and coins. Partner 1 makes a money amount using play bills and coins and writes the amount with a dollar sign and decimal point on a dry-erase board or paper. Partner 2 must then come up with a different combination of bills and coins to make the same amount of money. Students check each other’s work and then switch roles.

Struggling Learners

Give students actual or play money to make the money amounts with. If needed, consider giving students a “cheat sheet” that shows the values of each coin and maybe even different ways to make that amount. You can have the students help you make this. For example, have students draw a quarter, then have them draw 5 nickels next to it and/or 2 dimes and 1 nickel to show that it is the same amount.

Early Finishers

Go back and find ANOTHER way to make each money amount on the exercise page.

$67.75

Show $21 56 with the fewest possible coins and bills.

Show $16 76 with the fewest possible coins and bills.

Challenge and Explore

Challenge students to make $16.76 in as many ways as they can. Have them draw each solution they come up with and then share solutions with the class.

[answers will vary. There are MANY ways to do this. Have students count their amounts for the class and accept anything that adds up to $16.76]

Apply and Develop Skills (Practice / Exercise page)

Read the directions and do the first problem with the students. Show them that $20.30 was made with 2 $10 bills, 1 quarter and 1 nickel. Ask students for suggestions for how to make $20.30 a different way and write down whatever they say as long as it is the correct amount. Tell students that in the rest of the problems, they will come up with 2 ways to make the amount shown on the price tag. Read numbers 5 and 6 to the students and get them thinking about

Common Errors

Watch for students who have trouble coming up with the fewest number of coins possible to make certain amounts. For example, students may say that 5 dimes is the fewest amount of coins one can use to make 50 cents instead of realizing that they can use 2 quarters. Also, watch for students who write down the same bills and coins but simply write them in a different order.

how to go about solving the problems by saying: “I could make $21 with 2 $10 bills and 1 $1 bill. That is 3 bills. Is there a way I can make $21 with fewer than 3 bills?” [yes, with a $20 bill and a $1] Then say: “I could make 56 cents with 10 nickels and 6 pennies. That is 16 coins. Is there a way to make 56 cents with fewer coins?” [yes, a few ways] “Use the fewest possible coins when drawing these money amounts.”

Assess

Check work for numbers 2 and 3.

Objective and Learning Goals

y Review

y Tell time and find elapsed time

y Count money and make change

Vocabulary

y Hour hand - the short hand on the clock that tells the hour

y Minute hand - the long hand on the clock that tells the minutes

y Elapsed time - the amount of time that passed from one time to another

y Decimal point - the period that goes between dollars and cents or whole numbers and fractions of a whole number

y Dollar sign - the symbol that represents dollars; $

y Change - the money you get back when you pay with more than the cost of the item

Materials

y Play money - bills and coins

y Dry-erase board and marker or paper/ pencil

y Printable fraction cards (for game)

Pre-Lesson Warm-up Guiding Questions

Skip count out loud by 5s. Skip count out loud by 10s. Skip count out loud by 25s.

Guiding Questions

1. How do we figure out how much time has elapsed (or passed) between two times? [begin at the start time, count up by 5s and 1s as you move the minute hand to the end time]

2. How can we count the amount of change we should get back?

[start at the cost of the item and count up by coins and bills until you reach the amount you paid]

Let’s learn!

We can count by 5 s to read the minute hand and to determine elapsed time.

use di erent groups of bills and coins for the same value or to make the same change.

Introduce the Lesson (Try it Together)

Read the review information in Let’s Learn and do the examples with the students.

For the clock examples, have students explain how to find the times on each clock by counting by 5s and 1s. Write the times under the clocks. [9:07 and 1:22] Then ask them to find what time it would be 43 minutes later for the first clock. [9:50] For the money example, ask students another way they can make a dollar besides with 4 quarters. [answers will vary, there are lots of possibilities] Then say: If I want to buy some candy that costs 56 cents and I pay with $1, how much change will I get back? Have students draw the coins and count up as you draw them on the board. [1 possible solution = 4 pennies, 4 dimes = $0.44]

Go through the examples in Try it Together with the students. Have the students do as much of the work as possible since this is a review.

Activities

Count and write the amount of money.

Write the elapsed time.

Elapsed time: Elapsed time: Elapsed time:

Write the amount with a dollar sign and decimal.

John buys chips for $2 00 , a water for $0 50 and candy for $0 25 . He uses a ﬁve dollar bill to pay. How much change does he get back?

Show $12 36 with the fewest possible coins and bills.

Struggling Learners

Provide students with hands-on resources such as play clocks to move the hands on and play money to make change with.

Early Finishers

Show more ways to make $12.36. See how many you can come up with.

Challenge and Explore

Write the time that your school starts and ends on the board. Challenge students to find the amount of time they spend in school. [answers will vary depending on start and end times]

Discuss the strategies that students used.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Remind students to count by 25s, 10s, 5s and 1s to count the money. Read the directions for the clocks and tell students that they should count by 5s and 1s to tell how much time passed from the time on the first clock to the second clock. Read number 10 to the students. Ask: What is the first step? [add to find out how much the items cost altogether] Then what will you do to find out how much change he gets back? [start with the total cost and count up coins and bills until you get to $5. Then add the coins and bills you counted together] For number 11, tell students: I can make $12.36 with 12 $1 bills and 36 pennies, but that is a lot of bills and coins! You can make it with a lot less.

Common Errors

Students often ignore the hours when finding elapsed time and may only focus on the minute hand. Students may not be careful to keep track of the coins and bills they are counting up when making change.

Games

Play Race to Noon to practice finding elapsed time. p. 320

In Chapter 14, we will review basic addition, subtraction, multiplication and division facts. We will also review place value, operations with larger numbers, measurement, perimeter, area, money and fractions.

Addition:

• Basic facts

• Adding 2 -, 3 - and 4 -digit numbers with and without regrouping

Subtraction:

• Basic facts

• Subtracting 2 -, 3 - and 4 -digit numbers with and without regrouping

Multiplication:

• Basic facts

• Multiplying 2 - and 3 -digit

Vocabulary Words

numbers with and without regrouping

• Partial products

• The standard algorithm

• Multiplying money

Division:

• Basic facts

Counting money and making change

Representing fractions and fractions of a group

Objective and Learning Goals

y Recall basic addition facts from memory

y Add 3 and 4-digit numbers with and without regrouping

Vocabulary

y Addition - the act of adding or putting numbers together

y Ones place - the digit on the far right in a whole number, represents single units

y Tens place - the 2nd digit from the right in a whole number, represents groups of 10 units

y Hundreds place - the 3rd digit from the right in a whole number, represents groups of 100 units

y Cubes - the base-10 block that represents ones

y Rods - the base-10 block that represents tens

y Flats - the base-10 block that represents hundreds

y Regroup - make groups of ten when carrying out operations such as addition, subtraction and multiplication

Materials

y Base-10 blocks

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed

Pre-Lesson Warm-up

Guiding Questions

Practice basic addition facts. Have students write the sums on a dry-erase board or on paper.

5 + 6 = [11]

7 + 8 = [15]

3 + 9 = [12]

4 + 7 = [11]

6 + 4 = [10]

Guiding Questions

In this lesson we will review addition of

help you regroup when necessary.

Chase has 376 marbles and Danny has 245 marbles. How many marbles do they have altogether?

Circle groups of ten cubes and rods to regroup in the place value chart.

They have marbles altogether.

Use

1. How can we add 3 and 4-digit numbers? [start in the ones place and add. If there are too many ones, regroup and add the tens. If there are too many tens, regroup and add the hundreds. Continue until all place values have been added]

Read the example in Let’s Learn to the students. Have the students help you solve the problem by circling a group of ten cubes in the chart and adding a rod to the tens place. Then circle 10 rods and add a flat to the hundreds place. Then add the base-10 blocks in each column to get the answer. Tell students that they should have basic addition facts memorized and give them a minute to fill in Try it Together numbers 1-7. Then go over the answers with them. Solve problems 8-11 together with the students using the standard algorithm. Show base-10 blocks for the problems as needed to help students conceptualize the addition.

Activities

Students will practice trading in groups of ten base-10 cubes or rods to regroup when adding. Give students containers with base-10 blocks. Have students make two 3-digit numbers by drawing cards and putting the digits in any order they want. Then add the 2 numbers together by making the numbers with base-10 blocks, trading groups of 10 cubes for rods and groups of 10 rods for flats when they can, and then adding the numbers.

28. Mom has 146 buttons in a jar. Grandma has 275 buttons. How many buttons do they have altogether?

Struggling Learners

Allow students to use base-10 blocks to solve the problems. Give students grid paper or place value charts if they have trouble lining up the digits in the correct places.

Early Finishers

Choose some practice problems. Write and illustrate story problems to go with the equations.

Challenge and Explore

Complete the addition square so that each row and column adds to the sum on the outside of the square.

Mike flew on a trip to California. His first flight was 1 ,285 miles and the second flight was 1 ,475 miles. How many total miles did Mike travel to get to California?

Have student share their solutions and strategies. (It is possible that there is more than 1 correct solution.)

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Tell students that the first problems are basic facts which they hopefully have memorized, and the next problems will require them to slow down and be careful about regrouping. Read the story problems to the students and ask them to tell you the keywords that tell them they need to add, and underline these words in the problems. [altogether and total]

Common Errors

Watch for students who don’t line up the place values correctly. Some students will forget to add the regrouped tens and hundreds.

Games

Play Race to 1,000 to practice adding 3-digit numbers. p. 312

Assess

Check work for numbers 19, 23 and 27.

Objective and Learning Goals

y Recall basic subtraction facts from memory

y Subtract 3 and 4-digit numbers with and without regrouping

Vocabulary

y Subtraction - the act of subtracting or taking a number away from another number

y Ones place - the digit on the far right in a whole number, represents single units

y Tens place - the 2nd digit from the right in a whole number, represents groups of 10 units

y Hundreds place - the 3rd digit from the right in a whole number, represents groups of 100 units

y Cubes - the base-10 block that represents ones

y Rods - the base-10 block that represents tens

y Flats - the base-10 block that represents hundreds

y Regroup - make groups of ten when carrying out operations such as addition, subtraction and multiplication

Materials

y Base 10 blocks

y Number cards 0-9 or a deck of playing cards with the queens, kings and jokers removed

Pre-Lesson Warm-up Guiding Questions

Practice basic subtraction facts. Have students write the sums on a dry-erase board or on paper.

11 - 6 = [5]

15 - 8 = [7]

12 - 9 = [3]

11 - 7 = [4]

10 - 4 = [6]

Guiding Questions

In this lesson we will review subtraction of large

blocks to help you regroup when necessary.

Chase has 266 marbles and he gave 178 to Ethan. How many marbles does Chase have left?

The chart to the right shows how we have to regroup since we do not have enough tens or ones to subtract.

Chase has marbles left.

Use the

1. How can we subtract 3 and 4-digit numbers? [start in the ones place and borrow from the tens place if there aren’t enough ones to subtract, then subtract the ones. Move to the tens place and subtract, borrowing from the hundreds if there are not enough tens to subtract, continue until all place values have been subtracted]

Read the example problem to the students. Show students the base-10 blocks for 268 and how a rod and a flat were borrowed since there were not enough ones and tens to subtract the bottom numbers from. Then solve the problem with the students using the standard algorithm.

Tell students that they should have basic subtraction facts memorized, and give them a minute to fill in Try it Together numbers 1-7. Remind students to use the related addition facts to help them. Then go over the answers with them. Solve problems 8-11 together with the students using the standard algorithm. Show base-10 blocks for the problems as needed to help students conceptualize the subtraction.

Activities

Students will practice borrowing and regrouping rods and flats as needed when subtracting. Give students containers with base-10 blocks. Have students make two 3-digit numbers by drawing cards and putting the digits in any order they want. Then subtract the smaller number from the larger number by making the larger number with base-10 blocks, borrowing and regrouping rods and flats as needed and then subtracting the numbers.

Fill in the missing digits.

Struggling Learners

Give students base-10 blocks to use or help them to draw the base-10 blocks to represent the numbers.

Early Finishers

Read each problem. Solve. Show your work.

17. There are 146 buttons in Mom’s jar. Grandma has 275 buttons. How many more buttons does Grandma have than Mom?

19. When Paul got to Mexico he had to drive 832 miles to get to his hotel. He drove 281 miles on the ﬁrst day and 304 miles on the second day. How many more miles does Paul have to drive?

One way to solve: 832- 281= 551- 304= 247 more miles. Another way to solve: 281 + 304= 585 miles driven

832-585= 247 more miles

18. When Paul flew to Mexico for a vacation, his first flight was 915 miles and the second flight was 687 miles. How many more miles was the second flight than the first?

20. On his ﬁrst day in Mexico Paul had $100 to spend on food. He spent $12 on breakfast, $26 on lunch and $48 on dinner. Does Paul have any money left? If so, how much does he have left?

One way to solve: $100- $12= $88$26=$62- $48= $14 left Another way to solve: $12 +$26= $38 +$48= $86 spent. $100-$86= $14 left.

Apply and Develop Skills (Practice / Exercise page)

Make up your own subtraction problems that require regrouping. Make the number you are starting with using base-10 blocks or draw the blocks to show the number. Think of a number to subtract from your blocks. Challenge yourself to come up with a number that will require regrouping. Then write your problem vertically, cross out or take away blocks and record the algorithm on your paper.

Challenge and Explore

Present the following problem which requires regrouping 3 times to students: 7,343 - 2,957 = [4,386]

Discuss what makes this problem more challenging [you must regroup or “borrow” 3 times] and how students solved it [answers will vary. Some students may draw or use base-10 blocks and borrow a group of 10 from the next higher place value. Other students may know how to use the algorithm to borrow from the thousands place the same way they have for other places]

Read the directions to the students. Tell students that the first problems are basic facts which they hopefully have memorized, and the next problems will require them to slow down and be careful about regrouping. For the fill in the missing digits, complete the first one with students. Have students work with a partner for number 14 and have student work on numbers 15-16 on their own. Read the word problems to the students and ask them to tell you the key words that tell them what they need to do to solve. [how many more tells you to subtract.] Questions 19 and 20 are multi-step problems. Depending on the level of your students you can have students work independently, in partners or work together as a whole class.

Common Errors

Some students will subtract the top number from the bottom number when there isn’t enough to subtract the bottom number from on the top. For example, in 34 - 7, they may subtract 4 from 7 in the ones place and say the answer is 33 instead of borrowing a ten and subtracting 7 from 14. Watch for students who borrow tens or hundreds and then forget to cross out and record the new number of tens or hundreds that are left.

Games

Play The Biggest Difference to practice subtracting 3 and 4-digit numbers. p. 313

Assess

Check work for numbers 8-12, 17-18.

Lighthouse Math | Level C Chapter 14 Exercise 2

Objective and Learning Goals

y Understand multiplication using equal groups, arrays, repeated addition and skip counting

y Know all multiplication facts 0-12 Vocabulary

y Equal groups - a multiplication and division strategy in which equal groups of objects are circled

y Array - an arrangement of objects in equal rows and columns used as a multiplication or division strategy

y Repeated addition - a multiplication strategy in which groups are added

y Skip counting - counting by multiples of a certain number

y Factors - the numbers being multiplied in a multiplication equation

y Product - the answer to a multiplication equation

Materials

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice skip counting out loud:

By 2s

By 5s

By 10s

By 3s

By 4s

If your students are doing well, challenge them to skip count by 6, 7, 8, 9, 11 and 12 as well.

Guiding Questions

1. How can we solve a multiplication fact we don’t know?

[skip count, draw equal groups, make arrays or use repeated addition]

Let’s learn!

Together)

Review the multiplication strategies in the chart using 3 x 4 = 12 as an example. Explain to students that all of these strategies are different ways of showing the meaning of multiplication, “groups of.” All of the strategies for solving 3 x 4 are different ways of finding how much 3 groups of 4 is. Show the students the fact triangle and review the vocabulary, factors and product. Do the Try it Together problems with the students. Have students suggest strategies to use to show the facts. If students say that they have the fact memorized, tell them that’s great! Then ask them how they could use a strategy to prove that their answer is correct. Try to make sure all of the 4 main strategies are represented and accept any strategy that makes sense and gets to the correct answer. You may want to show more than 1 strategy for each example. For numbers 5-11, have students write the products as quickly as they can. Tell them that hopefully, they have most of these memorized by now but to use a strategy when they are unsure. Go over the answers after a couple of minutes. Have students show a strategy for any that they missed.

Activities

Have students choose some facts that they are still working to memorize (if they have them all memorized, ask them to choose facts that they think are tricky for others) and make charts like the one in the Let’s Learn section to show the fact with all 4 strategies. Introduce

Fill in the products.

Struggling Learners

Provide counters to make equal groups, grid paper to make arrays and number lines and hundreds charts to skip count on for students.

Early Finishers

Draw your own wheel like the ones in numbers 22 - 25. Use a different factor in the center. Solve the wheel.

Challenge and Explore

Ask students to think about problem number 27. Ask “How many eggs are in 6 dozen?” [72] Have students draw a strategy to show the problem. [strategies will vary. They might draw 6 dozen eggs, make an 6 x 12 array, skip count by 12s 6 times or add 12 6 times.]

Solve the problems.

26. There are 8 juice boxes in a carton. Todd bought 3 cartons. How many juice boxes did he buy?

There are 12 eggs in a dozen. How many eggs are in 3 dozen?

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Tell them to work quickly to write the products that they have memorized but to always stop and use a strategy if they are unsure. Show them the wheels in numbers 22 - 25 and remind them how these work by completing one fact from number 22. Read the word problems to the students and ask them how they will solve the problems. [8 x 3 for number 26 and 12 x 3 for number 27]

Common Errors

Assess

Games

Play Heads Up to practice finding missing factors in multiplication equations. p. 316

Show a strategy to solve each of the following facts:

8 x 7 = [56, strategies will vary. Students may show 8 groups of 7, an 8 by 7 array, skip count by 7s eight times or add 7 eight times]

9 x 6 = [54, strategies will vary. Students may show 9 groups of 6, a 9 by 6 array, skip count by 6s nine times or add 6 nine times]

Objective and Learning Goals

y Use equal groups, arrays, skip counting and related multiplication facts to solve division facts

y Know all division facts 0-12

Vocabulary

y Divide - to split a number into equal groups

y Division - the act of dividing or splitting a total into equal groups

y Dividend - the number that you start with in a division equation

y Divisor - the number of equal groups you divide the dividend into in a division equation

y Quotient - the answer to a division equation

y Long division - a division notation where the dividend is inside the division symbol, allowing students to handle larger quantities

y Division notations - different ways of writing a division equation

Materials

y Counters, beans or other small objects

y Number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed (for game)

Pre-Lesson Warm-up

Guiding Questions

Practice multiplication facts:

8 x 3 = [24]

7 x 7 = [49]

6 x 5 = [30]

4 x 9 = [36]

9 x 8 = [72]

8 x 6 = [48]

Guiding Questions

Let’s review division.

1. How can we figure out a division fact we do not know?

[use the related multiplication fact, make equal groups out of the total or distribute the total into rows in an array, skip count until you reach the total and keep track of how many skip counts]

Review division. Read the example problem in Let’s Learn. Point out to students that we know the total number of plants, and we need to divide them equally among the rows. Show students both notations and review the vocabulary of dividend, divisor and quotient, as well as where these are located in each notation. Show students the strategies on this page of making an array and using the related multiplication equation. Ask students to suggest other possible strategies [they may suggest skip counting. Accept any strategy that makes sense and gets the correct answer]

Have students help you complete the table in Try it Together. Stop to ask for strategies for a few of the problems. Then have students solve the rest of the Try it Together problems on their own, and go over the answers after a couple of minutes. Use strategies to prove the answers when students disagree.

Activities

Games

Play Heads Up to practice division facts and/or find missing factors. p. 316

Students will practice dividing counters into equal groups. Give students a list of division equations without the quotients. Have students demonstrate the problems by counting out the total number of counters and splitting them into equal groups.

24 ÷ 3 = [8, 3 groups of 8]

42 ÷ 7 = [6, 7 groups of 6]

45 ÷ 5 = [9, 5 groups of 9]

33 ÷ 3 = [11, 3 groups of 11]

28 ÷ 4 = [7, 4 groups of 7]

56 ÷

7. Complete the table.

Struggling Learners

Early Finishers

Write a related multiplication fact for numbers 8 - 25.

Challenge and Explore

Solve the problems.

26. Mom has 25 lettuce plants in her garden. There are 5 lettuce plants in each row. How many rows of lettuce plants does Mom have?

27. Mom picked 21 peppers from her garden and shared them equally with 3 friends. How many peppers did each of her friends get?

Students solve for the missing boxes in this problem:

Apply and Develop Skills (Practice / Exercise page)

Read the directions and do number 1 with the students to help them remember how to use the related multiplication fact to help them solve division facts. Say: “I know that 6 x 9 is 54, so 54 divided by 9 equals 6.” Remind students how to fill in the table in number 7 and do the first problem with the students. Tell them to work quickly to write the quotients that they have memorized in numbers 8 - 25 but to always stop and use a strategy if they are unsure.

Read the story problems to the students and ask them what they will do to solve the problems. [in number 26, 25/5 and in number 27, 21/3]

Common Errors

Students may think they have problems memorized but get quotients confused. Have them use a strategy to check their work.

Assess

Check work for numbers 2 - 6.

Objective and Learning Goals

y Review

y Measuring to the nearest centimeter, inch, ½ inch, and ¼ inch

y Finding the area and perimeter

Vocabulary

y Inch - a unit of measurement that is onetwelfth of a foot; there are 12 inches in 1 foot

y Perimeter - the distance around the outside; found by adding all of the side lengths

y Area - the space inside an object or shape; measured in square units

y Square units - the units used to measure area; 1 square unit equals the area taken up by a square with all sides 1 unit in length

Materials

y Centimeter and inch rulers

y Small common objects to measure

y Blank paper

y Grid paper

Pre-Lesson Warm-up

Guiding Questions

Have students measure their pencil or another common object from their desk to the nearest centimeter, inch, ½ inch and ¼ inch. Compare and contrast the different measurements.

Guiding Questions

1. How can we measure more accurately when measuring in inches? [use the lines in between the inch marks on the ruler to measure to the nearest ½ inch or ¼ inch]

2. How can we find the perimeter of a rectangle? [add all of the side lengths]

3. How can we find the area of a rectangle using multiplication? [multiply the number of rows of squares, by the number of squares in each row; or multiply length times width]

Look at Let’s Learn and review with students how to measure carefully and accurately to the nearest centimeter, inch, ½ inch and ¼ inch. Then review the meaning of perimeter and area and how to calculate each. Go through the Try it Together problems as a class, having the students take the lead as much as possible.

Activities

Have students measure common classroom objects. Have students make a 5 column chart. In the first column write the name of the object they measured. In the second column write the length to the nearest centimeter. In the third column, write the length to the nearest inch. In the fourth column, write the length to the nearest ½ inch, and in the fifth column, write the length to the nearest ¼ inch.

Measure the side lengths to the nearest centimeter. Find the perimeter and area. Write the equations you used to ﬁnd both. Find the area and perimeter.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Have a student remind the class of the equations they can use to find the perimeter and area of a rectangle. When students are finished, have them share their answers to number 6. Then, as a class, try to come up with every possible rectangle they could have drawn. Discuss their strategies for coming up with these.

Struggling Learners

Practice counting by ½ inches and ¼ inches. If possible, give students paper rulers and have them write in the counts at the correct marks on the ruler. Have students come up with clever ways to remember which is area and which is perimeter such as the word peRIMeter having the word rim in it.

Early Finishers

Students can draw rectangles on a piece of paper using a straight edge, measure the side lengths to the nearest centimeter, and find the perimeter and area of each rectangle.

Challenge and Explore

Provide grid paper to students and present the following problem:

Draw as many different rectangles that have a perimeter of 20 units as you can. Find the area of each rectangle. [a 1x9 rectangle has an area of 9 sq units, a 2 x 8 rectangle = 16 sq units, a 3x7 rectangle = 21 sq units, a 4 x 6 rectangle = 24 sq units, a 5 x 5 rectangle = 25 sq units]

Give students time to draw as many rectangles as they can and then discuss how they found all of the rectangles that have a perimeter of 20. [since 10 + 10 = 20, you can break 10 apart to find the top/bottom and side length combinations] Then ask if they notice any patterns. [students should notice that the longer the rectangle is, the smaller the area is and as the rectangle gets closer to a square, the area increases] If time, have students try this with a different perimeter to see if this rule holds true.

Common Errors

Assess

Play The Measurement is Right to practice estimating and measuring length. p. 314

Check work for numbers 1, 2, and 3.

Objective and Learning Goals

y Count bills and coins to find money amounts

y Make change

Vocabulary

y Decimal point - the period that goes between dollars and cents or whole numbers and fractions of a whole number

y Dollar sign - the symbol that represents dollars; $

y Change - the money you get back when you pay with more than the cost of the item

Materials

y Play money - bills and coins

y Copies of open number lines to help students count on to find change.

Pre-Lesson Warm-up Guiding Questions

Practice skip counting by money amounts. Give students a starting point and have them practice counting up by money amount.

Start at 0, count by $20.

[$20, $40, $60, ec.]

Start at $40, count by $5.

[$45, $50, $55, $60, etc.]

Start at $25, count up by $1.

[$26, $27, $28, etc.]

Start at $2, count up by 25 cents.

[$2.25, $2.50, $2.75, etc.]

Start at $1.25, count up by 10 cents.

[$1.35, $1.45, $1.55, etc.]

Start at $5.35, count up by 5 cents.

[$5.40, $5.45, $5.50, $5.55, etc.]

Start at $1.75, count up by 1 cent.

[$1.76, $1.77, $1.78, etc.]

Guiding Questions

1. How can we count money amounts with dollars and cents?

[start with the largest bills and count up by their values, then start with the largest coin and count up by their values until you have counted all of the bills and coins]

2. How can we count the amount of change we should get back?

[start at the cost of the item and count up by coins and bills until you reach the amount you paid]

Read the example problems in Let’s Learn. Have the students help you count Lou’s money in the first example. Write the amounts under the coins as you count up. [$5.25, $5.35, $5.36, $5.37, $5.38] Then have students look at the second example. Remind them that when making change, we want to count up starting with smaller coins. Since the chips cost $3.73, we can count up to $3.75 with 2 pennies. Then we see that we are at a multiple of 25, so we can count up by a quarter to the next dollar - $4.00. Then we can count up by dollars to the amount Lou paid. Work the Try it Together examples with students in a similar manner. In problem 2, model how to count on using an open number line first. Show students how to add a penny to get to a friendly amount [$3.90]. Next, add a dime to get to the next dollar [$4.00]. Finally, add a dollar to get to [$5.00]. Now count up what you added on [ 1 penny + 1 dime + 1 dollar= $1.11]

Activities

Students act out purchasing items and making change with a partner. Give students play money - bills and coins. Have students pretend they are at a candy store. You can give them an imaginary price list, or let them make up the prices, but you may need to set some boundaries (nothing costs more than $10, for example). Partner 1 pretends to be the cashier, and Partner 2 is the customer. Partner 2 will tell the cashier what they want to buy, and Partner 1 will tell Partner 2 how much it costs. Then Partner 2 will give Partner 1 a round dollar amount to pay for the item(s) and Partner 1 will make change. Have Partner 2 count the change to make sure it is correct as well. Then the two students switch roles.

4. Joe bought a bag of chips for 2 dollars and 80 cents. He paid with a $5 bill. How much change did he get back? $

5. Bob bought ice cream cones for $7 56 . He paid with a $10 bill. How much change did he get back? $

6. Otto bought a box of sour candy for 163¢ . He paid with 200¢ . How much change did he get back? ¢

7. Dustin bought nachos for $6 49 . He paid with a $10 bill. How much change did he get back?

8. Seth bought an ice cream cone and a box of sour candy for $5 41 . He paid with a $5 bill and a $1 bill. How much change did he get back? $

9. Jake bought a drink for 109 cents. He paid with 500 cents. How much change did he get back? ¢

Apply and Develop Skills (Practice / Exercise page)

Struggling Learners

Early Finishers

Write, illustrate and solve your own making change word problems.

Challenge and Explore

Challenge students to solve the following problem.

Ben buys a science kit that costs $64.49. He pays with a $100 bill. How much change will Ben get back?

Count up with coins and bills to find the change.

1 penny - $64.50

2 quarters - $65.00

$5 bill - $70.00

3 $10 bills - $100.00 (or 1 $10, and 1 $20)

Total change = $35.51

Read the directions to the students. For numbers 1-3, remind students that they can write the counts underneath the bills and coins as they count up the money. In the rest of the problems, students will be making change. Tell them to count up and write down the counts or draw the coins to keep track of how much they counted up to get to the price. Some students may benefit from using an open number line to determine amounts of change. Provide students with blank open number lines to help them count on. Other students may benefit from using the standard subtraction algorithm to count change. For these students help them see the connection that $5 is the same as 500 cents or $5.00. This will help students line up the place values. Remind students to line up the decimal points when subtracting.

Common Errors

Students may not be careful to keep track of the coins and bills they are counting up when making change. If students choose to use the standard subtraction algorithm students may need to be reminded how to regroup and to line up the decimal places.

Assess

Check work for numbers 3, 4 and 5.

Objective and Learning Goals

y Review

y Identify fractions, equivalent fractions and compare fractions.

Vocabulary

y Benchmark fraction - commonly used fractions that are easy to visualize and identify.

y Equivalent - the same, as in fractions that are the same size

y Whole - the entire thing or group of things that is divided into fractional parts.

Materials

y Fraction images

Pre-Lesson Warm-up Guiding Questions

Show students images of fractions. They can be real life objects cut into equal size pieces, fraction circles, fraction bars, fractions of a group of objects, number lines, etc. Ask the students to identify the fraction shown in the image.

Guiding Questions

1. What is the meaning of the numerator and denominator in a fraction? [the numerator tells how many pieces of the whole are shaded or marked and the denominator tells how many total pieces the whole is cut into]

2. How can we compare fractions? [draw shapes or number lines of the same size, cut them into equal size pieces, shade or mark the correct number of pieces, and look to see which is more or less or if they are equivalent]

Introduce the Lesson (Try it

Look at Let’s Learn and remind students what the numerator and denominator of a fraction mean. Have them check each picture and number line in Let’s Learn to be sure they understand how the picture shows the fraction. Have students use the pictures to describe how they compare the fractions. Have the students complete the Try it Together problems and then go over the answers and clear up any misconceptions.

Activities

Pass out index cards to students. Give students a way to show a fraction such as fraction circle, fraction of a group of objects, number line, etc. All students must use the same type of image to show their fraction, but tell them to make any fraction they wish on their card. Then partner students up and have them place their cards on their dry-erase boards, compare the fractions and write <, >, or = between the two cards. Check students work and then have them compare with a different partner.

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Have students complete the page independently to review. Then go over the answers with the students and answer any questions they still have.

Struggling Learners

Remind students to say “out of” when they see the bar between the numerator and denominator. Have them say it out loud as they read the fractions and make sure that is what the pictures show.

Early Finishers

Students can represent the fractions on the page in different ways. For example, number 1 shows ¾ on a fraction bar. They could draw ¾ of a fraction circle, on a number line, or of a group of objects.

Challenge and Explore

Present the following problem to students:

Mom made 2 cookie cakes. She cut the first one into 8 equal size pieces and Dad ate one piece. She cut the second cookie cake into 12 equal size pieces and Dad ate two of them. Which cookie cake did Dad eat the most of? [the second one]

Have students draw a picture or fractions circles, fraction tiles, or another fraction manipulative to help them solve the problem.

When students are finished, have them work with a partner to try to come up with more equivalent fractions to numbers 5, 6, and 7.

Common Errors

Some students may still confuse the numerator and denominator when shading, marking, or naming fractions.

Games

Play Fraction Card Memory to practice identifying fractions. p. 318

Assess

Check work for numbers 7 and 8.

Objective and Learning Goals

y Review

y Know all basic addition, subtraction, multiplication, and division facts

y Add and subtract multi-digit numbers, multiply by multiples of 10

Vocabulary

y Addition - the act of adding or putting numbers together

y Subtraction - the act of subtracting or taking a number away from another number

y Multiplication - the act of multiplying or finding the total of a certain number of equal groups

y Division - the act of dividing or splitting a total into equal groups

y Regroup - make groups of ten when carrying out operations such as addition, subtraction and multiplication

Materials

y Base-10 blocks

Pre-Lesson Warm-up Guiding Questions

Reinforce the difference between the operations by having students perform all 4 operations on the same pair of numbers. For example:

6 + 2 = [8]

6 - 2 = [4]

6 x 2 = [12]

6 ÷ 2 = [3]

Other number pairs that will work are: 4 and 2, 8 and 4, 8 and 2, 6 and 3, 9 and 3, any number and 1

Guiding Questions

Let’s play a game to practice and become more automatic with addition, subtraction, multiplication and division facts.

• Partner up.

• The teacher calls out a fact such as 3 × 4

• Partners 1 and 2 should simply write the answers down.

• The ﬁrst partner to show their answer to the other is the winner.

• Be ready! The teacher could call out any fact - addition, subtraction, multiplication or division!

1. Why is it important to memorize basic math facts?

[it makes learning multi-digit operations and other more difficult math skills easier]

Read the directions for the game in the Let’s Learn section to the students. Ask if they have any questions about how to play and answer those. Partner them up and spend some time reviewing math facts. Switch it up so that they really have to listen for which operation they are doing. Then review the operations with larger numbers by doing the Try it Together problems with the students. For the addition and subtraction examples, ask students to first tell you how they will know if they need to regroup. [for addition, if the sum in any place value is greater than 9. For subtraction, if in any place value, there is not enough in the top number to subtract the bottom number from] When multiplying by multiples of 10, remind the students that if they know a basic fact such as 3 x 5, they can multiply by multiples of 10 because it is just 3 x 5 tens, 3 x 5 hundreds, and 3 x 5 thousands.

Activities

Practice multi-digit addition and subtraction using base-10 blocks to regroup. Have students pull cards to make two 3-digit numbers, making the larger number with base-10 blocks. Then subtract the smaller from the larger number, regrouping with the base-10 blocks as necessary. Next, have students use addition to check their work. They should make both numbers that they are adding together with base-10 blocks and then regroup as necessary to add. For example, if a student makes the numbers 635 and 284 with their cards, they should make the number 635 with base-10 blocks and try to subtract 284. They will need to trade in a flat for 10 rods in order to subtract in the tens place. Then after they have subtracted, they will add the answer to 284 to see if they get 635. If their answer is 351, they should make 351 and 284 with base-10 blocks and add them together. They will need to regroup 10 rods into a flat since they will end up with more than 9 in the tens place.

Add.

Struggling Learners

Make materials available to students, such as hundreds charts, number lines, grid paper, counters and base-10 blocks. Help students set up problems and start regrouping. For some students, you may want to assign only the odd-numbered problems.

Early Finishers

Use the inverse operation (add to check subtraction and subtract to check addition) to check your work on numbers 21 - 28.

Subtract.

Use

Challenge and Explore

Solve the following problem:

The band plays 234 sold-out concerts each year. Each concert lasts 3 hours. About how many hours does the band perform each year? Estimate by rounding to the nearest hundred. [200 x 3 = 600 hours]

31. The teacher had 6 stacks of paper with 30 pieces of paper in each stack. She dropped them and lost 25 pieces of paper in the wind. How many pieces of paper does she have left?

Apply and Develop Skills (Practice / Exercise page)

Read the directions to the students. Emphasize the importance of watching the signs in the first set of problems by pointing out that in number 2, 3 + 9 is a very different answer than 3 x 9. Read the rest of the directions on the page to the students and have students complete the page independently.

When they are finished, have students try to use estimation to check their work on the larger addition and subtraction problems. They can work with a partner to determine what to round the numbers to and then add or subtract the close, but easier numbers.

Common Errors

Watch for students who confuse the multiplication and addition signs on the basic facts. Some students will still struggle with knowing when to regroup or with recording those regroupings.

Games

Choose a game to practice addition, subtraction, multiplication or division.

Assess

Check work for numbers 17 - 20 and 21, 23, 25, 27, 29 and 31.

Assessments

Chapter assessments cover skills learned throughout the chapter. Use lesson 8 to help students review and prepare for the assessment and go over questions students might have. Review the previous lessons and help students practice skills covered in the chapter.

Tips for administering the assessment

y Read the Teacher Notes at the bottom of the page.

y Make sure you have enough copies for each student.

y Be prepared with sharpened pencils and other tools if needed.

y Have students clear their desks and wait quietly. When passing out the tests, remind students not to begin until you tell them to.

y Tell students to write their name and date on the test and put their pencils down.

y Help students understand the reasons for assessments or tests. An assessment is a way to show what you know. The test helps both the student and the teacher see what skills they know and what skills they may need to review.

y Read the instructions out loud with the students and work through example problems. Point out which problems may take longer or include more than one step. For example, some problems may need a picture and an answer.

y Remind students to take their time and show their work as they work independently to complete the assessment.

y Tell students that when they are finished, they should look over their work and turn their paper over.

y It’s a good idea to have students check back over their work one more time before turning it in.

y If a student gets stuck, you can have them reread the problem or read the problem with you. Tell them to try their best, find important information in the problem and come up with an answer. Remind them to think about what the chapter was about. All assessments were designed and derived from the lessons of that chapter.

Level C assessments include 8 skill-based problems plus 2 problem solving or word problems and are scored out of 10 points.

12/12 Student demonstrates a strong understanding of the chapter skills

10/12-11/12 Student has a solid understanding of the chapter skills and may need some clarification for a skill or reminder to reread the problem

7/12-9/12 Student has a basic understanding of most skills but may need review or clarification with certain concepts. Check that those students took their time and showed their work to determine where errors occurred

4/12-6/12 Student is missing skills from the chapter and needs assistance or extra review

0/12-3/12 Student has minimal understanding of the skills covered in the chapter and will need review or intervention for these skills

ASSESSMENT

Level C I Chapter 1

3.OA.8

3.NBT.1/2

Addition without Regrouping (Lesson 1.1)

3.OA.8

3.NBT.1/2 Addition with One Regrouping (Lesson 1.3)

3.OA.8

3.NBT.1/2 Round to Estimate and Add (Lesson 1.5)

3.OA.8

3.NBT.1/2

Solving Two-Step Story Problems with Addition and Subtraction (Lesson 1.7)

3.OA.8

3.NBT.1/2

Solving Two-Step Story Problems with Addition and Subtraction (Lesson 1.7)

3.OA.8

3.NBT.1/2

Addition of MultiDigit Numbers (Lesson 1.2)

3.OA.8

3.NBT.1/2

Addition with Two Regroupings (Lesson 1.4)

3.OA.8

3.NBT.1/2 Estimate to Check (Lesson 1.6)

3.OA.8

3.NBT.1/2

Review Addition with One Regrouping (Lesson 1.8)

3.OA.8

3.NBT.1/2

Solving Two-Step Story Problems with Addition and Subtraction (Lesson 1.7)

Level C I Chapter 2 ASSESSMENT

3.OA.8

3.NBT.1/2 Subtraction without Regrouping (Lesson 2.1)

3.OA.8

3.NBT.1/2

Subtraction with One Regrouping (Lesson 2.3)

3.OA.8

3.NBT.1/2

Adding to Check Subtraction (Lesson 2.5)

3.OA.8

3.NBT.1/2 Metric Units of Length and Subtraction (Lesson 2.7)

3.OA.8

3.NBT.1/2 Subtraction without Regrouping (Lesson 2.1)

3.OA.8

3.NBT.1/2

Subtraction of Larger Numbers (Lesson 2.2)

3.OA.8

3.NBT.1/2

Subtraction with Two Regroupings (Lesson 2.4)

3.OA.8

3.NBT.1/2

Estimate to Check (Lesson 2.6)

3.OA.8

3.NBT.1/2

Subtraction with Two Regroupings (Lesson 2.8)

3.OA.83.NBT.1/2

Subtraction with One Regrouping (Lesson 2.3)

ASSESSMENT

Level C I Chapter 3

3.OA.1/7/9 Understanding Multiplication through Equal Groups and Repeated Addition (Lesson 3.1)

3.OA.1/7/9

Multiplying by 2s Using Skip Counting (Lesson 3.3)

3.OA.1/7/9 Multiplying by 3s Using Skip Counting, Arrays and Equal Groups (Lesson 3.5)

3.OA.1/7/9 Multiplication Using Factors 0 and 1 (Lesson 3.7)

3.OA.1/7/9 Understanding Multiplication through Equal Groups and Repeated Addition (Lesson 3.1)

3.OA.1/7/9 Multiplication Arrays (Lesson 3.2)

3.OA.1/7/9

Multiplying by 5s Using Skip Counting (Lesson 3.4)

3.OA.1/7/9 Multiplying by 4s (Lesson 3.6)

3.OA.1/7/9

Review Understanding Multiplication through Equal Groups and Repeated Addition (Lesson 3.8)

3.OA.1/7/9 Understanding Multiplication through Equal Groups and Repeated Addition (Lesson 3.1)

Level C I Chapter 4 ASSESSMENT

3.OA.1/4/5/7/9

Review Multiplication Using Arrays and Groups (2,3) (Lesson 4.1)

3.OA.1/7/9

Multiplication with 7s (Lesson 4.3)

3.OA.1/7/9

Multiplication with 9s (Lesson 4.5)

3.OA.1/4/7/9 Factor Practice 6-9 (Lesson 4.7)

3.OA.1/7/9

Multiplication with 8s (Lesson 4.4)

3.OA.1/4/5/7/9

Multiplication with 6s (Lesson 4.2)

3.OA.1/7/9

Multiplication with 8s (Lesson 4.4)

3.OA.1/4/7/9

3.NBT.3

Multiplication with 10s (Lesson 4.6)

3.OA.1/7/9

Review of Multiplication Factors of 0-10 (Lesson 4.8)

3.OA.1/4/7/9

3.NBT.3 Multiplication with 10s (Lesson 4.6)

Level C I Chapter 5 ASSESSMENT

3.OA.1/4/5/7

Using the Commutative Property in Multiplication (Lesson 5.1)

3.OA.1/4/5/7

Identity and Zero Properties with Larger Numbers (Lesson 5.3)

3.OA.1/4/5/7/9

Multiplying by 11s and 12s Using the Distributive Property to ﬁnd Patterns (Lesson 5.5)

3.OA.1/4/7 Using Estimation in Multiplication (Lesson 5.7)

3.OA.1/4/5/7

Identity and Zero Properties with Larger Numbers (Lesson 5.3)

3.OA.1/4/5/7

Using the Associative Property in Multiplication (Lesson 5.2)

3.OA.1/5/7 The Distributive Property (Lesson 5.4)

3.OA.1/5/7 Multiplying by Multiples of 10 (Lesson 5.6)

3.OA.1/4/5/7

3.NBT.3 Multiplication Review (Lesson 5.8)

3.OA.1/4/5/7 Using the Associative Property in Multiplication (Lesson 5.2)

Level C I Chapter 6 ASSESSMENT

3.OA.2/4/7

Introduction to Division (Lesson 6.1)

3.OA.2/3/4/6/7

Dividing by 2 (Lesson 6.3)

3.OA.2/3/4/6/7

Dividing by 3 (Lesson 6.5)

3.OA.2/3/4/6/7

Dividing by 0-5 (Lesson 6.7)

3.OA.2/3/4/6/7

Dividing by 3 (Lesson 6.5)

3.OA.2/4/6/7

Dividing by 1 and Dividing by 0 (Lesson 6.2)

3.OA.2/3/4/6/7

Dividing by 5 (Lesson 6.4)

3.OA.2/3/4/6/7

Dividing by 4 (Lesson 6.6)

3.OA.2/3/4/6/7

Division Review

Dividing by 0-5 (Lesson 6.8)

3.OA.2/3/4/6/7

Dividing by 2 (Lesson 6.3)

Level C I Chapter 7 ASSESSMENT

3.OA.2/4/7

Representing, Understanding, and Solving Problems: Division (Lesson 7.1)

3.OA.2/3/4/6/7

Dividing by 6 (Lesson 7.3)

3.OA.2/3/4/6/7

Dividing by 8 (Lesson 7.5)

3.OA.2/3/4/6/7

Dividing by 6,7,8,9 (Lesson 7.7)

3.OA.2/3/4/6/7

Dividing by 6,7,8,9 (Lesson 7.7)

3.OA.2/4/6/7

Representing, Understanding, and Solving Problems: Multiplication and Division (Lesson 7.2)

3.OA.2/4/6/7

Dividing by 7 (Lesson 7.4)

3.OA.2/3/4/6/7

Dividing by 9 (Lesson 7.6)

3.OA.2/4/7

Representing, Understanding, and Solving Problems: Division Review (Lesson 7.8)

3.OA.2/3/4/6/7

Dividing by 6,7,8,9 (Lesson 7.7)

3.OA.3/7/8 Representing, Understanding, and Solving Problems Involving Operations (Lesson 8.1)

3.OA.3/7/8 Representing, Understanding, and Solving Problems Involving Operations (Lesson 8.3)

3.OA.3/7 Representing, Understanding, and Solving Problems Involving Operations (Lesson 8.5)

4.0A.4 Factors and Multiples (Lesson 8.7)

3.OA.3/7/8

3.NBT.1 Representing, Understanding, and Solving Problems Involving Operations (Lesson 8.2)

Solve the problem and use estimation to check. Solve the problem and use estimation to check.

Select the correct factors for the number below. Answer:

Look at the multiplication chart below.

3.OA.3/7/8

3.NBT.1 Representing, Understanding, and Solving Problems Involving Operations (Lesson 8.2)

3.OA.3/7/8 Representing, Understanding, and Solving Problems Involving Operations (Lesson 8.4)

3.OA.4 Determining the Unknown Number (Lesson 8.6)

4.0A.4 Factors and Multiples (Lesson 8.8)

3.OA.3/7/8

3.NBT.1 Representing, Understanding, and Solving Problems Involving Operations (Lesson 8.4)

Level C I Chapter 9 ASSESSMENT

3.NF.1/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.1)

3.NF.1/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.3)

3.NF.1/2/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.5)

3.NF.1/2/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.7)

3.NF.1/2/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.3)

3.NF.1/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.2)

3.NF.1/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.4)

3.NF.1/2/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.6)

3.NF.1/2/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.8)

3.NF.1/2/3

3.G.2

Understanding and Comparing Fractions (Lesson 9.4)

Level C I Chapter 10 ASSESSMENT

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.1)

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.3)

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.5)

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.7)

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.5)

Teacher's notes

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.2)

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.4)

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.6)

3.NF.1/3

Understanding and Comparing Fractions Fraction Review (Lesson 10.8)

3.NF.1/3

Understanding and Comparing Fractions (Lesson 10.4)

3.MD.4

Represent and Interpret Data (Lesson 11.1)

3.MD.8

Geometric Measurement (Lesson 11.3)

3.MD.7/8 Geometric Measurement (Lesson 11.5)

3.MD.2

Measuring Liquids/ Volumes/Mass (Lesson 11.7)

3.MD.4

Represent and Interpret Data (Lesson 11.1)

3.MD.4 Represent and Interpret Data (Lesson 11.2)

3.MD.5/6/7 Geometric Measurement (Lesson 11.4)

3.MD.2 Liquid Volume (Lesson 11.6)

3.MD.7/8

Geometric Measurement Review (Lesson 11.8)

3.MD.2 Measuring Liquids/ Volumes/Mass (Lesson 11.6)

Level C I Chapter 12 ASSESSMENT

3.MD.3

Represent and Interpret Data (Lesson 12.1)

3.MD.3

Represent and Interpret Data (Lesson 12.3)

3.G.1

Shapes and Attributes (Lesson 12.6)

3.G.1

Shapes and Attributes (Lesson 12.7)

3.MD.3

Represent and Interpret Data (Lesson 12.2)

3.MD.3

Represent and Interpret Data (Lesson 12.2)

3.MD.3

Represent and Interpret Data (Lesson 12.4)

3.G.1

Shapes and Attributes (Lesson 12.6)

3.G.1

Shapes and Attributes (Lesson 12.8)

3.MD.3

Represent and Interpret Data (Lesson 12.2)

Level C I Chapter 13 ASSESSMENT

3.MD.1

4.NBT.4 Multi-digit Arithmetic (Lesson 14.1)

3.OA.1 Multiplication (Lesson 14.3)

3.MD.7/8 Measurement,

(Lesson 14.5)

3.NF.2 3.G.2 Fractions (Lesson 14.7)

3.OA.8/9 Solving Problems Involving Operations (Lesson 14.2)

4.NBT.4 Multi-digit Arithmetic (Lesson 14.2)

3.OA.1 Division (Lesson 14.4)

3.NBT.1 2.MD.10 Money (Lesson 14.6)

3.OA.4 3.0A.9

3.NBT.3 Multiplication (Lesson 14.8)

3.OA.8/9 Solving Problems Involving Operations (Lesson 14.3)

Game resources

Coins front/back

Base-10 blocks blackline images - 4 flats, 10 rods, 10 cubes

Number cards 0-9

Hundreds chart

Blank number line 0-10

10 frame

Base-10 blocks - rods, cubes, flats

Dry-erase boards and markers Counters

1/4inch grid paper

Deck of cards

Dice

Game resources

Printable: Fraction cards

Printable: Find My Triangle

Rulers

Chart paper/poster paper

Pencil

Play or paper clocks

Index cards

Sticky notes, slips of paper

3D shape blocks or models

Scissors

Flashcards

Games

CHAPTER R1

6s are Wild

Materialss 6-sided dice

Instructions Pairs of students play with one six-sided die. Partner 1 rolls the die twice and adds the two numbers they rolled together. Partner 2 does the same, and whichever partner has the largest sum wins the round. *There are two exceptions: If a player rolls two 6s or a 6 and a 5, they score 20 points. They do not need to add the numbers.The players take turns rolling and adding. Students should keep tallies for how many rounds they win, and the player who has won the most rounds when time is up wins the game.

Teacher Guidance You may need to model how to keep score for the students. Make sure they understand that they score 20 points for rolling two 6s OR one 6 and one 5, but all other turns they add their two rolls together. Circulate and remind students to let the partner whose turn it is do the adding but that they should let them know if they disagree. They can solve disagreements by using a strategy such as counting on or drawing pictures.

Skills addition facts to 10

Level_Chapter_Lesson

Brain vs. Hand

Materialss paper/pencil or dry-erase board/marker

Instructions Students will play in groups of 3. Student one will ask students 2 and 3 a math (addition, subtraction, multiplication, division) fact. Student 2 will mentally compute and call out the answer. Student 3 MUST write the answer and SHOW the answer to student 1 (student 3 may not talk). If student 2 calls the answer out before student 3 shows the answer to student 1, student 2 wins. If student 3 shows the answer to student 1 before student 2 calls it out, student 3 wins. The students then rotate roles - student 3 passes the paper or dry-erase board to student 1.

Teacher Guidance Circulate and encourage students to use strategies to help settle any disagreements. *The student with the paper/dry-erase board may get frustrated if they know the answer before they have time to write it. Point out that they will get a turn to call out answers quickly as well, and praise them for showing self-control.

Skills addition facts to 18  subtraction facts to 18  multiplication facts  division facts

Level_Chapter_Lesson

Draw and Subtract

Materialss a deck of playing cards

Instructions Pairs of students play with one deck of cards. Student 1 draws 2 cards from the deck and subtracts the smaller number from the larger number. The difference is their score. If the student draws a face card (jack, queen, king or ace), that card is wild, and they can make it any number they want. If the student draws a Joker, their score for that round is 0. Student 2 then draws 2 cards from the deck and subtracts for their score. The student with the highest score wins and keeps all 4 cards. Then they repeat this process until time is up. At the end of the game, the student with the most cards wins.

Teacher Guidance Circulate and encourage students to use strategies to help settle any disagreements. Help students to be strategic about the numbers they choose to use when they draw a face card. For example, if they draw a 10 and a queen, they would want the queen to be a 1 so that their equation is 10 - 1 = 9 and they score 9 points for that round.

Skills subtraction facts to 10

Level_Chapter_Lesson

Almost a Dollar

LC_R1_L4-11

Materialss play or real coins

Instructions This game can be played in partnerships or groups of 3 or more. Each student grabs a small handful of coins out of a container. They then sort and count the amount of money they pulled out. The winner is whoever is closest to 1 dollar without going over. That player gets a point, all students put their coins back in the container and start again. Students can play a certain number of rounds or stop when time is up and see who has the most points.

Teacher Guidance Circulate and help students solve disagreements. Be sure students are sorting their coins and counting the money amounts out loud for their opponents to hear.

Skills counting money

Level_Chapter_Lesson

Games

CHAPTER R2

The Biggest Handful

Materials containers of base-10 rods and cubes (and maybe flats)

Instructions This game can be played with 2-4 players. Each player should grab a handful of rods and cubes out of the container and sort them. If they need to, they can trade 10 cubes for a rod. Each player should read their number, and the other players must agree. Then the players decide together which player has the largest number. That player gets a point, the players put their blocks back in the container and then they each grab another handful. Players can play a certain number of rounds, up to a certain score or for a certain time period. When the game ends, the player with the most points wins.

Teacher Guidance Circulate to settle any disagreements and help students count their tens and ones. *This game can be modified to include flats and make 3-digit numbers, however you may need to change the rules by allowing students to use two hands to pull out their blocks.

Skills place value - making numbers with base-10 blocks

Level_Chapter_Lesson LC_R2_L1-23  LC_R2_L2-25

Draw and Round

Materials number cards 1-9 or a deck of cards with queens, kings and jokers removed

Instructions Students can play this game in groups of 2-4. Each player draws 2, 3 or 4 cards. If using playing cards, aces are 0 and jacks are 1. Each player makes a 2, 3 or 4-digit number with their cards by putting them in whichever order they choose. Then they round that number to the nearest ten, hundred or thousand depending on which skill they are practicing. Their rounded number is their score. The players settle any disputes about each player's score, and then they each draw more cards. Play continues until there are not enough cards left for each player to make another number. Students can count by tens, hundreds or thousands to add up their scores, and the player with the highest total wins.

Teacher Guidance Circulate to help settle any disputes and help students add up their scores. If some groups finish fast, they can always shuffle the cards and play again. Give students who are struggling or having frequent disputes tools like hundreds charts or number grids. Encourage them to draw "rounding hills" or look at a number line.

Skills rounding to the nearest ten or hundred

Level_Chapter_Lesson

Least or Greatest

Materials number cards 1-9 or a deck of cards with queens, kings and jokers removed

Instructions Students play in groups of 4. Before play begins, the teacher tells the students whether they should start with "greatest" or "least." If you tell them to start with greatest, the greatest number wins. If you tell them to start with least, the least number wins. Each player draws 3, 4 or 5 cards depending on how large the numbers you want them to practice ordering. The students then make a number by placing the cards they drew in any order they wish (aces are 0 and jacks are 1). For example, if a student draws a 5, 2 and ace, they can make the number 520, 250, 205, 502, 52 or 25. The group then works together to write their numbers in order from least to greatest if the teacher told them to start with least, and from greatest to least if the teacher told them to start with greatest. After the students have put the numbers in order, the student with the first number in the order gets 4 points, the student with the second number gets 3 points, the student with the third number gets two points and the student with the fourth number gets 1 point. Students should keep track of each player's score with tally marks. The student who "won" by getting 4 points gets to choose whether they will start with the greatest number or the least number for the next round. Students return their cards to the bottom of the deck and draw again. The teacher can choose a certain number of rounds, or the game can be played until time is up.

Teacher Guidance

Have 3 students come up to help you model a few rounds of the game so students can get the hang of it before they play on their own. Circulate to help students order their numbers and settle any disputes.

Skills Ordering numbers least to greatest and greatest to least

Level_Chapter_Lesson

LC_R2_L6-33 

LC_R2_L7-35

Games

CHAPTER 1

Race to 500

Materials number cards 1-9 or a deck of cards with queens, kings and jokers removed

Instructions Students play in pairs. Each student draws two cards and makes a 2-digit number (aces are 0 and jacks are 1). Then they draw two more cards and make another 2-digit number underneath their first number. They add their numbers, regrouping if necessary, and keep track of the answer. On the next round and every round after that, they draw two cards and make a 2-digit number to add to their previous total. The first player to reach 500 is the winner. If both students reach or pass 500 on the same round, the student with the higher total wins. If there happens to be a tie, they take one more turn, and the largest sum wins.

Teacher Guidance Circulate to help students keep track of their scores, regroup as necessary and settle any disputes between students.

Skills Adding 2-digit numbers with and without regrouping

Level_Chapter_Lesson

Race to 1,000

Materials number cards 1-9 or a deck of cards with queens, kings and jokers removed

Instructions Same as Race to 500 except students will draw 3 cards to make 3-digit numbers to add. The first player to reach 1,000 is the winner this time.

Teacher Guidance Sometimes students will reach 1,000 rather quickly (possibly even on their first turn). They can play multiple games in one sitting.

Skills Adding 3-digit numbers with and without regrouping

Level_Chapter_Lesson

The Biggest Difference

Materials number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed

Instructions Two students each draw 6 or 8 cards. Using their cards, they make two 3 or 4-digit numbers. They must put their cards down in the order that they draw them. Then they subtract the smaller number from the larger number. Whichever student has the larger number for their difference is the winner and they get a point. Students draw more cards and subtract again. Teachers can give students a certain number of rounds to play or a certain amount of time.

Teacher Guidance Encourage students to help each other and check each other's work when subtracting. Give students tools such as base-10 blocks or grid paper if needed to help them subtract.

Skills subtraction of 3 and 4-digit numbers

Level_Chapter_Lesson

CHAPTER 2 Draw and Subtract

Materials a deck of playing cards

Skills subtraction facts to 10

Level_Chapter_Lesson



Games

The Measurement is Right

Materials Rulers  small objects to measure

Instructions Students play in groups of 3. Student 1 chooses an object, measures it to the nearest 1/4 inch and records the measurement. Student 1 tells Students 2 and 3 the length of the object, and Students 2 and 3 look for a different object that they think is about the same length. After they have found an object, they measure their objects to the nearest 1/4 inch, and the player who is closest to the first player's measurement without going over is the winner. Now the winning player becomes Student 1 and measures a different object for Students 2 and 3 to try to match the length of.

Teacher Guidance Circulate and help students measure accurately, solving any disputes among students by having them all measure again and discuss how they know the correct measurement.

Skills Estimating length and measuring to the nearest 1/4 inch

Level_Chapter_Lesson

CHAPTER 3 Go Fishing

Materials counters  a die  number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed

Instructions Students play in pairs. Partners each pick a card and draw that many circles on a piece of paper or dry-erase board (aces are 1). These circles represent "ponds." Then they each roll the die to find out how many "fish" are in each "pond." They put that many counters in each of their circles. Whichever partner has the most total "fish" wins and gets a point. (Example: student draws an 8 and rolls a 3. They should draw 8 circles and put 3 counters in each circle. Their total is 24.) Then students put their counters and cards back, and round 1 is over. Students can play a certain number of rounds, for a certain amount of time or to a certain score.

Teacher Guidance Be sure students are making EQUAL groups. Help students to come up with efficient ways of counting their "fish" (repeated addition, skip counting, doubling, etc.)

Skills Making equal groups, multiplying by 1-6

Level_Chapter_Lesson

Times Table War

Materials number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed

Instructions Choose (or let students choose) a times table (x2s, x3s, x4s, etc.) that you want them to practice. This game is played just like the card game War except the students must multiply their card by the chosen factor. Pairs of students will each draw a card from the deck and multiply that number by the factor you have chosen (aces are 1). They must call out the product of their card times the chosen factor. Whoever has the larger product keeps both of the cards. If one student thinks that the other student called out the wrong answer and can prove it (by skip counting, drawing equal groups or arrays, etc.), then the student who caught the wrong answer automatically wins even if they had the smaller product. If both partners call out a wrong answer, then the partner with the largest product still wins. If the partners draw the same card, they each put a 2nd card face down and a 3rd card face up. They multiply that 3rd card by the factor that was chosen, and whoever has the higher product wins. The goal is for one partner to take all of the cards to win the game. If there is not enough time, whoever has the most cards when time is up wins.

Teacher Guidance If you want students to multiply the chosen factor by 11 and 12, leave in two of the face cards and tell students which face card is 11 and which is 12. Insist that students multiply and call out the product in each round. Don't let them get away with just playing War by letting the person who draws the larger number win. Encourage students to try to catch their partners in a wrong answer by reminding them that they can win even if they draw the smaller card.

Skills Multiplying by a given factor

Level_Chapter_Lesson

LC_C13_L2-257

Games

CHAPTER 4

Heads Up

Materials number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed

Instructions Students play in groups of 3. Two of the students each draw a card without looking at it and put it on their forehead so the other two players can see it. The third student multiplies the numbers on the other two students' foreheads together and calls out the product. Based on the product and the factor that they see on the other students' forehead, the students with cards on their foreheads have to determine what number is on their own forehead. (Example: Student 1 sees that Student 2's card is a 4. Student 3 calls out 28. Student 1 knows that 4 x 7 is 28, so they call out 7). Whichever student calls out the correct number first wins. That student keeps their card, and the students rotate so that a different player is calling out the product each time. At the end of the game, the student with the most cards wins.

Teacher Guidance If you want students to practice multiplying and finding missing factors with 11 and 12, leave in two of the face cards and tell students which face card is 11 and which is 12.

Skills Finding Missing Factors

Level_Chapter_Lesson

CHAPTER 5 Deal and Solve

Materials Student dry-erase boards  deck of cards per student pair

Instructions: With a partner, deal the cards between the two students. Each student receives half of the cards. Keep the cards face down. Face cards are worth 1. Have students on their dry-erase boards, draw the following math equation leaving blanks to fill in card values. Example: __ x (__ + __) = __ . Each student draws three cards and fills in their own equation and solves. Whomever has the higher value after solving the equation between the pair of students earns a point. Keep track of points earned on the top right of the student dry-erase board. Make a tally mark for every time a student earns a point. Play 7-8 rounds or until all cards have been used. If there is a tie, give both students a point.

Teacher Guidance Circulate around the room looking for any misunderstandings of the distributive property. Ask students to show you how they are using the distributive property. Have students rewrite the equation to show (__ x __) + (__ x__).

Skills The Distributive Property of Multiplication.

Level_Chapter_Lesson LC_C5_L3-117

CHAPTER 6

Around the World

Materials Flashcards

Instructions Sit in a circle. Ask one student to stand behind nother student in the circle. State a math problem aloud or show a flash card with a math problem on it, and ask both students to figure out the answer. The first student who calls out the correct answer moves to stand behind the next student in the circle. The object of the game is to see how far one student can "travel" without making any mistakes.

Teacher Guidance Establish rules: Only two students can call out an answer each time. Anyone who calls out an answer when it is not their turn is out of the game. Set a time limit, 30-60 seconds, depending on skill and practice. If a student gets it wrong, the other student has 5 seconds to answer. If neither student answers correctly in the allotted time, both sit down and two new students are chosen. When practicing a specific divisor, you can include the related multiplication facts, or include other divisors that the students have learned in previous lessons as well.

Skills Fact practice  Add, subtract, multiply, divide

Level_Chapter_Lesson

CHAPTER 9 AND 10

Fraction Card Memory

Materials Printable Fraction Cards

Instructions This game can be played with 2 - 4 players. Print (preferably on cardstock) the cards, cut them out and lay the cards out face down in a grid. One student flips over any two cards. If they match - a fraction and its picture - then they get to keep the cards. Otherwise, they turn the cards back over. The next student takes a turn doing the same thing. When all cards have been matched, the player with the most cards wins.

Teacher Guidance Circulate to make sure students are correctly matching the pictures with fractions and settle any disputes between students by asking them to prove that their cards match. They might say something like the fraction is 2-fourths and 2 out of 4 pieces are shaded.

Skills Identifying fractions

Level_Chapter_Lesson

LC_C9_L2-185 

LC_C9_L3-187 

LC_C9_L6-193 

LC_C9_L7-195 

LC_C10_L2-203 

LC_C10_L5-209 

LC_C10_L8-215 

LC_C9_L4-189 

LC_C9_L8-197 

LC_C10_L3-205 

LC_C10_L6-211 

LC_C14_L7-285

LC_C9_L5-191 

LC_C10_L1-201 

LC_C10_L4-207 

LC_C10_L7-213 

CHAPTER 12

2 Truths and a Lie

Materials models of 3D shapes

Instructions This game is played in partnerships. Partner 1 chooses a shape and shows it to Partner 2. Then Partner 1 says or writes 3 statements about the shape. Two of the statements should describe true attributes of that shape and 1 should describe an attribute that is false. (For example, when describing a cube, 2 truths might be: 1) The faces are all squares and 2) There are 6 faces. The lie might be: This shape has 4 vertices.) Student 2 must decide which statements are the 2 truths and which is the lie. Partners switch roles, and Partner 2 now chooses a shape to describe with 2 truths and 1 lie and Partner 1 decides which are the truths and which is the lie. They go back and forth, taking turns in this manner. Partners keep score by giving each other 1 point every time they decide correctly which are the truths and which is the lie.

Teacher Guidance Give students key words and phrases to use when coming up with the truths and lie about their shape such as "faces," "edges," "vertices" and "shape of the base." Before students play the game, model for them, coming up with 2 truths and a lie for a shape. During play, circulate and model again for partnerships who are struggling to describe their shapes accurately.

Skills Describing attributes of 3D shapes

Games

CHAPTER 13

Race to Noon

Materials Play clocks  number cards 1-9 or a deck of cards with jacks, queens, kings and jokers removed

Instructions Partners set their clocks to 8:00 a.m. Partner 1 draws 2 cards and puts them together in any order to make a 2-digit number. They will move the hands on their clock to show the time after that many minutes pass. For example, if they draw a 2 and a 5, they could move 52 minutes to 8:52. Partner 2 must check and agree with Partner 1's work and then draw 2 cards of their own and move the hands on their own clock. After both partners agree with each other's times, they repeat this process. So if Partner 1 draws an Ace (1) and a 3, they will start at 8:52 and move 31 minutes to 9:23. Then it is Partner 2's turn again. The first player to get to 12:00 noon wins.

Teacher Guidance Model a turn or two with a student as your partner. Circulate and make sure students are figuring out elapsed times correctly. Help students settle disputes if needed.

Skills Elapsed time

Level_Chapter_Lesson

Acute triangle a triangle in which all angles are less than 90 degrees 236 13-4

Bar graph

a representation of data using rectangular bars to show how large each value is

238 12-1

Base 10 blocks

Addend the numbers being added together in an addition equation

Addition the act of adding or putting numbers together

Area model of multiplication

4 R1-1

blocks that represent place values and can be combined in groups of tens to make the next higher place value

22 R2-1

4 R1-1

Capacity

the maximum amount a container can hold

230 11-6

a visual representation of the partial products method of multiplication

200 11-4

Centimeter

a unit of measurement; there are 100 centimeters in a meter

70 2-7

Area

the space inside an object or shape; measured in square units

226 11-4

Change the money you get back when you pay with more than the cost of the item 266 13-6

Commutative property

2 × 3 = 3 × 2 changing the order of the factors does not change the product

112 5-1

78 3-2

Array an arrangement of objects in equal rows and columns used as a multiplication or division strategy

Associative property

(3 × 2) × 1 = 3 × (2 × 1) in multiplication, when three or more numbers are multiplied they can be grouped in any order and the product will be the same

114 5-2

Computation

the act of ﬁnding an answer by using math; adding, subtracting, multiplying and/or dividing

288 14-8

Congruent having the same size and shape

248 12-6

Cubes the base 10 block that represents ones 22 R2-1

Data

a collection of facts, such as numbers or measurements, that can be represented in a graph

Decimal point

the period that goes between dollars and cents or whole numbers and fractions of a whole number

12-1

Dollar sign

the symbol that represents dollars; $

Dollars unit of money that represents 100 cents

Dot plot a representation of data using dots

13-5

Di erence the answer to a subtraction equation 10 R1-4

Dimes coin or unit of money that represents 10 cents 266 13-6

Divide to split a number into equal groups 130 6-1

6 ÷ 3 = 2

Dividend

the number that you start with in a division equation 132 6-2

Division the act of dividing or splitting a total into equal groups 130 6-1

Division notations

di erent ways of writing a division equation

Divisor

8 ÷ 4 = 2

the number of equal groups you divide the dividend into in a division equation 144 6-8

12-2

Edge the line formed on a 3D shape where two faces meet 246 12-5

Elapsed time the amount of time that passed from one time to another 260 13-3

Equal groups a multiplication and division strategy in which equal groups of objects are circled

3-1

Equivalent 1 2 3 6 = the same, as in fractions that are the same size

9-3

Estimate to ﬁnd a close enough answer when the exact answer is not needed

1-5

Estimate to check check if the answer is reasonable by rounding to close numbers

Face the ﬂat sides on a 3D shape

1-6

12-5

Glossary

Factors

the numbers being multiplied in a multiplication equation

Flats

the base 10 block that represents hundreds 24 R2-2

Fraction

3-5

a number that represents a part of a whole 184 9-1

Liquid volume

the amount of space a liquid takes up 230 11-6

Long division

a division notation where the dividend is inside the division symbol, allowing you to handle larger quantities

148 7-1

Minuend

the number that you start with in a subtraction equation

10 R1-4

Fractional part

each individual section or group that can be represented by a unit fraction, such as 1 2 195 9-6

Hour hand

the short hand on the clock that tells the hour 256 13-1

Hundreds place

the third digit from the right in a whole number represents groups of 100 units 28 R2-4

Identity property

5 × 1 = 5

Minute hand

the long hand on the clock that tells the minutes 256 13-1

Multiples

the product of multiplying one whole number by another 96 4-2

Multiplication

the act of multiplying or ﬁnding the total of a certain number of equal groups 76 3-1

Number line

a tool to help with counting

Ones place

8 R1-3

when multiplied by one, a number keeps its identity

Inch (in)

5-3

a unit of measurement that is one-twelfth of a foot 220 11-1

Inverse operations

the opposite operation that can be used to check your work

R1-6

the digit on the far right in a whole number; represents single units 24 R2-2

Order from greatest to least to put numbers in sequence from largest to smallest

32 R2-6

Order from least to greatest to put numbers in sequence from smallest to largest

32 R2-6

Parallel

side by side, always keeping the same distance apart

248 12-6

Parts

the equal size sections or groups that something is divided into when talking about fractions 184 9-1

Pennies

the smallest unit of money, representing 1 cent 266 13-6

Perimeter

the distance around the outside; found by adding all of the side lengths

224 11-3

Repeated addition

a multiplication strategy in which groups are added 76 3-1

Rods

the base 10 block that represents tens

Round

ﬁnd a close but easier-to-work-with number to a given number

R2-2

Pictograph

a representation of data using pictures or symbols

240 12-2

R2-3

Skip counting counting by multiples of a certain number 80 3-3

Square units

the units used to measure area; 1 square unit equals the area taken up by a square with all sides 1 unit in length

226 11-4

Prime number

a number that has exactly two factors—one and itself 178 8-7

Product

the answer to a multiplication equation 81 3-3

Quadrilateral a shape with four sides 248 12-6

Quotient

the answer to a division equation 144 6-8

Regroup

make groups of ten when carrying out operations such as addition, subtraction and multiplication 40 1-1

Subtraction

the act of subtracting or taking a number away from another number 10 R1-4

Subtrahend

the number that is being taken away in a subtraction equation 10 R1-4

Sum the answer to an addition equation 6 R1-2

Target number

the number that is in the place value that is being rounded to 36 R2-8

Tens place

the second digit from the right in a whole number; represents groups of 10 units

26 R2-3

Glossary

T-chart

a tool used to separate and organize information 260 13-3

= 1,000

Thousands

the fourth digit from the right in a whole number; represents groups of 1,000 units 34 R2-7

2 × 5 = 10

5 × 2 = 10

Turn around facts

the multiplication fact that results when the order of the factors is changed 127 5-8

Vertex

the point formed at the corners where edges meet on a 3D shape 246 12-5

Whole

the entire thing or group of things that is divided into fractional parts 184 9-1

Zero property

15 × 0 = 0

multiplying by zero always results in zero 116 5-3