Grade 4 - Smart to the Core (Student Booklet) - FULL by Educational Bootcamp

SMART TO THE CORE GRADE 4

Building Depth of Knowledge (DOK)

BOOKLET INCLUDES: Train the Brain Practice Drills - drills on the basic skills associated with each individual benchmark (DOK 1) Target Practice Activities - practice problems requiring the application of skills and real-world problem solving (DOK 2)

Think Tank Questions - non-routine task-based problem sets (DOK 3 and 4) Four-Star Challenge - assessments that measure students’ depth of knowledge including their ability to reason abstractly, create models, write arguments, and critique strategies Math Bootcamp (Grade 4) Publisher: Educational Bootcamp Content Development: Educational Bootcamp Senior Editor: Yasmin Malik Cover Design: Sadiq Malik Copyright © 2014 by J & J Educational Bootcamp Educational Bootcamp Sunrise, Florida 33351 All rights reserved. No part of this publication may be reproduced, transmitted, or stored in a retrieval system, in whole or in part, in any form or by any means, electronic or mechanical, including photocopying, recording, or otherwise, without written permission of Educational Bootcamp. Printed in the United States of America

SMART TO THE CORE TABLE

CONTENTS

Grade 4 SMART TO THE CORE LESSONS

CCSS Code

FOUR STAR CHALLENGE—SCORING RUBRIC

PAGE NUMBER 4

4.OA.1 (4.OA.1.1)

MISSION 1: Making Multiplicative Comparisons

5—14

4.OA.2 (4.OA.1.2)

MISSION 2: Making Multiplicative and Additive Comparisons

15—24

4.OA.3 (4.OA.1.3)

MISSION 3: Solving Multi-Step Word Problems

25—34

4.O.A.1.a & 4.OA.1b

MISSION 4: Using Comparative Relational Thinking

35—44

4.OA.4 (4.OA.2.4)

MISSION 5: Investigating Factors and Multiples

45—54

4.OA.5 (4.OA.3.5)

MISSION 6: Finding Number and Shape Patterns

55—64

4.NBT.1 (4.NBT.1.1)

MISSION 7: Understanding Place Value Relationships

65—74

4.NBT.2 (4.NBT.1.2)

MISSION 8: Reading, Writing, and Comparing Numbers

75—84

4.NBT.3 (4.NBT.1.3)

MISSION 9: Rounding Whole Numbers

85—94

4.NBT.4 (4.NBT.2.4)

MISSION 10: Adding and Subtracting Whole Numbers

95—104

4.NBT.5 (4.NBT.2.5)

MISSION 11: Multiplying Whole Numbers

105—114

4.NBT.6 (4.NBT.2.6)

MISSION 12: Dividing Whole Numbers

115—124

4.NF.1 (4.NF.1.1)

MISSION 13: Finding Equivalent Fractions

125—134

4.NF.2 (4.NF.1.2)

MISSION 14: Using Models to Compare Fractions

135—144

4.NF.3 (4.NF.2.3)

MISSION 15: Adding Fractions with Like Denominators

145—154

4.NF.4 (4.NF.2.4)

MISSION 16: Multiplying Fractions by a Whole Number

155—164

4.NF.5 (4.NF.3.5)

MISSION 17: Adding Fractions with Denominators of 10 & 100

165—174

4.NF.6 (4.NF.3.6)

MISSION 18: Converting Decimals and Fractions

175—184

4.NF.7 (4.NF.3.7)

MISSION 19: Comparing Decimals & Fractions to the 100th Place

185—194

4.MD.1 (4.MD.1.1)

MISSION 20: Using Custom and Metric Measurements

195—204

4.MD.2 (4.MD.1.2)

MISSION 21: Solving Problems Involving Measurement

205—214

4.MD.3 (4.MD.1.3)

MISSION 22: Calculating Area and Perimeter

215—224

4.MD.4 (4.MD.2.4)

MISSION 23: Solving Problems Presented in Line Plots

225—234

4.MD.5 (4.MD.3.5)

MISSION 24: Recognizing Angles

235—244

4.MD.6 (4.MD.3.6)

MISSION 25: Using a Protractor to Measure Angles

245—254

4.MD.7 (4.MD.3.7)

MISSION 26: Adding and Subtracting Angles

255—264

4.G.1 (4.G.1.1)

MISSION 27: Identifying Lines and Angles

265—274

4.G.2 (4.G.1.2)

MISSION 28: Classifying Two-Dimensional Figures

275—284

4.G.3 (4.G.1.3)

MISSION 29: Identifying Lines of Symmetry

285—294

ALL

Student Grids

295

SMART TO THE CORE Recommended Classroom Regimen (Includes all components of the classroom package)

DAY/ TIME

MATH BOOTCAMP: 5-Day Regimen DOK 1: BASIC RECALL & RECOGNITION

Day 1 (60 min.)

Benchmark Power Drill: Gradual Release of Basic Skills (10 min.) Hands On Math: Activity by Benchmark (20 min.) Smart to the Core Booklet: Train the Brain Practice 1 (Basic Skills) (15 min.) Smart to the Core Booklet: Target Practice 1 (Basic Application) (15 min.) DOK 1 & 2: BASIC APPLICATION

Day 2 (60 min.)

Rock Climbing Review: Mixed Daily Review - Day 2 (10 min.) Benchmark Power Drill: Gradual Release of Basic Application (20 min.) Smart to the Core Booklet: Train the Brain Practice 2 (Basic Skills) (15 min.) Smart to the Core Booklet: Target Practice 2 (Basic Application) (15 min.)

DOK 2 & 3: APPLYING SKILLS & CONCEPTS/STRATEGIC THINKING Day 3 (60 min.)

Rock Climbing Review: Mixed Daily Review - Day 3 (10 min.) Company Drill Game: Review by Benchmark (10 min.) Mathables® by Benchmark: Foldable Activity (20 min.) Mathables® by Benchmark: Think Tank Journaling (20 min.) DOK 3 & 4: STRATEGIC & EXTENDED THINKING

Day 4 (60 min.)

Day 5 (60 min.)

Rock Climbing Review: Mixed Daily Review - Day 4 (10 min.) Benchmark Power Drill: Modeling Strategic Thinking (25 min.) Smart to the Core Booklet: Train the Brain Practice 3 (Application) (15 min.) Smart to the Core Booklet: Think Tank Question (Strategic Thinking) (10 min.) ASSESSMENT BY BENCHMARK & DIFFERENTIATED INSTRUCTION Smart to the Core Booklet: Four-Star Challenge (20 min.) Smart to the Core Booklet: Review the Assessment (10 min.) Differentiated Instruction: Based on the Four-Star Challenge Results (30 min.) Group 1 - Hands On Math Activity with DOK Worksheet - 1 Star (Intensive) Group 2 - Hands On Math Activity with DOK Worksheet - 2 Stars (Strategic) Group 3 - Hands On Math Activity with DOK Worksheet - 3 Stars (Prevention) Group 4 - Triathlon Game and/or Company Drill Game (Enrichment)

INSTRUCTIONS FOR SCORING THE FOUR-STAR CHALLENGE (1) Multiple Choice Section: Assign one point to all multiple choice items answered correctly. (2) Short Answer Section: Assign a maximum of two points. 2 POINTS - Complete correct response, including correct work shown and/or correct labels/units if called for in the item. 1 POINT - Partial correct response. 0 POINTS - No response, or the response is incorrect.

(3) Think Tank Section: Assign a maximum of four points. 4 POINTS - Shows complete understanding of the problem’s mathematical concepts and principles; uses appropriate mathematical terminology; and executes computations correctly and completely. 3 POINTS - Shows nearly complete understanding of the problem’s mathematical concepts and principles; uses mostly correct mathematical terminology; and computations are generally correct, but may contain minor errors. 2 POINTS - Shows some understanding of the problem’s mathematical concepts and principles; uses some correct mathematical terminology, and may contain major computational errors.

1 POINT - Shows limited to no understanding of the problem’s mathematical concepts and principles; may misuse or fail to use mathematical terminology, but attempts an answer. 0 POINTS - No answer attempted.

Intensive Basic Skills Math Strategies

Application of Strategies

Target for Enrichment

The student earns ONE star for correctly answering 49% or less.

The student earns TWO stars for correctly answering 50 - 69%.

The student earns THREE stars for correctly answering 70 - 89%.

The student earns FOUR stars for correctly answering 90 - 100%.

Tier 3 In need of Intensive Support

Tier 2 In need of Strategic Support

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Tier 1 * Proficient, but in need of Benchmark

Tier 1 Proficient Target for Enrichment

MISSION 1: Making Multiplication Comparisons Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Bootcamp STRATEGY 1: Draw a bar model to represent 35 = 5 × 7. 5

7 7

5 times as many as 7 is 35

7 times as many as 5 is 35

Multiplication Comparison

Bootcamp STRATEGY 2: Use the number line to represent 35 = 5 × 7. 1

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Interpret the model as a multiplication comparison:

7 times as many as 5 is 35

Bootcamp STRATEGY 3: Use key words to interpret multiplication comparisons as multiplication equations. KEY WORD

same as

times

MEANING

Equals (=)

Multiply (×)

each row each shelf each ____ Multiply (×)

Multiply (×)

Example 1: 8 times as many as 9 is 72:

9 = 72

Example 2: 45 is 5 times as many as 9:

45 = 5

5 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.OA.1 (4.OA.1.1) DIRECTIONS: Use the arrays below to form multiplication equations.

DIRECTIONS: Use the number line below to model 45 = 9 × 5, and form a comparison. 3 0 1 2 3 4

5 6 7

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Verbal Comparison:

DIRECTIONS: Use the number line below to model 40 = 4 × 10, and form a comparison. 4 0 1 2

3 4 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Verbal Comparison:

DIRECTIONS: Interpret numeric equations as verbal comparisons. Numeric Equation Example:

35 = 5 × 7

9 × 5 = 45

32 = 8 × 4

3 × 8 = 24

Verbal Multiplication Comparison 35 is 5 times as many as 7.

DIRECTIONS: Represent verbal comparisons as numeric equations. Verbal Multiplication Comparison Example: 35 is 5 times as many as 7.

44 is 4 times as many as 11.

3 times as many as 5 is 15.

24 is 6 times as many as 4.

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Numeric Equation

35 = 5 × 7

Target PRACTICE 1 1

Peter colored 36 hard boiled eggs for the holiday. This is 9 times as many eggs as Sara colored. What equation shows the number of eggs Sara colored? A

36 = n × 9

n = 36 × 9

36 = 9 + n

n = 36 + 9

Select all of the statements that are true.

Patti’s mom needed 4 cars to transport neighborhood children to the museum. Each car can transport 5 children. Which equation shows how many children can be transported in the 4 cars? A

5+4=9

5 × 4 = 20

4 × 4 = 16

5 × 5 = 25

Select all of the statements that are true.

8 × 8 × 8 × 8 × 8 × 8 = 48

6 is 36 times as many as 6

6 × 8 = 48

3 × 2 × 2 × 2 × 3 = 36

6 × 6 × 6 × 6 × 6 × 6 = 48

12 × 3 = 36

8 times as many as 6 is 48

6 × 6 × 6 × 6 × 6 × 6 = 36

6 times as many as 8 is 48

9 × 4 = 36

48 is 8 times as many as 6

6 + 6 + 6 + 6 + 6 + 6 = 36

Which of the following statements represent the equation 15 = 3 × 5?

Which of the following statements represent the equation 16 = 4 × 4?

Mina bought 3 shirts last month and 5 shirts this month.

Leon has 16 apples and bought 4 more.

Mina bought 3 shirts every month for 5 months.

Leon has 16 apples and ate 4 apples.

Mina has 15 shirts and gave 3 of them away.

Leon has 4 apples and bought 4 more.

Mina has 15 shirts and gave 5 of them away.

Leon bought 4 apples from each of the 4 vendors.

7 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.OA.1 (4.OA.1.1) DIRECTIONS: Use the models below to form multiplication equations.

DIRECTIONS: Use the number line below to model 42 = 7 x 6, and form a comparison.

0 1 2

3 4 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Verbal Comparison: DIRECTIONS: Interpret numeric equations as verbal comparisons.

Numeric Equation Example:

35 = 5 × 7

28 = 4 × 7

6 × 9 = 54

36 = 6 × 6

Verbal Multiplication Comparison

35 is 5 times as many as 7.

DIRECTIONS: Represent verbal comparisons as numeric equations.

Verbal Multiplication Comparison Example: 35 is 5 times as many as 7.

7 times as many as 8 is 56.

63 is 7 times as many as 9.

3 times as many as 15 is 45.

10 50 is 5 times as many as 10.

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Numeric Equation

35 = 5 × 7

Target PRACTICE 2 1

Which of the following equations represent 27 is 3 times as many as 9?

There are 3 times as many pizza slices remaining than pizza slices eaten. What equation can be used to find how many pizza slices were remaining if 10 pizza slices were eaten?

3 = 27 + 9

3 = 27 × 9

27 = 9 + 3

10 − 3 = n

3 × 10 = n

27 = 9 × 3

3 + 10 = n

10 ÷ 3 = n

Sally has 7 boxes of chocolates. Each box contains c chocolates. If Sally has a total of 28 chocolates, which equation can be used to find c? Select all of the options that apply.

Melanie baked 6 apple pies. She used a apples for each pie. If Melanie used a total of 36 apples, which equation can be used to find a? Select all of the options that apply.

7 × 28 = c

36 × 6 = a

28 × 7 = c

6 × 36 = a

7 × c = 28

a × 6 = 36

c × 28 = 7

36 × a = 6

c × 7 = 28

6 × a = 36

28 × c = 7

a × 36 = 6

Which of the following statements represents the equation 12 × 4 = 48? A

Lisa travels 12 minutes to get to work. Vivian travels 4 times as long. Vivian travels 4 minutes longer than Lisa. Lisa travels 48 minutes to get to work. Vivian travels 4 times as long. Vivian travels 12 minutes longer for work than Lisa.

Which of the following statements represents the equation 9 × 10 = 90? A

9 more than 10 is 90

10 times as many as 9 is 90

90 subtracted by 10 is 9

90 times as many as 10 is 9

9 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.OA.1 (4.OA.1.1) DIRECTIONS: Create a multiplication equation from the problems below and solve. 1 Farah has 4 times as many pictures as Beth. If Beth has 12 pictures, how many pictures does Farah have?

2 Corey’s dog is 6 times heavier than his cat. His cat weighs 4kg. How much does Corey’s dog weigh?

The Johnson family is looking to adopt 4 new kittens. There are 9 times as many kittens at the local kennel than they can adopt. How many kittens does the local kennel have?

4 Terra’s goldfish is 4 centimeters long. Her new fish is 3 times longer. How long is the new fish?

5 An oak tree is 3 times taller than a pine tree. If the pine tree 14 feet tall, how tall is the oak tree?

6 Kalandra ran 5 laps around the track yesterday. Today she ran 3 times as many laps. How many laps did Kalandra run today?

7 This month, Cagney saved 3 times as much as last month. Last month he saved $9.00. How much did Cagney save this month?

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THINK TANK QUESTION DIRECTIONS: Use this family of numbers to complete the following tasks:

4 6 24

Part I: Create 2 multiplication equations using the numbers above.

Part II: Create 2 comparison statements based on the equations you made in Part I.

Part III: Draw 2 pictures to represent the statements you made in Part II.

Part IV: Create 2 story problems that represent the multiplication equations created in Part I.

11 I Copying is strictly prohibited

FOUR--STAR CHALLENGE - 4.0A.1 (4.0A.1.1) 1

Which of the following equations represent 42 is 7 times as many as 6?

There are 4 times as many giraffes than elephants at the zoo. There are 9 elephants. What equation can be used to find how many giraffes are at the zoo?

7 = 42 + 6

42 = 7 × 6

42 = 7 + 6

n×9=4

4+9=n

6 = 42 × 7

9×4=n

n=9+4

Carol bought 5 drinks at the food court. Each drink costs $3.00. Select all of the equations that could be used to find the total cost of all the drinks she bought.

Jordan bought 4 trays of eggs. Each tray has 8 eggs. Select all of the equations that could be used to find the number of eggs Jordan bought.

15 × 3 = 45

32 × 8 = 256

5 × 3 = 15

4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 = 32

5 + 5 + 5 = 15

4 × 8 = 32

3 × 5 = 15

8 × 32 = 256

3 × 3 × 3 × 3 × 3 = 15

8 × 8 × 8 × 8 = 32

15 × 5 = 75

8 × 4 = 32

Which of the following statements can be used to represent the equation 33 = 11 × 3?

Which statement below represents the number line?

Marla wrote 3 pages yesterday. She wrote 33 times that amount today.

5 times as many as 6 is 35

Marla wrote 33 pages yesterday. Today, she wrote 11 times more.

6 times as many as 5 is 30

Marla wrote 3 pages yesterday and 3 times that amount today.

5 times as many as 7 is 30

6 times as many as 4 is 24

Marla wrote 11 pages yesterday. Today, she wrote 3 more.

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Mrs. Brown has 4 times as many pairs of shoes as Mr. Brown. Complete the tables below to show 2 different possibilities for the number of pairs of shoes Mr. Brown might have.

POSSIBILITY # 1 Mr. Brown Mrs. Brown

POSSIBILITY # 2 Mr. Brown Mrs. Brown

(pairs of shoes)

A charity organization gave T-shirts to the local schools in the neighborhood. The number of classes that received the T-shirts can be seen in the table below.

Part I: Complete the verbal comparison by adding the school level or the number of classes to make each verbal comparison statement true. Fill in the multiplication equation to support your answer. School Level Number of Classes

Pre-K

Elementary

Middle

High

3 classes

12 classes

9 classes

48 classes

The ________________ school has 4 times as many classes as the elementary school.

Multiplication Equation: ______ × ______ = ______ Part II: Complete the verbal comparison to make the verbal comparison statement true. Create a bar model to support your answer. The middle school has ______ times as many classes as the Pre-K school.

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THINK TANK QUESTION DIRECTIONS: Use this family of numbers to complete the following tasks: 9

9 3 27

Part I: Create 2 multiplication equations using the numbers above.

Part II: Create 2 verbal comparison statements using the equations made in Part I.

Part III: Draw 2 pictures to represent the statements made in Part II.

Part IV: Create 2 story problems that represent the multiplication equations made in Part I.

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MISSION 2: Making Multiplicative And Additive Comparisons Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Bootcamp STRATEGY 1: Draw a bar model to represent multiplicative comparisons involving unknown numbers and to help solve multiplication or division word problems with an unknown or to solve for x. Example 1: 5 times as many as a number is 35.

Example 2: 5 times more than the number 3.

n 7n n n

35 5 × n = 35

5×3=n

Bootcamp STRATEGY 2: Use the number line to represent 7 times as many as a number. 1

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Interpret the model as a multiplication expression:

35 = 7 × n 35 = n × 5

Bootcamp STRATEGY 3: Use key words to interpret multiplication sentences. KEY WORD

same as

times

MEANING

Equals (=)

Multiply (×)

each row each shelf each ____ Multiply (×)

Multiply (×)

Example 1: 8 times as many as an unknown number is 72:

n = 72

Example 2: 45 is an unknown number times 9:

45 = n

9 15 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.OA.2 (4.OA.1.2) DIRECTIONS: Use the bar models below to solve multiplication equations. 1 5 times as many as a number is 25. 2 7 times more than the number 3.

n 7n n n

DIRECTIONS: Use the number line below to model 45 = n × 9 and form a verbal comparison.

3 0 1 2

3 4 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Verbal Comparison: DIRECTIONS: Use the number line below to model n = 4 × 10 and form a verbal comparison.

4 0 1 2

3 4 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Verbal Comparison: DIRECTIONS: Interpret a numeric equation as a verbal multiplication comparison.

Numeric Equation Example:

n × 7= 35

9 × n = 45

n × 4 = 32

24 = 3 × n

Multiplication (Verbal) Comparison An unknown number times 7 is 35.

DIRECTIONS: Represent verbal comparisons as numeric equations.

Multiplication (Verbal) Comparison Example: 35 is 5 times an unknown number

44 is 4 times an unknown number.

An unknown number times 5 is 15.

6 times an unknown number is 24.

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Numeric Equation

35 = 5 × n

Target PRACTICE 1 Amy made 72 pieces of jewelry this week. She made 8 times more necklaces than bracelets. How many necklaces did Amy make?

$48

$50

Select all of the word problems that can be represented by the equation 8 × t = 24.

Will has 24 eggs. He gave 8 eggs to his sister. If t represents the number of eggs left, what equation represents t? Will bought 24 eggs. The eggs are packed equally in 8 trays. If t represents the number of eggs in each tray, what equation represents t? Will bought 24 eggs. Each tray contains 8 eggs. If t represents the number of trays he bought, what equation represents t? Will has 24 eggs. He bought an additional 8 eggs. If t represents the total number of eggs he has, what equation represents t? 5

A box of pens cost $12. That is 4 times the cost of a box of pencils. How much does a box of pencils cost?

Mae Ling collected 56 seashells. Her brother collected 7 seashells. How many times more seashells did Mae Ling collect than her brother? Grid your answer.

Select all of the word problems that can be represented by the equation r × 9 = 45. Linda has 9 bags of hairclips. Each bag contains r clips. If Linda has a total of 45 clips, what equation represents r? Linda has 45 hairclips. She gave her sister r clips. If she was left with 9 clips, what equation represents r?

Linda has 9 hairclips. She bought an additional r clips. If Linda has a total of 45 clips, what equation represents r? Linda has 45 hairclips. The clips come in packages of 9. How many packages ( r ) does she have? 6

Jake counted a total of 55 traffic lights and stop signs in his town. There were 4 times the number of stop signs than traffic lights. How many stop signs did Jake count? Grid your answer.

17 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.OA.2 (4.OA.1.2) DIRECTIONS: Use the bar models below to solve multiplication equations.

1 5 times as many as a number is 55. n 7n n n n n n

7 times more than the number 4.

4 4

DIRECTIONS: Use the number line below to model 44 = n × 11 and form a verbal comparison.

3 0 1 2

3 4 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Verbal Comparison: DIRECTIONS: Use the number line below to model 40 = 8 × n and form a verbal comparison.

4 0 1 2

3 4 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Verbal Comparison: DIRECTIONS: Interpret numeric equations as verbal multiplication comparisons.

Numeric Equation

n × 7= 35 5

8 × n = 56

n × 7 = 42

36 = 6 × n

Multiplication (Verbal) Comparison An unknown number times 7 is 35.

DIRECTIONS: Represent verbal statements as numeric equations. Multiplication (Verbal) Comparison Example: 35 is 5 times an unknown number 8

54 is 9 times an unknown number.

An unknown number times 8 is 72.

4 times an unknown number is 48.

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Numeric Equation

35 = 5 × n

Target PRACTICE 2 1

Julio counted 72 boxes in 2 warehouses. He counted 7 times more boxes in the first warehouse than in the second. How many boxes are in the second warehouse?

Movie tickets cost $9. A circus ticket costs 5 times more than a movie ticket. How much do circus tickets cost?

$14

$55

$45

$112

Michael found 8 boxes of nails in the garage. Each box contains n nails. If Michael found a total of 48 nails, select all of the equations that can be used to find n.

Jordan bought 9 pairs of pants during a sale. Each pair of pants cost c dollars. If Jordan paid a total of $81 for all the pants, select all of the equations that can be used to find c.

8 × 48 = n

81 × 9 = c

48  8 = n

9 × 81 = c

8 × n = 48

c × 9 = 81

n × 48 = 8

81  c = 9

n × 8 = 48

9 × c = 81

48  n = 6

c  9 = 81

Jane sang 40 songs in her spring concert. She sang 10 songs in her fall concert. How many times more songs did Jane sing in her spring concert? Grid your answer.

Pablo has earned 36 A’s this year in science class. He earned 4 times the number of A’s than B’s. How many B’s did Pablo earn? Grid your answer.

19 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.OA.2 (4.OA.1.2) DIRECTIONS: Use drawings and equations to solve the problems below.

1 Maria made 60 donuts for a bake sale. She made 6 times more glazed donuts than chocolate donuts. How many chocolate donuts did Maria make?

2 A pack of dress socks cost $18. That is 3 times the cost of a pack of knee high stockings. How much does a pack of knee high stockings cost?

3 An airplane ticket costs $120 one way. That is 5 times the cost of a bus ticket. What is the cost of a bus ticket?

4 Valerie made 50 baskets in 2 basketball games. She made 9 times as many baskets in the first game than in the second game. Use an equation to solve for the number of baskets Valerie made in the first game.

5 Jamal counted 42 cars in the parking garage. He counted 6 times more sports cars than family cars. How many sports cars did Jamal count?

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THINK TANK QUESTION There are 2 girl scout troops competing for first place in the sale of cookies. Use the 2 bar models below to complete the following questions.

BAR MODEL 2

BAR MODEL 1

$400

Troop 1 Troop 2

Troop 1

$400

Troop 2

Part I: Which of the above bar models is best used to determine the amount of money Troop 2 made? Check one:

Bar Model 1

Bar Model 2

Part II: How much did both troops make in all? (Show your work)

Part III: Explain why you think the bar model you selected is the best choice.

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FOUR-STAR CHALLENGE - 4.0A.2 (4.0A.1.2) 1

A baker made a total of 49 cupcakes. She baked 6 times as many vanilla cupcakes than chocolate. How many vanilla cupcakes did the baker make? Grid your answer.

Norris has 3 times as many toy cars as Bradford. Together, they have 36 toy cars. How many toy cars does Norris have? Grid your answer.

Daryl wants to arrange 36 bottles equally on 4 shelves in his store. If each shelf will have b bottles, which equations can be used to find b? Select all of the equations that apply.

Sasha bought s skirts at the mall. Each skirt cost $7, and she paid a total of $28 for all the skirts. Which of the following equations can be used to find s? Select all of the equations that apply.

b  4 = 36

28  7 = s

b × 36 = 4

28  s = 7

36  4 = b

7  s = 28

36  b = 4

7 × 28 = s

4 × 36 = b

s × 7 = 28

4 × b = 36

s  28 = 7

Mr. Payton tiled his room floor using 5 times as many light tiles as dark tiles. He used a total of 60 tiles. How many light tiles did he use?

There are 132 patients admitted in the community hospital. That is 12 times the number of doctors. What equation shows the number of a doctors at the hospital?

12 + d = 132

d × 12 = 132

132 × 12 = d

d = 132 + 12

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Josie has 3 times as many purses as her sister McKenzie. Together, Josie and her sister have 36 purses.

Part I: How many purses does Josie have? How many purses does McKenzie have?

SISTER

Josie

McKenzie

NUMBER OF PURSES Part II: How many more purses does Josie have than McKenzie? _________

Part I: Create a story problem that supports the model on the right.

2 ft Dog House

Oak Tree

Part II: Form an equation based on the model and solve.

The Patterson family has 2 ladders. The ladder they use outside is 3 times as tall as the ladder they use inside.

Part I: Determine if the following tables could possibly be the heights of the ladders. Option A:

Option B:

Option C:

Indoor Ladder

Outdoor Ladder

Indoor Ladder

Outdoor Ladder

Indoor Ladder

Outdoor Ladder

12 feet tall

36 feet tall

3 feet tall

12 feet tall

8 feet tall

16 feet tall

Possible Not Possible

Part II: Explain how you made your selections in Part I.

23 I Copying is strictly prohibited

THINK TANK QUESTION DIRECTIONS: Use the table below to complete the following

questions. 10 PART I: Samantha needed to buy nails to finish her home renovation project. She bought a total of 150 nails. She bought 2 times more 1-inch nails than 2-inch nails. How many 2-inch nails did she buy? Create a bar model that represents this problem. Formulate an equation to solve for the total number of 2-inch nails she bought. BAR MODEL:

MULTIPLICATION EQUATION:

NUMBER OF 2-INCH NAILS PURCHASED: ________ Part II: Create a bar model to show that there are 3 times as many 3-inch nails in a pack than there are 4-inch nails in a pack. Write an equation and solve for the number of 4-inch nails in 1 pack. BAR MODEL:

Packs of Nails

MULTIPLICATION EQUATION:

NUMBER OF 4-INCH NAILS IN 1 PACK: ________

24 I Smart to the Core I Educational Bootcamp

Nail Size

Number of Nails per Pack

1-inch

100

2-inch

3-inch

4-inch

MISSION 3: Solving MULTI-STEP WORD PROBLEMS Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Bootcamp STRATEGY 1: Draw bar models to represent multi-step problems. Example: Mr. Gomez bought his son a game for $45 and his daughter a doll for $26. He paid with a $100 bill. How much change did he get? $45

$45 + $26 $71

$26 ?

$100 $71

$100 ‒ $ 71 $ 29

Bootcamp STRATEGY 2: Use a grid to solve word problems involving rows and columns. Example: A parking lot has 15 rows with 8 parking spaces in each row. In each of the first 6 rows, 5 parking spaces are reserved for staff. How many parking spaces are not marked reserved for staff? Answer: 120—30 = 90

Bootcamp STRATEGY 3: Use key words to interpret multiplication sentences. KEY WORD

less than

times

each

each row

and

left

MEANING

Equals (=)

Subtract (‒)

Multiply (×)

Divide/ Multiply (÷) or (×)

Multiply (×)

Add (+)

Subtract (‒)

Multiply (×)

Example: How many stamps are needed for 21 small envelopes and 17 medium-sized envelopes if each envelope needs 2 stamps? Step 1: Remember PEDMAS when solving multi-step problems. P (Parenthesis and Grouping), E (Exponents, Powers, and Square Roots), MD (Multiplication and Division from left to right), and AS (Addition and Subtraction from left to right)

n = (21 + 17) × 2 n = 38 × 2 n= 76

Step 2: In the problem, 21 and 17 must be added first. Step 3: The sum must then be multiplied by 2. 25 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.OA.3 (4.OA.1.3) 1

Caesar bought a box of copy paper for $48 and an ink cartridge for $31. He paid with a $100 bill. How much change did he receive?

Solve USING BAR MODELS (Show your work)

There are 10 rows of seats in a gymnasium with 9 seats in each row. Students fill in the 9 seats of the first 8 rows. How many empty seats are in the gymnasium?

Solve USING A Grid (Show your work)

A flower garden has 10 plots of tulip plants. There are 25 plants in each plot. There are also 15 rose bushes. How many tulip plants and rose bushes are there?

Solve USING EQUATIONS (Show your work)

26 I Smart to the Core I Educational Bootcamp

Target PRACTICE 1 1

What is the total cost of 4 meals at $12 each and 3 desserts at $10 each?

How many stamps are needed for 15 small envelopes and 19 medium-sized envelopes if each envelope needs 2 stamps?

$90

$78

$29

$22

Select all of the expressions below that equal to 21.

Select all of the expressions below that are equal to 35.

(5 × 5) - 4

(50 ÷ 5) + (3 × 11)

(80 ÷ 4) + (7 - 2 )

(7 × 9) - 44

(10 ÷ 5) + (12 × 2)

(50 ÷ 2) - (9 × 2)

(9 × 7) - 42

(5 × 5) + 10

(16 - 9) + (6 × 2)

(24 ÷ 2) + (51 - 28)

5 A bakery has 41 cookies left. The owner made 14 more cookies. Each cookie gives a profit of $2. What will be the profit for all of the cookies once they are sold? Grid your answer.

A restaurant has 226 bagels and 145 freshly baked cookies. Within a few minutes, the restaurant sold 112 freshly baked cookies. How many bagels and cookies are left? Grid your answer.

27 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.OA.3 (4.OA.1.3) 1

Mr. Bermudez bought a drill for $57 and a hammer for $9. He paid with a $100 bill. How much change did he get?

Solve USING BAR MODELS (Show your work)

A parking lot has 8 rows with 16 parking spaces in each row. In each of the first 7 rows, 4 parking spaces are marked handicapped. How many parking spaces are not marked handicapped?

Solve USING A Grid (Show your work)

A school cafeteria has 5 trays of food with 15 sandwiches on each tray. The cafeteria also has 4 trays of fruit cups with 15 fruit cups on each tray. If 30 fruit cups are sold, how many sandwiches and fruit cups are left?

Solve USING EQUATIONS (Show your work)

28 I Smart to the Core I Educational Bootcamp

Target PRACTICE 2 1

What is the total cost of 3 movie tickets at $9 each and 2 buckets of popcorn at $8 each?

How many sky lifts are needed for 18 ladies and 14 men if 4 people can ride each lift at a time?

$42

$11

$36

$43

Which of the following equations are correct? Select all of the equations that apply.

8 + (6 × 3) = 42

(28  4) + (7 − 5) = 9

(9  3) + (5 − 2) = 6

10 + (2 × 5) = 17

(27  9) − 1 = 2

35 − (4 × 7) = 12

(4 × 2) + (6 − 2) = 12

(24  8) − 2 = 5

19 − (5 × 3) = 42

(5 × 3) + (12  4) = 18

(4 × 8) − (36  6) = 8

(2 + 8) × (16  8) = 20

Vanady made 34 bracelets to sell at a yard sale. Her sister made 17 more bracelets for her to sell. Each bracelet will be sold for $7. What is the value of all of the bracelets Vanady has to sell? Grid your answer.

A bicycle shop had 210 trail bikes and 84 beach cruisers for sale. Last week, the store sold 110 trail bikes. How many bikes are left in the store in all? Grid your answer.

29 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.OA.3 (4.OA.1.3) DIRECTIONS: Solve the problems below.

1 Daniel had 5 boxes of nails. Each box had 63 nails. If he used 105 nails, how many nails does Daniel have left?

2 Mrs. Miller has 262 shampoo samples from the company she works for. She kept 57 of them for herself. She wants to use the rest of the samples to divide equally into 15 gift bags. How many samples will be in each gift bag? How many are left over?

3 Valerie has 26 brown pocketbooks and 43 black ones in stock at her store that she wants to put in storage. She wants no more than 7 pocketbooks in each storage box. How many boxes will she need?

4 A chemist has 88 mls of water. He wants to pour an equal amount of water into 8 beakers. Then he will add 73 mls of solution to each beaker. How much liquid will be in each beaker?

30 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION Saniya wants to buy herself a new tablet that costs $289. Saniya has saved $74, but needs to save the same amount of money (x dollars) each month for the next 5 months. Part I: Write an equation that helps Saniya determine the amount of money she .needs to save each month.

Equation _______________________________________________

Part II: Solve the equation to find the amount of money Saniya must save each .month to meet her goal of buying a new tablet. (Show your work)

31 I Copying is strictly prohibited

FOUR-STAR CHALLENGE - 4.0A.3 (4.0A.1.3) 1

What is the total cost of 4 hotdogs at $4 each and 6 buckets of popcorn at $4 each?

How many taxicabs are needed for 14 ladies and 13 men if 6 people can ride in each taxicab?

$40

122

$38

168

$30

128

$22

162

Michelle bought 6 plates and 4 cups during the mall sale. Each plate cost $12 while each cup cost $9. Select all of the statements that are true.

Jordan found 3 boxes of baseballs and 7 bags of tennis balls in the storage closet. Each box had 9 baseballs while each bag had 4 tennis balls. Select all of the statements that are true.

She spent $120 for all the items.

Jordan found 27 baseballs.

(6 × 4) + (12 + 9) = 108

Jordan found 55 balls in all.

She spent $108 for all the items.

Jordan found 63 tennis balls.

(6 × 4) + (12 × 9) = 120

Jordan found 39 balls in all.

(6 × 12) + (4 × 9) = 108

(3 + 7) × (9 + 4) = 39

Jameson made 46 dream catchers to sell at a fair. He already had 17 dream catchers leftover from the last sale. Each dream catcher will be sold for $5. What is the value of all of the dream catchers that Jameson has to sell? Grid your answer.

32 I Smart to the Core I Educational Bootcamp

A jewelry store has 61 gold watches and 49 silver watches for sale. This weekend, the store sold 19 silver watches. How many watches are left at the jewelry store in all? Grid your answer.

Mr. Bermudez took his wife to a restaurant and spent $31 for his wife's meal and $24 for his meal. He paid with a $100 bill. How much change did he get back?

Solve USING BAR MODELS (Show your work)

A farmer has 9 rows of corn with 14 corn stalks in each row. In each of the first 3 rows, 7 stalks are gathered and sold. How any corn stalks are remaining?

Solve USING A Grid (Show your work)

A hardware store has 3 shelves with 11 boxes of screws on each shelf. They also have 4 shelves with 26 boxes of nails on each shelf. If 80 boxes of nails are sold, how many boxes of screws and nails are left?

Solve USING EQUATIONS (Show your work)

33 I Copying is strictly prohibited

THINK TANK QUESTION 10 Boy scouts from 4 troops at Camp Boogaloo are planning a hike to Pikes Peak. In each troop, there will be 20 boy scouts. There will also be a total of 12 scout leaders and 11 chaperones. Part I: Write an equation that can be used to determine the number of tents (t), they will need if 6 people sleep in each tent.

Equation: t =______________________________________

Part II: How many tents will be needed if 6 people sleep in each tent? (Show your work)

34 I Smart to the Core I Educational Bootcamp

MISSION 4: USING COMPARITIVE RELATIONAL THINKING Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine whether the equation 60 + 24 = 57 + 27 is true or false. Determine the unknown whole number in an equation relating four whole numbers using comparative relational thinking. For example, solve 76 + 9 = n + 5 for n by arguing that nine is four more than five, so the unknown number must be four greater than 76.

Bootcamp STRATEGY 1: Determine whether an equation is true or false by using comparative relational thinking. When determining whether the equation 60 + 24 = 57 + 27 is true or false, we compare the first number on the left (60) to the first number on the right (57).

60 + 24 = 57 + 27 1st

LEFT

2nd

LEFT

1st

RIGHT

2nd

RIGHT

Since 60 is 3 more than 57, the second number on the right (27) must be 3 more than the second number on the left (24) in order for the 2 sides to be equivalent. Note: Because this scenario is true, the equation is true.

Bootcamp STRATEGY 2: Determine the unknown whole number in an equation relating 4 whole numbers using comparative relational thinking. When solving the equation 76 + 9 = n + 5 for n, we compare the second number on the left (9) to the second number on the right (5).

76 + 9 = n + 5 1st

LEFT

2nd

LEFT

1st

RIGHT

2nd

RIGHT

Since 9 is 4 more than 5, the unknown number on the right (n) must be 4 more than the first number on the left (76) in order for the 2 sides to be equivalent. Note: The unknown number is 80.

35 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.OA.1.ab 1

Use the comparative relational thinking strategy to identify the equation below as true or false.

71 − 28 = 53 − 46

True

False

Use Base 10 blocks to identify the equation below as true or false. (Show your work)

45 + 34 = 43 + 36

True

False

DIRECTIONS: Solve for n using comparative relational thinking. Equation Example:

43 + 6 = n + 4

25 + 6 = n + 3

84 − 9 = n − 5

58 + 4 = n + 9

36 − 5 = n − 6

71 + 2 = n + 7

36 I Smart to the Core I Educational Bootcamp

Solve for the unknown (n) If 6 is 2 more than 4, then 43 is 2 less than n

n = 45

Target PRACTICE 1 1

What is the value of n when using comparative relational thinking? Grid your answer.

74 − 21 = 57 − 42

54 − 8 = n − 4

3 Using comparative relational thinking, is the following equation true or false?

18 + 71 = 30 + 61

True

False

Use comparative rational thinking to 5 select all of the statements that are true.

Using comparative relational thinking, is the following equation true or false? Grid your answer.

True

False

What is the value of n when using comparative rational thinking? Grid your answer.

45 + 7 = n + 6

Use comparative rational thinking to 6 select all of the statements that are true.

16 + 8 = 20 + 12

17 - 5 = 25 - 13

25 + 6 = 28 + 3

26 - 8 = 21 - 4

31 + 7 = 25 + 13

34 - 7 = 29 - 2

15 - 2 = 20 - 8

14 + 9 = 20 + 3

22 - 6 = 19 - 3

28 + 5 = 30 + 4

39 - 11 = 29 - 1

36 + 6 = 41 + 5 37 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.OA.1.ab 1 Use the comparative relational thinking strategy to identify the equation below as true or false.

46 + 32 = 28 + 50

True

False

2 Use Base 10 blocks to identify the equation below as true or false. (Show your work)

73 − 21 = 64 − 30

True

False

DIRECTIONS: Solve for n using comparative relational thinking. Equation Example:

43 + 6 = n + 4

48 + 5 = n + 4

63 − 7 = n − 6

39 + 6 = n + 1

81 − 3 = n − 7

29 + 9 = n + 8

38 I Smart to the Core I Educational Bootcamp

Solve for the unknown (n) If 6 is 2 more than 4 then, 43 is 2 less than n

n = 45

Target PRACTICE 2 1

What is the value of n when we use comparative relational thinking? Grid your answer.

72 + 7 = n + 5

Using comparative relational thinking is the following equation true or false?

42 − 33 = 54 − 31

True

False

Use comparative rational thinking to select all of the expressions below that can be solved where m = 12.

Using comparative relational thinking, is the following equation true or false?

43 + 36 = 28 + 51

True

False

What is the value of n when we use comparative relational thinking? Grid your answer.

63 − 7 = n − 4

6 Use comparative rational thinking to select all of the expressions below that can be solved where n = 9.

m + 6 = 14 + 4

25 - n = 29 - 11

24 + m = 30 + 8

32 - 8 = 33 - n

20 + 4 = m + 12

27 - n = 40 - 22

m - 5 = 17 - 10

15 + 10 = 16 + n

26 - 9 = 29 - m

n + 12 = 15 + 5

18 - m = 28 - 20

28 + n = 31 + 7 39 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.OA.1.ab DIRECTIONS: Use drawings and equations to solve the problems below.

1 The bakery received a purchase order to make several donuts. Gloria and Katie decided to split the work in half. Gloria made 51 glazed donuts and 37 chocolate donuts. Meanwhile, Maria made 42 glazed donuts and 46 chocolate donuts. Did Maria and Gloria make an equal number of donuts? (Show your work)

Fantasy Elementary School admits the same number of students to each grade level. There are 37 boys and 39 girls enrolled in first grade. In second grade, there are 33 boys and 42 girls. Has Fantasy Elementary admitted the same number of students to first and second grade? (Show your work)

A travel agent prepares 2 travel packages to a remote island that includes a plane ticket and a ticket for a ferry ride. Package A offers $74 for the airplane ticket and $25 for the ferry ride. Package B offers $68 for the airplane ticket and $29 for the ferry ride. Which travel package is the better deal? (Show your work)

40 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION There are 2 girl scout troops competing for first place in the sale of cookies. Girl Scout Troop 1

Girl Scout Troop 2

TYPE OF COOKIES

NUMBER OF BOXES SOLD

TYPE OF COOKIES

NUMBER OF BOXES SOLD

Peanut Butter

Cranberry Citrus

Chocolate Chip

Dulce de Leche

Part I: Determine which 2 flavors each troop sold the most of.

Part II: Using the information from Part 1, determine if the troops sold the same amount of their 2 best selling flavors (greatest amount) cookies by using comparative relational thinking.

41 I Copying is strictly prohibited

FOUR-STAR CHALLENGE - 4.0A.1.ab 1

What is the value of n when using comparative relational thinking? Grid your answer.

46 − 9 = n − 3

3 Using comparative relational thinking, is the following equation is true or false?

58 − 37 = 55 − 40

True

False

Select all of the statements that are true.

15 − 6 = a − 2

6 is 4 more than 2, so a is 4 less than 15. 15 is 9 more than 6, so a must be 6 more than 2. 2 is 4 less than 6, so 15 is 4 more than a. 6 is 9 less than 15, so a must be 9 more than 15. 15 is 4 more than 2, so 15 must be 4 less than a. 42 I Smart to the Core I Educational Bootcamp

True

False

What is the value of n when using comparative relational thinking? Grid your answer.

45 + 3 = n + 5

58 + 15 = 30 + 42 A

Using comparative relational thinking, is the following equation true or false?

Select all of the statements that are true.

22 + b = 25 + 4

4 is 21 less than 25 so b must be 21 more than 22. 25 is 3 more than 22 so b must be 3 more than 4. 22 is 3 less than 25 so b must be 3 more than 4. 25 is 21 more than 4 so 22 must be b less than 21. 25 is 3 more than 22 so 4 must be b less than 3.

Clay has 35 blue marbles and 23 clear marbles. His brother Mark has 28 blue marbles and 39 clear marbles. Both boys should have the same number of marbles.

Part I:

Form an equation to show the relationship between Clay’s and Mark’s marbles.

Part II: Solve the equation to determine if the boys have the same number of marbles.

Part I: Form an equation based on the Base 10 blocks below.

−

Part II: Use the equation to determine if the equation is true or false.

True 9

False

Ann’s computer shows that she has 46 messages in her inbox and 31 messages in her sent box. Her coworker’s computer has 59 messages in the inbox and 24 messages in the sent box.

Part I: Form an equation to show the relationship between the number of messages Ann has in her computer in comparison to her coworker.

Part II: Solve the equation to determine if both computers have the same number of messages.

Yes

43 I Copying is strictly prohibited

THINK TANK QUESTION DIRECTIONS: Use the table below to complete the questions.

10 PART I:

PART II:

Create a story problem that supports the Base 10 model below.

Create and solve an equation to support your story problem.

44 I Smart to the Core I Educational Bootcamp

MISSION 5: Investigating FACTORS AND MULTIPLES Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Bootcamp STRATEGY 1: Use arrays to find the factors of a whole number. Example: Eliminate the numbers that are not factors of 18. 1

Factor Pairs

and

9 6

Bootcamp STRATEGY 2: Use the divisibility rules to find factors. Dividing by 2: All even numbers are divisible by 2, e.g., all numbers ending in 0, 2, 4, 6, or 8. Dividing by 3 : Add up all the digits in the number. Find out what the sum is. If the sum is divisible by 3, so is the number. For example, 12,123 (1+2+1+2+3=9); 9 is divisible by 3, therefore, 12,123 is, too. Dividing by 4: Are the last 2 digits in your number divisible by 4? If so, the number is, too. For example: 35,8912 ends in 12 which is divisible by 4; thus, so is 358,912. Dividing by 5: Numbers ending in a 5 or 0 are always divisible by 5. Dividing by 6: If the number is divisible by 2 and 3, it is divisible by 6, also. Dividing by 9: It is almost the same rule as dividing by 3. Add up all the digits in the number. Find out what the sum is. If the sum is divisible by 9, so is the number. For example, 43,785 (4+3+7+8+5=27); 27 is divisible by 9, therefore, 43,785 is, too. Dividing by 10: If the number ends in a 0, it is divisible by 10.

Bootcamp STRATEGY 3: Use skip counting or multiply to find multiples of a number. Example: Skip count by 3s: 3, 6, 9, 12, 15, 18, 21 ... ×1 ×2 ×3 Example: Find the multiples of 3: 3 3 6 9

×4

×5

×6

×7

Bootcamp STRATEGY 4: Finding prime and composite numbers. A prime number is a whole number greater than 1 that is only divisible by 1 and itself. A composite number is a number greater than 1 that has more factors than 1 and itself. Example 1: 3 is a PRIME number 1×3=3

Example 2: 4 is a COMPOSITE number 1 × 4 = 4 and 2 × 2 = 4 45 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.OA.4 (4.OA.2.4) Eliminate the numbers below that are not factors of 24.

1 1

14 15

16 17

Identify the numbers below as either prime or composite by placing a check mark in the appropriate box. 15

Prime

Composite

Prime

Composite

Prime

Composite

Prime

Composite

20 21 22 23

DIRECTIONS: Identify the factors for the following whole numbers. Whole Number

Circle the Factors

144

200

405

160

288

Multiply to find the first 7 multiples of 4. ×1

×2

×3

×4

×5

×6

×7

4 9

Skip count to find the first 7 multiples of 6.

6 , ____, ____, ____, ____, ____, ____ 46 I Smart to the Core I Educational Bootcamp

Target PRACTICE 1 1

Krishna made a list of all the factors of 81. Which of the following could be Krishna’s list?

Which of the following groups below include only prime numbers?

1, 3, 9, 27, 81

Group 1: 2, 3, 6, 90, 112

1, 3, 9, 27

Group 2: 2, 3, 5, 7 , 9

2, 3, 9, 27, 81

Group 3: 17, 19, 23, 29, 31

1, 2, 3, 9, 27, 81

Group 4: 15, 17, 11, 18, 21

Select all of the prime numbers from the list below.

Select all of the composite numbers from the list below.

Joy is in a drama club that meets the same number of times each month. After a number of months, Joy’s drama club had met 32 times. Which of the following could be the number of times the club meets each month? A

Which of the following statements below best describe the relationship between the numbers 4 and 6? A

4 is a factor of 6

4 is a multiple of 6

20 is a common multiple of 4 and 6

The greatest common factor of 4 and 6 is 2

2, 5, or 8 times per month

2, 4, or 8 times per month

4 or 6 times per month

2, 4, 6 or 8 times per month

47 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.OA.4 (4.OA.2.4) Eliminate the numbers below that are not factors of 20.

Identify the numbers below as either prime or composite by placing a check mark in the appropriate box.

Prime

Composite

Prime

Composite

Prime

Composite

Prime

Composite

DIRECTIONS: Identify the factors for the following whole numbers. Whole Number

Circle the Factors

135

305

207

440

.261

Multiply to find the first 7 multiples of 7. ×1

×2

×3

×4

×5

×6

×7

7 9

Skip count to find the first 7 multiples of 8.

8 , ____, ____, ____, ____, ____, ____ 48 I Smart to the Core I Educational Bootcamp

Target PRACTICE 2 1

Reece made a list of all the factors of 72. Which of the following could be Reece’s list? A

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

1, 2, 3, 6, 9, 18, 24, 36, 72

2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

1, 2, 3, 4, 6, 8, 9, 12, 16, 24, 36, 72

Select all of the statements that are true of the numbers 24 and 30.

Common factors of 24 and 30: 1, 2, 3, 6, and 8

4 or 6 weeks

7 or 8 weeks

9 or 10 weeks

7 or 9 weeks

Group 1: 22, 33, 24, 15, 50

Group 2: 5, 11, 15, 18, 31

Group 3: 2, 3, 13, 29, 41

Group 4: 5, 7, 11, 17, 21

Select all of the statements that are true of the numbers 12 and 20.

Factors of 12: 1, 2, 3, 4, 6, and 12 12 is a composite number. Common factors of 12 and 20: 1, 2, and 4 Factors of 20: 1, 2, 3, 4, 6, 12, and 20

30 is a composite number. Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24 Factors of 30: 1, 2, 3, 5, 6, 8, 10, 15, and 30

During baseball season, Dave’s team practiced the same number of times each week. They practiced 63 times in all. Which of the following could be the length of the baseball season?

Factors of 12: 1, 2, 3, 6, 8, 10, and 12

24 is a prime number. Common factors of 24 and 30: 1,2,3, and 6

Which of the following groups include only composite numbers?

Factors of 20: 1, 2, 4, 5, 10, and 20

Which of the statements below best describe the relationship between the numbers 7 and 42? A

7 is a factor of 42

42 is a factor of 7

42 is a common multiple of 4 and 7

The greatest common factor of 7 and 42 is 14

49 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.OA.4 (4.OA.2.4) DIRECTIONS: Use drawings and equations to solve the following problems. 1 What is the least common multiple for 3 and 8? (Show your work)

2 What are the multiples of 8 that are less than 50? (Show your work)

3 What whole number is between 45 and 50 that has exactly 10 factors including 1 and itself? (Show your work)

4 What numbers are both a factor of 100 and a multiple of 5?

5 Identify the numbers below as either prime or composite by placing a check mark in the appropriate box. 89

Prime

Composite

Prime

Composite

Prime

Composite

Prime

Composite

50 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION After learning about factors and multiples, Jane concluded that the number 40 is a multiple of 9. She also stated that all of the factors of 10 are factors of 40.

Is Jane’s first statement accurate? (Show your work)

YES

Is Jane’s second statement accurate? (Show your work)

YES

51 I Copying is strictly prohibited

FOUR-STAR CHALLENGE - 4.OA.4 (4.OA.2.4) 1

Ryan made a list of all the factors of 24. Which of the following could be Ryan’s list? A

2, 3, 4, 6, 8, 12, 24

1, 2, 3, 4, 6, 8

1, 2, 3, 4, 6, 8, 12, 24

2, 3, 4, 6, 9, 12

Which of the following lists of numbers show multiples of 7? Select all of the options that apply.

Which of the following groups below include only prime numbers?

Group 1: 12, 13, 14, 15, 50

Group 2: 5, 11, 15, 18, 31

Group 3: 5, 3, 13, 29, 41

Group 4: 5, 7, 11, 17, 21 Which of the following lists of numbers show the multiples of 9? Select all of the options that apply.

17, 27, 37, 47, 57, 67, and 77

27, 36, 45, 54, 63, 72, and 81

14, 21, 28, 35, 42, 49, and 56

19, 29, 39, 49, 59, 69, and 79

14, 17, 24, 27, 34, 37, and 44

14, 19, 24, 29, 34, 39, and 44

21, 24, 28, 31, 35, 42, and 47

18, 28, 38, 48, 58, 68, and 78

14, 28, 56, 112, 224, and 448

27, 46, 55, 64, 73, 82, and 91

7, 14, 21, 28, 35, 56, and 63

54, 63, 72, 81, 90, 99, and 108

Which statement below best describes the relationship between the numbers 6 and 24?

At the store, T-shirts are stored in bins. There are 72 T-shirts to store in bins and each has an equal number of T-shirts. Which of the following could be the number of bins used to store the T-shirts?

24 is a factor of 6

6 is a multiple of 24 A

2, 5, or 7

24 is a common multiple of 6 and 24

2, 4, 8, or 9

2, 5, 8, or 9

48 is the least common factor of 6 and 24

2, 3, 4, or 10

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The host of the annual Math Bowl asked a contestant to name all of the prime numbers between 15 and 40. Part I: What numbers should the contestant have named?

Part II: Explain how you identified the prime numbers between 15 and 40.

Circle the numbers that are multiples of both 4 and 6.

Ms. Perez, the fourth grade math teacher, starts each class with a problem of the day. Monday’s question was, “If I am the number 32, and the number I am hiding in my hand is an even number and a factor of 32, then what number might I be holding?”

List the possible numbers that Ms. Perez might be holding in her hand. (Show your work)

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THINK TANK QUESTION DIRECTIONS: Solve the problem below and show your work.

A teacher gave clues to the students to help build their investigative skills. The goal was to use the clues to identify 2 specific leaves.

• Each of the leaves needed are factors of 24. • 36 is a multiple of both leaves • 30 is a multiple of the first leaf, but not the second leaf. • The sum of the 2 leaves is 10. Use the teacher’s clues and the space below to help figure out which 2 leaves are being described. (Show your work)

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MISSION 6: Finding NUMBER AND SHAPE PATTERNS Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Bootcamp STRATEGY 1: Determine if the numeric pattern is increasing or decreasing. If the numbers in the pattern are increasing, then we add or multiply to find the next number. If the pattern is decreasing, then we know that we must subtract or divide to find the next number in the pattern.

Bootcamp STRATEGY 2: Look for additional patterns within numeric patterns such as alternating even and odd numbers. +5

Bootcamp STRATEGY 3: Determine if the shape pattern is repeating or growing. If the shape pattern is repeating, identify the location of the repeated pattern to determine the unknown sequence. If the shape pattern is growing, identify the number pattern and the positioning of the graphics in order to determine the unknown sequence.

Bootcamp STRATEGY 4: Look for additional patterns within shape patterns such as alternating even and odd numbers, sizes , colors, shapes, design, etc.

? SHAPES

Triangle

Rectangle

Pentagon

Hexagon

Triangle

Rectangle

Pentagon

Hexagon

Triangle

Rectangle

SIZE

Large

Small

Large

DESIGN

Vertical Stripes

Horizontal Stripes

Diamond Shaped

Dotted Pattern

Vertical Stripes

Horizontal Stripes

Diamond Shaped

Dotted Pattern

Vertical Stripes

Horizontal Stripes

Sides

The next shape would be a Five-sided Pentagon. It would be Large with a DiamondShaped design. 55 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.OA.5 (4.OA.3.5) DIRECTIONS: Complete the repeating patterns below. (Show your work) 1

2, 6, 7, 2, 6, 7, 2,

14, 2, 7, 8, 5, 14, 2, 7,

, ,

DIRECTIONS: Complete the increasing patterns below. (Show your work) 4 Rule: Add 4 −

9, 13, 17,

5 Rule: Add 3 −

68, 71, 74,

6 Rule: Multiply by 3 −

2, 6,

18,

21,

77, 54,

DIRECTIONS: Complete the decreasing patterns below. (Show your work) 7 Rule: Subtract 9 −

85,

98, 87,

8 Rule: Subtract 11 − 9 Rule: Divide by 2 −

76, 67, 76,

58,

65,

1,600, 800, 400, 200,

DIRECTIONS: Continue the pattern by shading in the fourth grid.

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, ,

Target PRACTICE 1 1

Rachel wrote a number pattern using the rule “multiply by 4”. Which of the following sequences of numbers could be the pattern she wrote? A

1, 4, 16, 64

4, 8, 12, 16

16, 12, 8, 4

16, 18, 20, 22

Figure 1

, 44

What number is missing from Anne’s pattern? Grid your answer.

Derrick made this pattern with sticks:

Figure 2

Figure 3

Figure 4

If Derrick continues the pattern with the rule “add 3”, what should be the total number of sticks in Figure 8? Grid your answer.

Anne used a rule to make this pattern: Rule: Subtract 12 92, 80, 68,

Study the input/output table below. Select all of the numbers that will complete the input/output table.

Elijah used the rule “minus 11” to make a number pattern. Which of the following could be Elijah’s pattern? A

3 , 14, 25, 36, 46

99, 88, 77, 66, 44

105, 94, 83, 72, 61

22, 33, 44, 55, 66

Study the input/output table below. Select all of the numbers that will complete the input/output table.

Rule: Multiply by 7 INPUT OUTPUT 2 14 A 21 6 B 7 49

Rule: Multiply by 5 INPUT OUTPUT 3 15 4 N M 30 10 50

A=3

B = 35

M=6

N = 20

A=4

B = 42

M=7

N = 25

A=5

B = 38

M=8

N = 35

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TRAIN THE BRAIN PRACTICE 2 4.OA.5 (4.OA.3.5) DIRECTIONS: Complete the shape patterns below. (Show your work) Complete the pattern here:

Complete the pattern here:

DIRECTIONS: Continue the function tables as indicated below. 4

n Term

Rule: Multiply by 12 1st 2nd 3rd 4th 12 24 36 48

5th ?

5th Term:

7th Term:

Rule: Multiply by 8 Number (n) of packs: Red M & M’s 2 3 4 5 6

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16 24 32 ? 48

Red M & M’s in 5th Pack:

Target PRACTICE 2 Robin wrote a number pattern using the rule “add 14”. Which of the following sequences of numbers could be the pattern she wrote?

Danielle made this pattern with circles:

Figure 1

1, 15, 19, 35

1, 14, 28, 42

14, 28, 32, 56

7, 21, 35, 49

Billy used a rule to make this pattern: Rule: Multiply by 2 12, 24, 48, , 192

Figure 3

Figure 4

The rule for the following table is “Multiply by 6”. Select all of the statements that could be true.

Chloe used the rule “minus 25” to make a number pattern. Which of the following could be Chloe’s pattern?

What number is missing from Billy’s pattern? Grid your answer.

Figure 2

If Danielle continues this pattern by adding 2, what should be the total number of circles in Figure 10? Grid your answer.

100, 75, 50, 25, 0

10, 35, 60, 85, 110

240, 215, 165, 90

5, 25, 125, 625, 3125

The rule for the following table is “Divide by 10”. Select all of the statements that could be true.

If x is 8, y is 46.

If s is 100, t is 10.

If x is 12, y is 72.

If s is 60, t is 6.

If x is 9, y is 54.

If s is 800, t is 8.

If x is 11, y is 66.

If s is 70, t is 7.

If x is 10, y is 60.

If s is 120, t is 12.

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TRAIN THE BRAIN PRACTICE 3 4.OA.5 (4.OA.3.5) DIRECTIONS: Use the rule to write the next 4 terms in the numerical patterns below.

1 RULE: Multiply by 2. (Show your work) 4,

2 Describe all of the features that help to identify the next shape in the pattern below.

A carpenter is installing decorative tiles in the living room of a home. The gold accent tiles increase by 3 tiles with each row. If the first row has 5 gold accent tiles, how many gold accent tiles does the fifth row have?

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THINK TANK QUESTION Part I: Draw inside the squares below to design a repeating pattern.

Part I: Describe the features of the pattern you created.

Part II: Create a numerical pattern 8 digits long using the rule: Subtract 11. (Note: Prove your numerical pattern by showing your work.)

Part III: Describe the features of the pattern you created.

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FOUR-STAR CHALLENGE - 4.OA.5 (4.OA.3.5) 1

Palin wrote the number 200. If the rule is “divide by 2”, what is the fourth number in the pattern? Grid your answer.

Suzanne used a rule to make this pattern: Rule: Add 12 18, 30, 42,

, 66

What number is missing from her pattern? Grid your answer.

Tina used the rule “minus 15” to make a number pattern. Which of the following could be Tina’s pattern?

Ron used the rule “multiply by 10” to make a number pattern. Which of the following could be Ron’s pattern?

A 100, 75, 50, 25, 0 B 10, 25, 40, 55, 70 C 240, 225, 210, 195 D 5, 25, 125, 625, 3125

James arranged chairs in the library in the following manner: Row 1: 12 chairs, Row 2: 15 chairs, Row 3: 18 chairs, and Row 4: 21 chairs. If the pattern continues using the rule “add 3”, select all of the statements could be true.

1,000, 100, 10, 1

1, 10, 100, 1,000

10, 20, 30, 40

40, 30, 20, 10

A farmer planted oranges in the following manner: Acre 1: 256 oranges, Acre 2: 128 oranges, Acre 3: 64 oranges, and Acre 4: 32 oranges. If this pattern continues using the pattern “divide by 2”, select all of the statements could be true.

Fifth row: 25 chairs

Seventh acre: 12 oranges

Sixth row: 27 chairs

Sixth acre: 8 oranges

Seventh row: 30 chairs

Fifth acre: 16 oranges

Fifth row: 24 chairs

Sixth acre: 16 oranges

Sixth row: 30 chairs

Seventh acre: 8 oranges

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Part I: Fill in the missing numbers in the table below. Rule: Multiply by 4 Input

Output

3 6 9 12 15

24 36 48

Part II: Write 2 more input/output terms that can belong in the table above.

Part I: Complete the pattern below.

5 × 8=

5 × 80 = 5 × 800 = 5 × 8,000 = Part II: Describe the rule in the pattern above.

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THINK TANK QUESTION 9

Part I: Draw inside the squares below to design an increasing pattern.

Part I: Describe the features of the pattern you created.

Part II: Create a numerical pattern 5 digits long using the Rule: Multiply 2. (Note: Prove your numerical pattern by showing your work.)

Part III: Describe the features of the pattern you created.

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MISSION 7: Understanding place value relationships Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Bootcamp STRATEGY 1: Use a place value chart to determine the value of each digit in a number. Example: 7,463. HUNDRED THOUSANDS

TEN THOUSANDS

THOUSANDS

HUNDREDS

TENS

ONES

The value of the digit 7 is 7 thousands or 7,000. The value of the digit 4 is 4 hundreds or 400. The value of the digit 6 is 6 tens or 60. The value of the digit 3 is 3 ones or 3.

Bootcamp STRATEGY 2: Compare values to show that a digit in one place represents 10 times what it represents in the place to its right. HUNDRED THOUSANDS

TEN THOUSANDS

THOUSANDS

HUNDREDS

TENS

ONES

Compare 5,000 and 500: The value of the 5 in 5,000 is 10 times the value of the 5 in 500. Compare 500 and 50. The value of the 5 in 500 is 10 times the value of the 5 in 50. Compare 50 and 5. The value of the 5 in 50 is 10 times the value of the 5 .

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TRAIN THE BRAIN PRACTICE 1 4.NBT.1 (4.NBT.1.1) DIRECTIONS: Determine how much greater the place values are between each other. 1

How many times greater is the tens place than the ones place?

2 How many times greater is the hundreds place than the tens place?

3 How many times greater is the thousands place than the hundreds place?

DIRECTIONS: Locate the digit 5 in each number below. Which digit has a value 10 times greater than the digit 5?

609,537

2,5031

805

45,273

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Target PRACTICE 1 1

Timothy wrote an incomplete number. The digit 6 and 7 will need to be sorted into the number in order to complete it. What will the number be if the 7 digit has a value 10 times greater than the digit 6 in the number? Grid your answer. 123,8

Alicia wrote an incomplete number. The digit 9 and 2 will need to be sorted into the number in order to complete it. What will the number be if the 2 digit has a value 10 times greater than the digit 9 in the number? Grid your answer. 5 , 03

Sammy wrote 2 numbers on the board: 7,541 and 713 What is true of the value of the digit 7 in both numbers?

Lenny wrote 2 numbers on the board: 541,732 and 304,156 What is true of the value of the digit 4 in both numbers?

The value of 7 in 7,541 is 10 times less than in 713

The value of 4 in 304,156 is 10 times more than in 541,732

The value of 7 in 713 is 10 times more than in 7,541

The value of 4 in 541,732 is 10 times more than in 304,156

The value of 7 in 713 is 100 times less than in 7,541

The value of 4 in 304,156 is 100 times more than in 541,732

The value of 7 in 7,541 is 10 times more than in 713

The value of 4 in 541,732 is 10 times less than in 304,156

Select all of the numbers where the digit 2 is 10 times the value of 7.

Select all of the numbers where the digit 3 is 10 times the value of 1.

157,236

31,402

72,394

1,389

127,680

403,122

274

314

1,027

413

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TRAIN THE BRAIN PRACTICE 2 4.NBT.1 (4.NBT.1.1) DIRECTIONS: Locate the digit 9 in each number below. Which digit has a value 10 times greater than the digit 9? 1

1,907

269,372

3,291

489

DIRECTIONS: Locate the underlined digit in each number below. Write the digit that has a value 10 times greater than the underlined digit. 5

34,269

502,912

82,379

608,423

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Target PRACTICE 2 1

Which number below shows the digit 1 having a value 10 times greater than the digit 2?

52,106

198,700

432,198

5,091

612

64,901

1,027

819

Lance wrote the 3 numbers below: 364,128 821,643 184,236

Which number shows the digit 8 having a value 10 times greater than the digit 2? Grid your answer.

Which number below shows the digit 9 having a value 10 times greater than the digit 1?

Select all of the statements that are true for the numbers below.

A: 7,546,321

B: 5,476,231

The 7 has a value 10 times more in Option A than the 7 in Option B. The 4 has a value 10 times more in Option B than the 4 in Option A. The 5 has a value 10 times more in Option B than the 5 in Option A. The 6 has a value 10 times less in Option A than the 6 in Option B. The 3 has a value 10 times more in Option A than the 3 in Option B.

Emma wrote the 3 numbers below: 14,317 70,134 17,143

Which number shows the digit 4 having a value 10 times less than the digit 3? Grid your answer.

Select all of the statements that are true for the numbers below.

A: 9,753,186

B: 7,538,691

The 7 has a value 100 times less in Option A than the 7 in Option B. The 8 has a value 10 times less in Option A than the 8 in Option B. The 3 has a value 10 times more in Option B than the 3 in Option A. The 5 has a value 10 times less in Option A than the 5 in Option B. The 1 has a value 100 times less in Option A than the 1 in Option B. 69 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NBT.1 (4.NBT.1.1) DIRECTIONS: Determine what the number would be if the value of the underlined digit is 10 times more than the number given. 1 90,734

631

86,402

DIRECTIONS: Determine what the number would be if the value of the underlined digit is 10 times less than the number given. 5 570 6

3,980

73,400

105,560

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THINK TANK QUESTION

Part I: Write 2 different six-digit numbers following the steps listed below. Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7:

Note that the first number must have only one 4, 7, and 9 digit. Place the number 4 in the tens place. Place the number 7 in the hundreds place. Place the number 9 in the thousands place. Place a number greater than 7 in the one hundred thousands place. Place the number 5 in the ten thousands place. Place a number greater than 5, that has not been used, in the ones place.

, (first number)

Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7:

Note that the second number must have only one 4, 7, and 9 digit. Place the number 4 in the thousands place. Place a number less than 4 in the one hundred thousands place. Place the number 7 in the tens place. Place the number 9 in the hundreds place. Place a number greater than 7 in the ten thousands place. Place a number greater than 5, that has not been used, in the ones place.

, (second number) Part II: Use numbers, drawings, or descriptions to determine how many times greater the 7 in the first number is worth than the 7 in the second number.

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FOUR-STAR CHALLENGE - 4.NBT.1 (4.NBT.1.1) 1

A B C D

Judy wrote 2 numbers on the board: 12,389 and 83,219. What is true of the value of the 3 digit in both numbers? The value of the digit 3 in 12,389 is 100 times less than in 83,219. The value of the digit 3 in 12,389 is 10 times more than in 83,219. The value of the digit 3 in 83,219 is 10 times less than in 12,389. The value of the digit 3 in 83,219 is 10 times more than in 12,389.

Xavier wrote 2 numbers on the board: 1,953 and 235. What is true of the value of the digit 5 in both numbers? The value of the digit 5 in 235 is 10 A times more than in 1,953. The value of the digit 3 in 1,953 is 10 B times more than in 235. The value of the digit 3 in 1,953 is 100 C times less than in 235. The value of the digit 5 in 235 is 100 D times less than in 1,953. 2

Which of the 3 numbers below shows the digit 8 with a value 10 times that of the digit 9? Grid your answer.

Select all of the statements that are true for the numbers below.

Which of the 3 numbers below shows the digit 4 with a value 10 times that of the digit 8? Grid your answer. 842 10,481 34,187

568,903 2,819 49,807

A: 37,196

B: 31,769

The value of the digit 7 in Option A is 10 times more than in Option B The value of the digit 1 in Option B is 10 times more than in Option A The value of the digit 9 in Option A is 10 times more than in Option B The value of the digit 3 in Option A is 10 times more than in Option B The value of the digit 7 in Option B is 10 times more than in Option A

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Select all of the statements that are true for the numbers below.

A: 294,037

B: 309,472

The value of the digit 3 in Option B is 10 times more than in Option A The value of the digit 9 in Option A is 10 times more than in Option B The value of the digit 7 in Option B is 10 times more than in Option A The value of the digit 0 in Option B is 10 times more than in Option A The value of the digit 4 in Option A is 10 times more than in Option B

Ms. Morgan wrote 2 numbers on the board as seen below.

78,298

and

41,925

Part I: How many times greater is the 9 in number on the right than the 9 in the number on the left?

Part II: Explain your reasoning using numbers, drawings, or descriptions.

Use the 2 numbers listed below to compare the values of the underlined digits.

485,316

and

3,562

Select all of the numbers where the digit 3 is 10 times the value of the digit 7 and the digit 9 has a value 10 times greater than the digit 6. 596,738 23,796 693,789

596,371 370,691

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THINK TANK QUESTION 10

Part I: Use all of the numbers from the blocks below to create 2 different 4-digit numbers. In both numbers, the digit 5 must have a value 10 times that of the digit 3 and the digit 7 must have a value 10 times that of the digit 8.

(First Number)

(Second Number)

Part II: Using the same digits in Part I, rearrange and write 6 four-digit numbers where the digit 3 has a value 10 times more than the digit 5.

A. B. C. D. E. F.

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MISSION 8: reading, writing, and comparing numbers Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Bootcamp STRATEGY 1: Use a place value chart to read and write multi-digit whole numbers. Example: 57,463. THOUSANDS HUNDRED THOUSANDS

HUNDREDS

TEN THOUSANDS

THOUSANDS

HUNDREDS

TENS

ONES

Written Form:

Fifty-seven thousand four hundred sixty-three

Bootcamp STRATEGY 2: Use place values to compare 2 multi-digit numbers and identify them as >, <, or =. Example: 57,463 THOUSANDS HUNDRED THOUSANDS

57,563 HUNDREDS

TEN THOUSANDS

THOUSANDS

HUNDREDS

TENS

ONES

LEFT

RIGHT Equal

Equal

Compare 4 and 5 from the hundreds place.

57,463

Different 4 is less than (<) 5, therefore:

57,563

75 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NBT.2 (4.NBT.1.2) DIRECTIONS: Name the following numbers. 1

7,421

348,208

49,235

DIRECTIONS: Write the expanded notation for the numbers below. Example: 13,427 = (1 × 10,000) + (3 × 1,000) + (4 × 100) + (2 × 10) + (7 × 1) 13,427 = 10,000 + 3,000 + 400 + 20 + 7

458,356 =

56,065 =

1,236 =

DIRECTIONS: Compare (>, <, or =) the values for each pair of numbers below.

44,599

57,590

280,563

208,563

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5,800

10 70,408

5,781

70,488

Target PRACTICE 1 1

Tom played a number game. He said, “My number has 6 hundred thousands, 4 ten thousands, and 4 tens.” Each of the remaining digits in Tom’s number is a 0. What is Tom’s number? Grid your answer.

There were three hundred sixty-four thousand one hundred twenty-six people in attendance at a basketball game. What is this number written in standard form? Grid your answer.

Which of the following expressions is the expanded form for the number 4,358?

In 2010, there were about eight hundred five thousand two hundred thirty-five people living in a city. What is this number written in standard form?

4(100) + 3(100) + 5(10) + 8(1)

43(1,000) + 58(100)

805,253

850,253

4(4,000) + 3(300) + 5(50) + 8(5)

850,235

805,235

4(1,000) + 3(100) + 5(10) + 8(1)

Select all of the statements that are true of the number 4,506.

4,506 = Forty-five thousand six 4,506 = 4,000 + 500 + 6 4,506 = Four thousand five hundred six

This number has 6 ones 4,506 = 4,000 + 500 + 60 This number has 4 ten thousands

Select all of the options that show 54,625 written in expanded form. 5 ten-thousands, 46 hundreds, 25 ones 5 ten thousands, 4 thousands, 62 hundreds, 5 ones 50 thousands, 46 hundreds, 20 tens, 5 ones 50 thousands, 40 hundreds, 60 tens, 25 ones 54 thousands, 6 hundreds, 2 tens, 5 ones 77 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NBT.2 (4.NBT.1.2) DIRECTIONS: Name the following numbers. 1

33,208

725,652

9,640

DIRECTIONS: Write the expanded notation for the numbers below. Example: 13,427 = (1 × 10,000) + (3 × 1,000) + (4 × 100) + (2 × 10) + (7 × 1) 13,427 = 10,000 + 3,000 + 400 + 20 + 7

508,569 =

93,872 =

6,506 =

DIRECTIONS: Compare (>, <, or =) the values for each pair of numbers below.

35,609

589,874

35,690

589,784

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7,895

10 59,605

7,889

59,615

Target PRACTICE 2 1

Dreaka told her classmates to guess a mystery number. She told her classmates that her number had 7 hundred thousands, 3 thousands, 4 hundreds, 5 tens, and 8 ones. What is Dreaka’s number? Grid your answer.

In 2010, there were about four hundred eighty-nine thousand four hundred eighty-eight people living in a state. What is this number written in standard form? Grid your answer.

Which of the following expressions is the expanded form for the number 7,095?

There were nine hundred three thousand seven hundred fifteen people in attendance at a baseball game. What is this number written in standard form?

7(1,000) + 9(100) + 0(10) + 5(1)

70(1,000) + 95(100)

7(1,000) + 9(100) + 5(10)

7(1,000) + 9(10) + 5(1)

Select all of the correct representations of the numbers in expanded notation. 405,607 = 400,000 + 5,000 + 600 + 7 45,607 = 40,000 + 5,000 + 600 + 70 4,567 = 4 + 5 + 6 + 7 45,670 = 45,000 + 6 + 7

45,067 = 40,000 + 5,000 + 60 + 7 4,567 = 4,000 + 500 + 60 + 7

903,715

9,003,715

903,751

903,715,000

Select all of the options that show 62,781 written in expanded form. 6 ten-thousands, 2 thousands, 78 hundreds, 1 ones 6 ten-thousands, 27 hundreds, 81 ones 60 thousands, 20 hundreds, 70 tens, 81 ones 60 thousands, 27 hundreds, 80 tens, 1 ones 62 thousands, 7 hundreds, 8 tens, 1 ones 79 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NBT.2 (4.NBT.1.2) DIRECTIONS: Solve the problems below. 1 Use words to represent the expanded form of the number 78,593.

2 Create 2 different 4-digit numbers and explain how to determine which number is greater.

3 Write the standard form of the number 70,000 + 8,000 + 5. Explain how to write the number in standard form.

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THINK TANK QUESTION

Part I: Make the greatest 6-digit number possible using the digits below. Be sure to Part I: use all of the digits listed below. Note: Your number must not start with a zero.

, Written Form:

Expanded Form:

Part II: Make the smallest 6-digit number that can be made using the digits below. Be Part II: sure to use all of the numbers listed below. Note: Your number must not start Part II: with a zero.

, Written Form:

Expanded Form:

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FOUR-STAR CHALLENGE - 4.NBT.2 (4.NBT.1.2) 1

Vicky played a number game. She said, “My number has 8 hundred thousands, 5 ten thousands, and 5 tens.” Each of the remaining digits in Vicky’s number is a 0. What is Vicky’s number? Grid your answer.

There were five hundred seventy-two thousand three hundred eighty-six people in attendance at the Olympics. What is this number written in standard form? Grid your answer.

Which of the following expressions is the expanded form for the number 8,483?

In 2010, there were approximately seven hundred sixty-five thousand two hundred twenty people that visited the local mall. What is this number written in standard form?

8(100) + 3(100) + 5(10) + 3(1)

8(1,000) + 4(100) + 3(1)

765,220

765,202

8(1,000) + 4(100) + 8(10) + 3(1)

705,220

765,200

8(1,000) + 8(100) + 4(10) + 3(1)

Select all of the number comparison statements that are correct. 89,555 > 98,555 760,560 > 760,506 3,908 > 3,980 45,678 = 45,678

209,564 < 290,564 4,585 < 4,858 12,541 < 12,514

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Select all of the options with 73,493 written in expanded form. 70 thousands, 34 hundreds, 90 tens, 3 ones 70 thousands, 30 hundreds, 40 tens, 93 ones 7 ten-thousands, 3 thousands, 49 hundreds, 3 ones 73 thousands, 4 hundreds, 9 tens, 3 ones 7 ten-thousands, 34 hundreds, 93 ones

Re-write the information from the table in order from least to greatest. CITY

POPULATION

Placerville

10,389

Diamond Springs

11,037

El Dorado Springs

42,108

Cameron Park

18,228

South Lake Tahoe

21,403

CITY

POPULATION

Use the number 852,904 to answer the following questions:

Part I: Write the number in expanded form.

Part II: Calculate 100 less than the number.

Part III: Identify the value of the underlined digit. Part IV: Identify the place value of the underlined digit.

Analyze the statement below. Determine if the statement is true or false.

806,056 > 806,506 TRUE

FALSE

Explain your answer.

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THINK TANK QUESTION 10

Part I: Use words to explain how these phrases correctly describe the number.

46: = 4 tens 6 ones = 3 tens 16 ones

Part II: Use drawings to explain how these phrases correctly describe the number.

46: = 4 tens 6 ones = 3 tens 16 ones

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MISSION 9: rounding whole numbers Use place value understanding to round multi-digit whole numbers to any place.

Bootcamp STRATEGY 1: Use place values to round multi-digit whole numbers to the nearest ten thousands.

Example: 5 ,6 5 9 , 2 0 3

STEP 1: Underline the targeted digit to be rounded. STEP 2: Look at the number to the right of the underlined digit. If that number is 0 - 4, then the underlined digit stays the same. If the number is 5 - 9, then the underlined digit must be increased by 1. STEP 3: Change all of the digits to the right of the targeted digit to zeros. The rounded number becomes:

5 ,6 6 0 , 0 0 0

Bootcamp STRATEGY 2: Use a number line to round multi-digit whole numbers to the nearest ten thousands.

Example: 5 ,6 5 9 , 2 0 3

STEP 1: Underline the targeted digit to be rounded. STEP 2: Draw a number line. Make lines for intervals at the far right and the left sides of the line. STEP 3: Keeping the targeted digit the same, change all of the digits to the right of it to zeros. The new number will be (5,650,000). Place this number on the far left side of the number line. 5,650,000

STEP 4: Increase the targeted digit by 1 number, and change all of the digits to the right of the targeted digit to zeros. Place this number on the far right of the number line. 5,650,000

5,660,000

STEP 5: Add interval lines in to allow for the actual numbers to be placed on the number line. Place a dot on the line that represents the number to be rounded, and label this number. 5,650,000

5,659,000 5,660,000

The number is closest to 5 ,6 6 0,0 0 0. Therefore, 5,659,203 is rounded to 5,660,000. 85 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NBT.3 (4.NBT.1.3) DIRECTIONS: Round numbers to the nearest hundreds. 1

55,346 = _______________

634,428 = ________________

109,896 = _________________

4 7,644 = _______________

DIRECTIONS: Round numbers to the nearest thousands. 5

55,346 = _______________

6 634,428 = ________________

109,896 = _________________

8 7,644 = _______________

DIRECTIONS: Round numbers to the nearest ten thousands. 9

55,346 = _______________

11 109,896 = _________________

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10 634,428 = ________________

12 97,644 = _______________

Target PRACTICE 1 1

Over the past 3 years, 87,429 people attended a May Day festival What is 87,429 rounded to the nearest thousands? Grid your answer.

Over the past 3 years, 93,512 people visited the River National Park. What is 93,512 rounded to the nearest hundreds? Grid your answer.

Select all of the statements that are true based on the information from the table.

Mrs. Ruiz set a goal of selling 70,000 flowers in 12 months at her flower shop. What is the greatest whole number that rounds to 70,000? A

70,100

69,800

60,999

69,942

4 Mr. Lattisi sold approximately 80,000 pairs of shoes over a 3 year period at his shoe store. Which of the following is the actual number of pairs sold before it was rounded to the nearest hundreds? A 80,545 B

80,045

80,400

80,785

6 Select all of the statements that are true based on the information from the table.

EMPLOYEE

Check

WATER TANK

CAPACITY

Manny

$378.00

Tank 1

3,460 gallons

Jessica

$432.00

Tank 2

2,780 gallons

Manny’s check rounded to the nearest ten is $380.

Tank 1’s capacity can be rounded to the nearest hundred as 3,500 gallons.

Manny’s check rounded to the nearest hundred is $400.

Tank 1’s capacity can be rounded to the nearest thousand as 3,000 gallons.

Jessica’s check rounded to the nearest ten is $440.

Tank 2’s capacity can be rounded to the nearest hundred as 2,800 gallons.

Jessica’s check rounded to the nearest hundred is $500.

Tank 2’s capacity can be rounded to the nearest thousand as 2,000 gallons. 87 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NBT.3 (4.NBT.1.3) DIRECTIONS: Round to the nearest hundreds. 1

3,802 = _______________

500,637 = ________________

920,467 = _________________

37,621 = _______________

DIRECTIONS: Round to the nearest thousands. 5

3,802 = _______________

6 500,637 = ________________

920,467 = _________________

8 37,621 = _______________

DIRECTIONS: Round to the nearest ten thousands. 9

503,802 = _______________

10 500,637 = ________________

920,467 = _________________

12 37,621 = _______________

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Target PRACTICE 2 1

Mrs. Carrizo set a company goal of $640,000 in jewelry sales for the year. What is this number rounded to the nearest hundred thousand? Grid your answer.

In 2008, there were 830,558 people living in a city. What is the number 830,558 rounded to the nearest ten thousands? Grid your answer.

Over the past 3 years, 6,500,000 people visited the Eiffel tower in Paris. What is the greatest whole number that rounds to 6,500,000?

Mr. Monte set a goal for his company to sell 15,000 condominiums in 3 years. What is the greatest whole number that rounds to 15,000?

6,570,506

15,005

5,725,400

15,710

6,489,020

14,500

6,400,860

14,908

Select all of the statements that are true based on rounding.

6,431 rounded to nearest thousand is 6,000

24,971 rounded to the nearest hundred is 25,000

568,795 rounded to nearest ten is 600,000

107,102 rounded to nearest ten is 107,100

70,695 rounded to nearest ten is 70,700

3,174 rounded to nearest ten is 3,180

550,458 rounded to nearest ten is 550,500

90,531 rounded to nearest hundred is 90,400

141,371 rounded to nearest hundred is 141,400

869,246 rounded to nearest thousand is 870,000

89 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NBT.3 (4.NBT.1.3) DIRECTIONS: Use number lines to solve the problems below.

1 Round 32,843 to the nearest thousands using the number line below.

Round 608,275 to the nearest ten thousands using the number line below.

Round 506,891 to the nearest hundred thousands using the number line below.

Round 5,784 to the nearest tens using the number line below.

Round 74,068 to the nearest ten thousands using the number line below.

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THINK TANK QUESTION The airport is planning an emergency evacuation of the residents of a particular island. There are exactly 67,030 residents. The airline wants to determine how many planes they will need to transport the residents.

Part I: Explain how to round 67,030 to the nearest ten thousands.

Part II: Explain how to round 67,030 to the nearest hundreds.

Part III: Determine which rounded number from Part I or Part II would be necessary to use to evacuate the residents from the island. Why would this be important?

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FOUR-STAR CHALLENGE - 4.NBT.3 (4.NBT.1.3) 1

A national park covers 508,537 acres. What is 508,537 rounded to the nearest hundred thousands? Grid your answer.

A city has a population of 405,956. What is 405,956 rounded to the nearest hundred thousands? Grid your answer.

Mrs. Parks set a goal to make 550,000 pieces of candy to sell in six months. What is the greatest whole number that rounds to 550,000?

A park covers 217,403 acres. What is 217,403 rounded to the nearest ten thousands?

560,800

207,000

558,800

210,000

540,800

200,000

548,800

220,000

Select all of the numbers that round to 1,500 when rounded to the nearest hundred.

Select all of the numbers that round to 58,000 when rounded to the nearest thousand.

1,447

58,490

1,549

58,722

1,537

57,501

1,450

57,623

1,562

57,489

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Write 4 different numbers that round to 582,000.

1st number here:

2nd number here:

3rd number here:

4th number here:

When rounded to the nearest thousands, an elephant’s weight is 5,000 pounds. What is the least amount that the elephant could weigh that would round to 5,000 to the nearest thousands? Use pictures, numbers, or words to represent your thinking.

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THINK TANK QUESTION 9

An airport reports that 300,000 passengers a year for the passed 3 years have traveled through the local airport during the first quarter. The Number of Travelers in First Quarter YEAR

TRAVELERS

2011

328,648

2012

341,560

2013

310,450

Is it possible that all the numbers listed in the table have been rounded to get 300,000? YES

Explain your answer:

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MISSION 10: ADDING AND SUBTRACTING WHOLE NUMBERS Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Bootcamp STRATEGY 1: Use place value charts to add whole numbers.

35,273 + 12,451 = 47,724 Stack the numbers by place value and place them in the appropriate group. THOUSANDS HUNDRED THOUSANDS

TEN THOUSANDS

HUNDREDS

THOUSANDS

HUNDREDS

TENS

ONES

Explain regrouping as: 10 ones equals 1 ten 10 tens equals 1 hundred 10 hundreds equals 1 thousand 10 thousands equals 1 ten hundred

Bootcamp STRATEGY 2: Use place value charts to subtract whole numbers.

35,273 - 12,451 = 22,822 Stack the numbers by place value, and subtract in the appropriate group.. THOUSANDS HUNDRED THOUSANDS

TEN THOUSANDS

HUNDREDS

THOUSANDS

HUNDREDS

TENS

ONES

Explain regrouping as: 10 ones equals 1 ten 10 tens equals 1 hundred 10 hundreds equals 1 thousand 10 thousands equals 1 ten hundred 95 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NBT.4 (4.NBT.2.4) 1

Use a place value chart to add the following whole numbers:

48,256 + 5,653 = HUNDRED TEN THOUSANDS HUNDREDS THOUSANDS THOUSANDS

TENS

ONES

+ Use a place value chart to add the following whole numbers:

332,703 + 64,654 = HUNDRED TEN THOUSANDS HUNDREDS THOUSANDS THOUSANDS

TENS

ONES

+ 3

Use a place value chart to subtract the following whole numbers:

37,274 - 4,051 = HUNDRED TEN THOUSANDS HUNDREDS THOUSANDS THOUSANDS

TENS

ONES

−

Use a place value chart to subtract the following whole numbers:

876,543 - 65,432 = HUNDRED TEN THOUSANDS HUNDREDS THOUSANDS THOUSANDS

−

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TENS

ONES

Target PRACTICE 1 1

The Mojave desert covers about 25,000 square miles. The Gobi desert covers 500,002 square miles. How much do both deserts cover?

252,002

552,002

225,002

525,002

A city is 800,000 square feet. A neighboring city is 746,000 square feet. What is the difference in square feet?

50,000

52,000

54,000

64,000

Select all of the statements that can be true based on the information from the table. MONTH INCOME March $65,789 April $34,576 May $54,385 The sum of March and April income is $100,365. The sum of April and May income is $78,961. The sum of March and May income is $120,174. The sum of March and April income is $110,365. The sum of April and May income is $98,961.

Mr. Smith drove 14,386 miles last year. This year he drove 21,562 miles. How many miles did Mr. Smith drive in the 2 years? Grid your answer.

Antofalla and Guallatiri are 2 of the largest active volcanoes in the world. Antofalla is 21,161 feet in height. Guallatiri is 19,882 square feet in height. How much taller is Antofalla than Guallatiri in square feet? Grid your answer.

Select all of the statements that can be true based on the information from the table. YEAR 2005 2010 2015

POPULATION 348,643 572,973 892,847

2010 population is greater than 2005 by 224,330. 2015 population is greater than 2010 by 319,874. 2015 population is greater than 2005 by 544,204. 2010 population is greater than 2005 by 124,330. 2015 population is greater than 2010 by 309,874. 97 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NBT.4 (4.NBT.2.4) 1

Use a place value chart to add the following whole numbers:

71,356 + 8,452 = HUNDRED TEN THOUSANDS HUNDREDS THOUSANDS THOUSANDS

TENS

ONES

+ Use a place value chart to add the following whole numbers:

523,502 + 24,532 = HUNDRED TEN THOUSANDS HUNDREDS THOUSANDS THOUSANDS

TENS

ONES

+ 3

Use a place value chart to subtract the following whole numbers:

568,865 - 30,589 = HUNDRED TEN THOUSANDS HUNDREDS THOUSANDS THOUSANDS

TENS

ONES

−

Use a place value chart to subtract the following whole numbers:

983,561 - 572,638 = HUNDRED TEN THOUSANDS HUNDREDS THOUSANDS THOUSANDS

−

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TENS

ONES

Target PRACTICE 2 The number of people who took the metro bus on Tuesday was 18,732. The number of people who took the metro bus on Friday was 17,456. How many more people took the bus on Tuesday?

The car that Lyle owns costs $39,486. The car his wife owns costs $48,379. How much more does Lyle’s wife’s car cost? A

$8,893

$8,993

1,286

1,276

$87,855

35,188

36,188

$87,865

There were 7,287 seats sold for a Broadway play this month. Last month, 6,806 seats were sold. How many tickets were sold in both months? Grid your answer.

The local cable company opened 15,687 new contracts last year. This year, the number of contracts increased by 1,694. How many cable contracts does the cable company have? Grid your answer.

Select all of the combinations of numbers that have a sum of 3,363.

Select all of the combinations of numbers that have a difference of 1,078.

1,088

1,256

2,107

2,275

1,256 & 2,107

2,275 & 2,107

1,256 & 1,088

2,275 & 1,088

1,256 & 2,275

2,275 & 1,256

4,903

5,464

5,981

6,542

5,981 & 5,464

6,542 & 4,903

6,542 & 5,464

5,464 & 4,903

6,542 & 5,981

5,981 & 4,903

99 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NBT.4 (4.NBT.2.4) DIRECTIONS: Use place value charts and regrouping to solve the following problems.

1 The Nile River is 4,145 miles long. The Mississippi River is 3,790 miles long. How many miles long are both the rivers? (Show your work)

2 Kirk drove 13,879 miles last year. This year, he drove 14,986 miles. How many miles did Kirk drive in all? (Show your work)

3 In 1995, the population of a city was 350,000. If the population in the year 2012 was 880,000, what is the increase in the population? (Show your work)

4 The number of domestic visitors to a theme park was 732,600 and the number of international visitors was 227,504. How many visitors did the theme park get in all? (Show your work)

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THINK TANK QUESTION The table below shows the favorite sport of various spectators. Favorite Sport Basketball Baseball Rugby Soccer

Number of People 1,547 1,114 4,574 875

Part I: Which 2 sports have a difference of more than 3,500 people? (Show your work)

Part II: Which 2 sports have a sum of more than 6,000 people? (Show your work)

101 I Copying is strictly prohibited

Four-STAR CHALLENGE - 4.NBT.4 (4.NBT.2.4) 1

Jim sold his boat for $24,429. Charles sold his boat for $1,725 more. How much did Charles sell his boat for? Grid your answer.

Susan’s annual income is $254,356. If she spends $152,287 a year, what will be the amount she will be saving annually? Grid your answer.

Kevin and Patrick started a business partnership. Kevin contributed $43,845 to the business and Patrick contributed $49,276. How much did they contribute in all?

Samantha is a pilot. She flew 423,870 miles last year. This year, she flew 368,987 miles. How far did she travel in these 2 years?

$82,021

781,757 miles

$93,121

782,857 miles

$82,121

791,747 miles

$93,011

792,847 miles

Select all of the numbers that will make the equation below true.

5,A34 + 2B8 5,912

Select all of the numbers that will make the equation below true.

7,1C5 - D59 6,586

A=4

B=7

C=4

D=3

A=6

B=9

C=8

D=7

A=5

B=6

C=9

D=5

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Fill in the missing digits. (Show your work)

2 3, 6 +

2 8 7

9, 3 8 9 8

Fill in the missing digits. (Show your work)

8, 4 5 1 -

5, 6 8 7 2, 7

Part I: Explain when it is necessary to regroup in an addition problem.

Part II: Explain when it is necessary to regroup in a subtraction problem.

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THINK TANK QUESTION 10 Part I: Write a subtraction word problem that has a difference of 3,467. (Show your work)

Part II: Write a different subtraction word problem using different digits that has a difference of 3,467. (Show your work)

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MISSION 11: Multiplying whole numbers Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Bootcamp STRATEGY 1: Use place value strategies to multiply whole numbers. 1) 7 × 8 = 56 (multiplication fact) 2) 7 × 80 = 560 (multiply by tens —> the last digit is a zero) 3) 7 × 800 = 5,600 (multiply by hundreds —> the last 2 digits are zeros) 4) 7 × 8,000 = 56,000 (multiply by thousands —> the last 3 digits are zeros)

Bootcamp STRATEGY 2: Use rectangular arrays to multiply whole numbers. Example: 8 × 4 = 32 STEP 1: Create an array of 8 objects

STEP 2: Multiply the array by 4 groups

STEP 3: Count the total number of objects

8 objects

3 4 Groups

Bootcamp STRATEGY 3: Use area models to find the product of double digit numbers. Example: 23 × 14 = 322 STEP 1: Create a horizontal rectangle.

20 × 10 =

3 × 10 =

20 × 4 =

3×4=

STEP 2: Divide the rectangle into 4 parts. STEP 3: Break apart the digits and the value they represent of the first multiplier. Place the resulting numbers on the vertical axis of the rectangle.

STEP 4: Break apart the factors of the second multiplier. Place the resulting numbers on the horizontal axis of the rectangle. STEP 5: Find the products of the smaller rectangles. STEP 6: Add all 4 products to find the sum.

200 80 30 + 12 322

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TRAIN THE BRAIN PRACTICE 1 4.NBT.5 (4.NBT.2.5) DIRECTIONS: Multiply the following multi-digit numbers using partial products and regrouping. (Show your work) 1

7 × 43 =

53 × 46 =

15 × 49 =

DIRECTIONS: Multiply the following multi-digit numbers using area models and expanded form. (Show your work) 4

7 × 43 =

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53 × 46 =

15 × 49 =

Target PRACTICE 1 1

A farm has 20 rows of cabbage plants with 65 plants in each row. How many cabbage plants does the farm have? Grid your answer.

Divine can read 278 pages of a book every night. If she reads the book for 8 days, how many pages will she read in all? Grid your answer.

Mia wants to buy 4 new chairs that cost $57.00 each. How much will Mia pay for the 4 chairs?

There are 35 rows of chairs in an auditorium with 25 chairs in each row. How many chairs are there in the auditorium in all?

$200

$228

875

$240

857

$300

578

Select all of the equations that are equivalent to the product of the multiplication equation below.

36 × 73 = ?

Select all of the equations that are equivalent to the product of the multiplication equation below.

54 × 29 = ?

657 × 4

66 × 42

370 × 6

522 × 3

1,314 × 2

1,010 × 2

1,237 × 3

261 × 6

98 × 32

399 × 4

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TRAIN THE BRAIN PRACTICE 2 4.NBT.5 (4.NBT.2.5) DIRECTIONS: Multiply the following multi-digit numbers using partial products and regrouping. (Show your work) 1

5 × 613 =

1,538 × 3 =

6,708 × 8 =

DIRECTIONS: Multiply the following multi-digit numbers using area models and expanded form. (Show your work) 4

5 × 613 =

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1,538 × 3 =

6,708 × 8 =

Target PRACTICE 2 1

A new store opened recently. Each week since its opening, the store sold 245 ice cream bars. The store has been open for 7 weeks. How many ice cream bars has the store sold? Grid your answer.

Sean bought a new printer for his office. It can print 43 pages each minute. How many pages can the printer print in 24 minutes? Grid your answer.

Which expression below has a product of 4,840?

A concert hall has 120 rows of seats. There were 9 seats in each row. How many seats did the concert hall have in all?

(2,400 × 2) + (400 × 2)

(2,000 × 2) + (420 × 2)

108

2,240 × 2

1,008

1,220 × 4

1,080

1,200

Select all of the combinations of numbers that have a product of 544.

Select all of the combinations of numbers that have a product of 1,431.

159

16 and 17

17 and 32

9 and 27

9 and 53

17 and 34

16 and 34

27 and 53

53 and 159

16 and 32

32 and 34

27 and 159

9 and 159

109 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NBT.5 (4.NBT.2.5) 1 Use the digits 2, 4, 5, and 7 to write a two-digit by two-digit multiplication problem that will give the greatest possible product. NOTE: All 4 digits must be used only once in your problem.

2 The neighborhood elementary school has 18 students in each fourth grade class. There are 5 fourth grade classes. How many students are there in all? Use a rectangular array to solve this problem. (Show your work)

3 Juan is required to complete 22 boxing drills per kick boxing session he attends. If Juan attends 33 sessions, how many boxing drills will he complete? Use an area model to solve this problem. (Show your work)

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THINK TANK QUESTION Part I: Dorothy earns $8 an hour working at the videogame store. If she works 160 hours this month, how much will she earn? (Show your work)

Part II: Show a second strategy for calculating Dorothy's earnings.

Part III: Which of the 2 methods used above do you prefer for determining Dorothy’s earnings? Explain.

111 I Copying is strictly prohibited

Four-STAR CHALLENGE - 4.NBT.5 (4.NBT.2.5) 1

Mandy walked 5 miles each day for 120 days. How many miles did Mandy walk in all? Grid your answer.

Which expression below has a product of 15,175?

(305 × 5) + (300 × 5)

(3,000 × 5) + (35 × 5)

95 × 25

6,015 × 3

Select all of the equations below that are correct.

Vito is renovating his condo and wants to buy closet doors that cost $224 each. If Vito buys 5 closet doors, how much does he spend in all? A $45 B

$1,120

$229

$219

There are 52 rows of seats in a theater with 15 seats in each row. How many seats are there in the theater? Grid your answer.

Select all of the equations below that are correct.

1,132 × 5 = 5,660

912 × 24 = 21,888

73 × 12 = 876

7,627 × 5 = 36,235

5,301 × 2 = 9,702

5,017 × 4 = 20,284

48 × 77 = 3,696

42 × 91 = 42,222

54 × 32 = 1,728

82 × 17 = 1,394

6,596 × 8 = 52,768

9,173 × 7 = 64,211

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Libby wants to use an area model to help her determine the size of her garden in square feet. She multiplied 43 × 14.

Use the box below to create an area model that Libby can use to multiply 43 × 14.

Show 2 strategies for multiplying 3,421 and 8 to find the same product.

Strategy 1:

Strategy 2:

Use the digits 3, 5, 8, and 9 to write a two-digit by two-digit multiplication problem that will give the greatest possible product. NOTE: All 4 digits must be used only once in your problem.

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THINK TANK QUESTION 10

PART I: During Maiko’s first tutoring session, the tutor taught her how to multiply. Using the example 56 × 14, show the process that the tutor may have used to demonstrate this multiplication problem.

Part II: Show a second strategy for multiplying 56 × 14.

Part III: Explain which of the 2 methods used to multiply 56 × 14 in Part I and Part II you prefer and why.

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MISSION 12: DIVIDING whole numbers Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Bootcamp STRATEGY 1: Use place value models to find whole number quotients and remainders. Example: 260 ÷ 5 = 52 STEP 1: Divide the 2 hundreds by 5. This will result in 4 tens Base 10 blocks for each of the 5 groups. STEP 2: Divide the 6 tens by 5. This will result in 1 tens with 2 ones leftover. STEP 3: Once you have done so, you will see that you will now have each of 5 groups comprised of 5 tens and 2 ones, which means 260 divided into 5 groups is 52.

Bootcamp STRATEGY 2: Use area models to find whole number quotients and remainders. Example: 260 ÷ 5 = 52

50 2 STEP 2: Try to divide the divisor by the highest place of the dividend as 5 −260 − 10 possible. For example, 5 cannot go into 2, so find out how many 250 10 times 5 goes into 26. Add zeros for the remaining places of the 10 0 STEP 1: Place the dividend in a box and write the divisor to the left of it.

dividend that were not divided. STEP 3: Multiply the quotient by the divisor and subtract. For example, 50 times 5 is 250. Step 4: Subtract the product (250) from the original divisor (260), repeat the process for the amount left over (10), and write it in a box to the right of the dividend box. Step 5: You will see that 5 divided by the amount left over (10) is equal to 2. Add the quotients to determine the quotient for the original problem (50 + 2 = 52). 52 5 260 -5 0 Example: 260 ÷ 5 = 52 210 -5 0 STEP 1: Use any times table that you are comfortable with. STEP 2: Set up your division problem, then multiply the divisor by the times 1 6 0 -5 0 table you chose (10) and write the product under your dividend and 1 1 0 -5 0 subtract. 60 STEP 3: Continue Step 2 until your difference is less than the divisor. -5 0 Step 4: Add all the numbers that you multiplied by. That sum will be your 10 quotient. - 10 0

Bootcamp STRATEGY 3: Use partial quotient strategy to solve.

10 × 5 10 × 5

10 × 5 10 × 5 10 × 5 2×5 52

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TRAIN THE BRAIN PRACTICE 1 4.NBT.6 (4.NBT.2.6) DIRECTIONS: Use area models to find the quotients below. (Show your work) 1

84 ÷ 3 =

72 ÷ 4 =

196 ÷ 7 =

DIRECTIONS: Use partial quotient strategy to find the quotients below. (Show your work) 4

84 3

72 4

196 = 7

DIRECTIONS: Use the standard strategy to find the quotients below. (Show your work) 7

3 84 =

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4 72 =

7 196 =

Target PRACTICE 1 1

Daniel cut a 64-centimeter long wire into 4 equal pieces. What is the length of each piece of wire Daniel cut? Grid your answer.

Which number sentence below is not correct? A

1,200 ÷ 6 = 200

2,400 ÷ 8 = 300

140 ÷ 7 = 20

6,400 ÷ 8 = 80

Select all of the expressions that have a value of 105.

Don received a $285.00 commission from a previous sale. He wants to split his commission equally between 3 of his coworkers. How much will each coworker get? A

$95

$185

$100

$200

Michael needs to arrange 66 chairs into 6 rows. Each row must have the same number of chairs. How many chairs will there be in each row? Grid your answer.

Select all of the expressions that have a value of 340.

330 ÷ 3

1,020 ÷ 3

420 ÷ 4

1,720 ÷ 4

665 ÷ 7

2,040 ÷ 6

840 ÷ 8

2,380 ÷ 7

945 ÷ 9

3,060 ÷ 8

117 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NBT.6 (4.NBT.2.6) DIRECTIONS: Use the distributive or area model strategy to find the quotients below. (Show your work)

272 ÷ 6 =

3,296 ÷ 8 =

2,375 ÷ 3 =

DIRECTIONS: Use the partial quotient strategy to find the quotients below. (Show your work)

272 = 6

3,296 = 8

2,375 = 3

DIRECTIONS: Use the standard strategy to find the quotient. (Show your work) 7

6 272 =

118 I Smart to the Core I Educational Bootcamp

8 3,296 =

3 2,375 =

Target PRACTICE 2 1

James has 2,169 ounces of juice. He needs to pour 9 ounces in each glass at the party he is catering. How many glasses can he fill? Grid your answer.

Tanya can make 1 bracelet using exactly 8 beads. If she has a total of 1,098 beads and she makes as many bracelets as possible, how many beads will she have left over? Grid your answer.

Steve needs to pack 1,800 apples into baskets for a food drive. Each basket can hold 9 apples. How many baskets does Steve need?

Herbert needs to arrange 222 books on a bookshelf. If the bookshelf has 6 shelves, how many books can Herbert place on each shelf equally?

200

2,000

Select all of the combinations of numbers that will form a division equation with a quotient of 192.

1152

1536

Select all of the combinations of numbers that will form a division equation with a quotient of 304.

1216

2432

6 and 8

6 and 1,152

4 and 2,432

8 and 1,216

1,152 and 1,536

8 and 1,536

8 and 2,432

4 and 1,216

8 and 1,152

6 and 1,536

4 and 8

1,216 and 2,432

119 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NBT.6 (4.NBT.2.6) DIRECTIONS: Use place value models to find the whole number quotients and remainders for the following problems. =

1 Aileen sorted the Base 10 blocks shown below into 5 equal groups.

Draw the 5 groups that Aileen most likely made.

2 Charles sorted the Base 10 blocks shown below into 5 equal groups.

Draw the 5 groups that Charles most likely made.

120 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION Part I: Write and solve a division problem using a 3-digit dividend and a 1-digit divisor that results in a quotient with no remainder. (Show your work)

Part II: Explain how you came up with the division problem that has a quotient with no remainder.

121 I Copying is strictly prohibited

Four-STAR CHALLENGE - 4.NBT.6 (4.NBT.2.6) 1

Ms. Wu made 138 quarts of lemonade. She poured the lemonade into bottles that hold 4 quarts each. What is the greatest number of bottles she could have completely filled?

A hardware store has a total of 2,280 yards of wire in stock. The wire is divided into 6 rolls, and each roll contains the same amount of wire. How many yards of wire does each roll contain?

450

380

300

400

A set of rocks have a mass of 3,200 grams. There are 8 rocks in the set, and each rock has the same mass. What is the mass of each rock? Grid your answer.

Vicky baked 287 mini cakes for a bake sale. She had several trays that each hold 9 mini cakes each. After all of the trays are filled to capacity, how many mini cakes will be on the last tray? Grid your answer.

Select all of the equations that are correct.

296 ÷ 5 = 59 r. 1

734 ÷ 2 = 367 r. 1

134 ÷ 7 = 23 r. 3

329 ÷ 5 = 65 r. 4

835 ÷ 3 = 278 r. 1

435 ÷ 6 = 70 r. 3

671 ÷ 8 = 83 r. 7

891 ÷ 7 = 127 r. 2

349 ÷ 4 = 87 r. 5

537 ÷ 2 = 268 r. 1

628 ÷ 6 = 102 r. 4

578 ÷ 4 = 144 r. 2

122 I Smart to the Core I Educational Bootcamp

Nancy sorted the Base 10 blocks shown below into 8 equal groups.

Which model below could represent 1 of the groups of Base 10 blocks? A

Show 2 strategies for dividing 424 by 8 to find the same quotient.

Strategy 1:

Strategy 2:

Divide 1,414 ÷ 7 using partial quotient to solve.

123 I Copying is strictly prohibited

THINK TANK QUESTION 10

Part I: Write a story problem for the equation 1,952 ÷ 8. Use an area model to solve the story problem you created.

Part II: Use an equation, rectangular array, and/or area model to solve the division problem you created above.

124 I Smart to the Core I Educational Bootcamp

MISSION 13: Finding equivalent fractions Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Bootcamp STRATEGY 1: Use fraction models to find equivalent fractions. Write 2 fractions that are equivalent to

.3 5

Step 1: Create a model to represent 3 . 5

Step 2: Divide the model in half and use the model to determine the equivalent fraction. 6 10 Step 3: Divide the model from Step 2 in half to determine the equivalent fraction. 12 20

Bootcamp STRATEGY 2: Use multiplication to find equivalent fractions. Step 1: Multiply the numerator and denominator by the same number. Each fraction used represents 1 whole, and therefore, will give an equivalent product. 6 3 2 5 × 2 = 10

9 3 3 5 × 3 = 15

3 4 12 5 × 4 = 20

3 5 15 5 × 5 = 25

Equivalent fractions

Bootcamp STRATEGY 3: Find equivalent ratios by multiplying or dividing both the numerator and the denominator by the same number. 3 5 ×

9 3 3 5 × 3 = 15

3 5 ×

= 25

3 5 = 15 5 × 5 25

6 10 ÷

= 5

6 2 3 10 ÷ 2 = 5

12 20 ÷

4 12 3 ÷ = 4 5 20 125 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NF.1 (4.NF.1.1) DIRECTIONS: Identify 3 equivalent fractions that are represented by the shaded areas below. 2

DIRECTIONS: Circle the equivalent fractions.

4 5

16 20

10 20

20 30

20 25

1 3

3 6

6 9

4 12

24 32

9 12

3 4

18 24

1 3

4 5

126 I Smart to the Core I Educational Bootcamp

Target PRACTICE 1 1

In the school chorus, 25 of the 1 students are fourth graders and 4 .of the students are third graders. How 1 can you write 25 and 4 as a pair of fractions with a common denominator?

James divided a cake into 5 equal pieces. He gave 1 piece of cake to his friend. Which of the fractions below 1 is equivalent to 5 ?

1 1 and 20 20

4 1 and 10 4

3 10

4 25

8 5 and 20 20

2 4 and 5 16

3 15

4 15

Joey knows he needs go 45 of a mile. 1 He wants to use 10 -liter bottles of gas to go an equivalent number of 1 miles. How many 10 -liter bottles of gas will he need? A

Select all of the models that have 1 been shaded to show the fraction 4 .

Herbert counts 40 trees in an orchard. The apple trees make up 15 of the trees in the orchard. What fraction does not represent the number of apple trees? A B

8 20 2 10

8 40

4 20

Select all of the models that have 2 been shaded to show the fraction 5 .

1 127 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NF.1 (4.NF.1.1) DIRECTIONS: Identify 3 equivalent fractions that are represented by the shaded areas below. 1

DIRECTIONS: Circle the equivalent fractions. 3

1 2

6 10

5 10

20 40

15 32

3 5

9 15

12 20

6 15

15 25

3 4

6 8

30 40

9 20

12 16

128 I Smart to the Core I Educational Bootcamp

Target PRACTICE 2 5

In an amusement park, 6 of the visitors are children and 5 of the

visitors are adults. What fractions with a common denominator can

There are 7 rotten apples in a basket of 8 apples. Which equivalent fraction below denotes the amount of rotten apples?

replace 5 and 5 ? 6

5 5 and 48 48

48 48 and 40 30

40 30 and 48 48

48 and 48 5 5

Select all of the models that show 1 the fraction 2 shaded. 0

A billiard set contains 16 balls and 7 16 of them are striped balls. How many striped balls are there in 6 sets?

28 32

21 26

14 18

30 40

Alex has 35 toy cars in his collection. If 35 of the cars are red, what fraction represents the number of red cars in his collection?

A B

21 35 21 30

3 25

35 5

Select all of the models that show the fraction 3 shaded. 8

112

129 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NF.1 (4.NF.1.1) 1 . 1 Draw models to demonstrate 3 equivalent fractions for 2

1 2 Select all of the number lines that have the fraction 3 shaded. 0

130 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION Bernie and Valerie were both given apple pies as a gift for the holidays. Bernie ate 3 4 of his pie as shown in Part I. Valerie cut her pie into smaller pieces, but still ate the same amount of pie as Bernie. Part I: Divide and shade in the pie that could possibly represent Valerie’s pie.

Part II: Explain how you know the pie you created for Valerie is equivalent to Bernie’s pie.

131 I Copying is strictly prohibited

Four-STAR CHALLENGE - 4.NF.1 (4.NF.1.1) 1

In the zoo, Jerry sees that 8 of the 4 birds are white and 5 of the birds 4 are black. How can he write 38 and 5 as a pair of fractions with a common denominator?

15 and 32 40 40

3 4 and 40 40

3 15 and 40 40

40 40 and 32 15

Todd made a quilt with 50 squares. There were 25 black squares. Which fraction below is equivalent to the amount of black squares on the quilt? 50 1 C A 25 5 50 100

Each cup of fruit punch requires 1 cup of sugar. If Ricky used 6 cup 8 8 of sugar in all, how many cups of fruit punch did he make?

Mila’s iced tea stand will sell sweetened and unsweetened tea. Mila wants 14 of the cups she sells to be unsweetened. If the greatest number of cups that will fit on the stand is 24, what fraction represents the number of cups that will be unsweetened?

Select all of the numbers that represent the letters that make these fractions equivalent.

4 12 16 24 C = = = = 5 A 20 B 40

2 5

6 24 4 24

8 24

24 6

Select all of the numbers that represent the letters that make these fractions equivalent.

A 10 20 30 40 = = = = 6 12 B 36 C

A = 15

B = 30

A=2

B = 16

A = 10

C = 32

A=5

C = 54

B = 32

C = 36

B = 24

C = 48

132 I Smart to the Core I Educational Bootcamp

Part I: Use the models below to draw lines that demonstrate 2 different equivalent fractions. Record the equivalent fractions in the boxes below.

1st equivalent

2nd equivalent

Part II: Explain how you identified the 2 equivalent fractions.

8 Part I: What fraction is represented by the model below? Fraction: Part II: Select all of the number lines that show an equivalent fraction to the figure shown. 0

133 I Copying is strictly prohibited

THINK TANK QUESTION 9

Jake wanted to evenly divide a plot of land into 2 sections. One section will be used for a flower garden and the other for a vegetable garden.

Part I: Divide the plot of land below to give Jake an equal amount of land for both the flower and the vegetable garden. What fraction makes up the flower garden? (Write the answer in the boxes below.) What fraction makes up the vegetable garden? (Write the answer in the boxes below.)

Flower

Vegetable Plot of land

Part II: Use the diagram above to further divide the plot of land into 8 sections for the flowers and 8 sections for the vegetables. What equivalent fraction makes up the flower garden?

Flower What equivalent fraction makes up the vegetable garden?

Vegetable

134 I Smart to the Core I Educational Bootcamp

MISSION 14: Using Models to compare fractions Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Bootcamp STRATEGY 1: Use fraction models to compare fractions. Example: Compare the fractions 3 and 1 using fraction models. 5 2 3 Step 1: Create a model to represent . (Shown in Step 2) 5 Step 2: Create a second model directly below the first model to represent 1 . 2 3 5 1 2 Step 3: Draw a line through the shaded region of both rectangles. 3 5 1 2 Step 4: The longer line represents the greater fraction. 3 5

1 2

Bootcamp STRATEGY 2: Use common denominators to compare fractions. Example: Compare 3 and 1 by writing equivalent fractions using common denominators. 5 2 Step 1: Find the common denominator by finding the least common multiple. 3 5 1 2

5 10 15 20 25 2

4 6 8 10

Step 2: To determine which fraction is larger, create equivalent fractions with common denominators. 6 3 × 2 1 × 5 = 5 = 2 10 5 10 5 2 6 10

5 3 Therefore, 10 5

1 2 135 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NF.2 (4.NF.1.2) DIRECTIONS: Place the fractions below in order from least to greatest. 2

1 < 5

1 < 3

1 < 4

DIRECTIONS: Compare the fractions below (>, <, or =). 5

3 4

2 3

6 10

136 I Smart to the Core I Educational Bootcamp

4 5

1 3

3 4

4 5

1 4

2 8

1 2

4 8

Target PRACTICE 1 1

A charitable institution’s budget 4

allows 8 to be spent on rent and 1 utilities, 6 for food, and 34 for

Linda sewed 2 yard of fringe on her blouse, 64 on her scarf, and 41 on her jacket. Which fraction below has the

planting trees. Which fraction below

least value?

has the greatest value?

4 8

1 6

3 4

There are 2 friends debating who has done more homework. John said he 5 has done 6 of his homework and Tim 9 said he has done 12 .... Which of the statements below correctly compares the fractions? A

5 6

9 < 12

5 6

9 > 12

5 6

9 = 12

9 12

1 4

12 < 12 12 B 12 =

4 9

A recipe calls for 10 cup of lemon juice and 12 cup of water. Which 12 statement below correctly compares the fraction?

5 6

Select all of the statements that can be true based on the information from the table. RIBBON LENGTH 4 yards Red ribbon 5 5 yards Pink ribbon 6 2 yards Blue ribbon 3 red ribbon > pink ribbon

1 2

8 10

12 12

8 > 10

8 10

> 12 12

Select all of the statements that can be true based on the information from the table. PIPE DIAMETER 3 inches Pipe 1 8 2 inches Pipe 2 5 1 inches Pipe 3 2 Pipe 1 is larger than Pipe 2.

pink ribbon > blue ribbon

Pipe 2 is larger than Pipe 3.

red ribbon > blue ribbon

Pipe 1 is larger than Pipe 3.

pink ribbon > red ribbon

Pipe 2 is larger than Pipe 1.

blue ribbon > pink ribbon

Pipe 3 is larger than Pipe 2. 137 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NF.2 (4.NF.1.2) DIRECTIONS: Place the fractions below in order from greatest to least. 2

1 >

4 > 6

6 > 7

DIRECTIONS: Compare the fractions below (>, <, or =). 5

1 4

1 3

2 3

4 5

138 I Smart to the Core I Educational Bootcamp

4 5

6 8

1 4

2 3

1 2

4 5

3 4

4 8

Target PRACTICE 2 1

Evangeline baked a peach pie. She

Jeff is making a rice cake. He adds

5 used 6 peaches, 1 dough, and 10

2 cup coconut milk, 3 cup rice, and 1 3 4 5

honey. Which fraction below has the

sesame seeds. Which fraction below

greatest value?

has the least value?

6 8

1 4

5 10

Select all of the fractions that could be true. 1 > 2 2 3 3 3 > 4 5 1 > 1 3 4 2 2 > 5 3 4 1 > 5 4

Select all of the fractions that could be true.

2 3 10 < 12

2 4

3 5

1 3

Lucy has a lawn. This week she mowed 4 of the lawn. Last week she 6 mowed 1 of the lawn. Which 3 inequality below correctly compares the fractions? A

1 3

4 6

1 3

6 4

1 3

4 6

1 3

Henry drank 35 of a glass of water. 7 Ron drank 8 of a glass of water. Which inequality below correctly compares the fractions?

4 5 8 < 6 8 10 < 10 12

1 whole 1 5 1 8

1 2 < 3 5 5 4 < 8 10

A B

3 5 3 5

1 5 1 8

< =

1 8

7 8 7 8

1 5 1 8

1 8

3 5

7 8

1 8

7 8 3 5

139 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NF.2 (4.NF.1.2) DIRECTIONS: Use fraction models to compare the fractions below.

4 10

5 8

2 3

6 10

3 6

10 12

140 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION Jerome wants to use a number line to plot the following points from least to greatest. 1 3 4 6 4 8

Part I: Determine how you would find the best interval to use on a number line based on the fractions given.

Part II: Write the fractions for the intervals on the number line. Explain why you chose those fractions.

PART III: Plot Jerome’s fractions on the number line. What fractions on the number line

are equivalent to Jerome’s fractions?

141 I Copying is strictly prohibited

FOUR-STAR CHALLENGE - 4.NF.2 (4.NF.1.2) 1

10 2 mile, Silva skated 5 12 1 mile, and Lynn skated 2 mile. Who

Bryan skated

The trail mix that Grace made had 6 cup of cashews, 5 cup of almonds, 8 1 and 4 cup of walnuts. What ingre-

skated furthest?

dient did she use the least of? A Bryan

B Silva

Lynn A Walnuts

Ryan ate 8 of a pizza and Demi ate 6 of a pizza. Which statement below correctly compares the fractions?

3 8

4 6 4 6

3 8

4 6

3 8

Study the following sets of fractions. Select all of the fractions that are listed in the correct order either from least to greatest or greatest to least. 7 4 3 > > 10 5 4

11 < 12 11 B 12 =

9 10

11 12

9 10

9 11 > 10 12

9 10

Study the following sets of fractions. Select all of the fractions that are listed in the correct order either from least to greatest or greatest to least. 4 3 2 > > 5 4 3

3 7 4 < < 4 10 5 3 4 7 4 < 5 < 10

3 4 2 < < 4 5 3 4 3 2 5 < 4 < 3

4 3 7 5 > 4 > 10

2 3 4 3 > 4 > 5

7 3 4 10 < 4 < 5

2 3 4 3 < 4 < 5

142 I Smart to the Core I Educational Bootcamp

C Almonds

Kylee walks 12 mile to school each 9 day, and Mark walks 10 mile to school each day. Which statement below correctly compares the fractions?

B Cashews

Boxes were organized by their fraction number in order from least to greatest. The warehouse team noticed that 2 of the boxes were missing the fractions. Determine 2 possible fractions that may have been missing from the 2 boxes to maintain the order of least to greatest.

1 4

3 5

7 10

4 5

Draw a line to match the fractions from least to greatest on the steps of the ladder. 3 4 1 2 1 8 5 8

1 1 4

3 8 7 8

143 I Copying is strictly prohibited

THINK TANK QUESTION 9

Tia wants to use a number line to plot the following points from least to greatest. 3 1 6 1 3 2 12 12 4

Part I: Determine how you would find the best interval to use on a number line based on the fractions given.

Part II: Write the fractions for the intervals on the number line. Explain why you chose those fractions.

PART III: Plot Tia’s fractions on the number line. What fractions on the number line are

equivalent to Tia’s fractions?

144 I Smart to the Core I Educational Bootcamp

MISSION 15: Adding Fractions with like denominators Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Bootcamp STRATEGY 1: Use fraction strips to find the sum of fractions with like denominators. Example: Add 2 fractions with common denominators. 1

Step 1: Create fraction strips that reflect the fractions being added. 1 1 7

1 7

1 1 7

1 7

Step 2: Add the wholes together, and then add the fraction pieces to get the sum. 1 1 1 1 + + + = 7 7 7 7

4 7

Bootcamp STRATEGY 2: Use fraction strips to find the difference of mixed numbers with like denominators. Example: Subtract 2 fractions with common denominators. 3

‒

1 17

Step 1: Create fraction strips that reflect the fractions being subtracted. 1 1 1 7

1 7

‒ 1 7

1 7

Step 2: Eliminate the numbers being subtracted by canceling out the matching sides as demonstrated above. 2 Step 3: List the remaining parts. remaining parts 1 7 145 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NF.3 (4.NF.2.3) DIRECTIONS: Use models to add and subtract the following fractions. 3 1 + 4 4 =

2 85 +

1 81 =

9 3 ‒ = 100 100

2 5 + 6 6 =

9 ‒ 3 = 10 10

2 81

‒

1 87

DIRECTIONS: Find 2 ways to decompose the following fractions into the sum of their fractions.

5 6 =

9 12 =

146 I Smart to the Core I Educational Bootcamp

Target PRACTICE 1 1

Ben hiked 10 mile on Saturday. He 2 hiked 10 mile more on Sunday.

Chris had a piece of wire 5 inch long. 1 He used 5 inch.

1 5

1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10

A B

1 5

Joni bought 9 yards of fabric. She 5 used 5 6 yards for a dress. How much fabric does she have left?

10 9

11 9

1 6

3 9

5 9

3 6

9 6

Select all the equations below that are correct. 1 4 9 3 12 7 42 8 4 10 1 31

Select all of the equations below that are correct.

+ 3 43 = 10

4 84 - 2 82 = 2 82

7 =74 + 412 12

9 43 - 7 41 = 1 42

+ 2 42 = 9 46

7 9 + 110 = 6 10

+ 7 32 = 9

1 5

How much wire does he have left? Grid your answer.

How many miles did he hike in all? Grid your answer.

A package of ground beef weighs 3 9 pounds. A package of ground pork 1 weighs 2 9 pounds more than the beef. What is the combined weight of the packages?

1 5

3 8 4 6 12 2 63

- 4 86

5 8

5 - 5 11 = 1 12 12

-1

4 6

5 6

147 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NF.3 (4.NF.2.3) DIRECTIONS: Use models to add and subtract the following fractions. 4 5 = + 10 10

2 43 + 1 41

4 =

2 7 ‒ 8 = 8

4 2 5 + 5 =

6 5 ‒ = 12 12

2 5 ‒ 1 54

DIRECTIONS: Find 2 ways to decompose the following fractions into the sum of their fractions.

3 4 =

3 = 4

14 = 100

148 I Smart to the Core I Educational Bootcamp

Target PRACTICE 2 1

To paint a room, Tim mixed 8 quarts of blue paint and 3 quarts of green 8 paint.

Jeffrey promised to do 12 hours of volunteer work this week. So far, he 3 has done 12 hours.

1 1 8

1 8

1 1 8

1 8

1 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 12 12

How much paint did Tim mix? Grid your answer.

How many more hours must he work this week? Grid your answer.

Benjamin spent 1 5 hours on math homework and 2 15 hours on history homework. How many hours did Benjamin spend on homework?

2 5

1 5

Paul and Max each travel to school 4 by bicycle. Paul’s house is 3 6 miles 1 from school. Max’s house is 5 6 miles from school. How much longer does Max travel than Paul?

2 5

3 5

9 6

3 6

Select all of the decomposed frac8

tions that have a sum of 12 . 1 2 3 4 12 + 12 + 12 + 12 3 2 3 + + 12 12 12 1 2 3 2 12 + 12 + 12 + 12 1 1 1 1 1 1 1 1 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 2 2 3 2 12 + 12 + 12 + 12

3 6

Select all of the decomposed frac7

tions that have a sum of 10 . 2 2 2 2 10 + 10 + 10 + 10 1 1 1 1 1 1 1 10 + 10 + 10 + 10+ 10 + 10+ 10 1 2 1 2 1 10 + 10 + 10 + 10 + 10 1 2 3 10 + 10 + 10 2 4 3 4 10 + 10 + 10 + 10

149 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NF.3 (4.NF.2.3) DIRECTIONS: Use fraction models or equations to solve the following problems.

Catherine has a blue string that is 1 4 meters long and a green string that is 10 4 5 10 meters long. How much longer is the green string than the blue string?

A tree in a backyard is 11 10 feet tall. A nearby rosebush is 2 10 feet tall. How much taller is the tree than the rosebush?

DIRECTIONS: Solve the fractions and convert into a mixed number when possible.

3 4

8 5

3 6

−

3 4

2 5

2 6

−

2 4

10 5

1 6

150 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION Part I: A softball player threw 3 pitches. He threw the first pitch 2 second pitch 1

4 10

yards, and the third pitch 3

5 10

1 10

yards, the

yards. Use a fraction

model to illustrate each distance.

Part II: Which addition problem can be used to determine the total distance of all 3 pitches? What is the total distance?

151 I Copying is strictly prohibited

FOUR-STAR CHALLENGE - 4.NF.3 (4.NF.2.3) 1

Heather added the fractions below.

Taylor has a green rope that is 9…. 8

Which expression below shows a

inches long and an orange rope that is

way she might have grouped the

6 58 inches long. How much longer is

addends to find the sum?

the orange rope than the green rope?

5 8

6 8

1 8

12 8

1 8

8 8

11 8

1 + 8

7 8

4 + 8

7 8 inches

3 inches

3 8 inches

1 8

7 An apple tree in a backyard is 1... 10

feet tall. A nearby pear tree is 4…5

Trevor drove 10 6 miles from home 5 to the store. Then he drove 7 6 miles

feet tall. How much shorter is the

from the store to his mother’s house.

apple tree than the pear tree? Grid

How many miles did Trevor drive

your answer.

from his house to his mother’s house? Grid your answer.

Lynn bought 1 13 gallons of milk at 2 the market. She used 3 gallons of the milk to make a cake. Select all of the correct phrases below that tell how much milk was left.

Carl bought a pipe 4 8 feet long. He used 2 58feet of the pipe for his crafts project. Select all of the correct phrases below that tell how much pipe he had left.

She has 13 gallon of milk left.

She has 23 gallon of milk left.

He has 8 feet of pipe left. 6 He has 2 8 feet of pipe left.

She has 1 + 1 gallon of milk left.

He has 1 8 feet of pipe left.

She has 2 gallons of milk left.

He has 8 feet of pipe left. He has 1 38 feet of pipe left.

She has 3 + 3 gallon of milk left. 152 I Smart to the Core I Educational Bootcamp

DIRECTIONS: Shade in the circles of all addends were the sums are greater than 1.

1 2 3 + 3

5 4 7 + 7

2 1 + 5 5

2 2 + 3 3

3 1 4 + 4

1 5 8 + 8

4 8 10 + 10

1 7 12 + 12

The Cumberland family ordered 2 pizzas that were both cut in 8 slices each. 6 Mr. Cumberland ate 8 of the pizza, and Mrs. Cumberland ate 84 of the pizza. The 2 daughters shared the pizza that was left over equally.

Part I: How much pizza did Mr. Cumberland and Mrs. Cumberland eat in all? (Show your work)

Part II: How much of the pizza did the girls eat? (Show your work)

Part III: How much of the pizza did the girls and Mr. Cumberland eat in all? (Show your work)

153 I Copying is strictly prohibited

THINK TANK QUESTION 9

1 percent interest rate on his home. What will Miguel's 5 interest rate be if he lowers his rate by 4 percent? 5

Part I: Miguel has a 5

4 percent interest rate on her home. What will Lidia's 5 interest rate be if she lowers her rate 2 percent? 5

Part II: Lidia has a 4

Part III: How much greater is Miguel's new interest rate than Lidia’s new rate?

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MISSION 16: multiplying Fractions by a whole number Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/ b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Bootcamp STRATEGY 1: Use repeated addition to multiply a whole number by a fraction.

Example: 4 × 5 Step 1: Write the fraction as 4 multiples of

2 5

4×5 2 5

2 5

Step 2: Add the fractions to find the sum. 2 5

2 5

8 5

Bootcamp STRATEGY 2: Use fraction strips to model the multiplication of a whole number by a fraction.

Example: 4 × 5 2 Step 1: Create a fraction strip that represents 5 . 1 5

1 5

1 5 2

Step 2: Create 4 identical fraction strips to represent 4 × 5 . 1 5

1 5

1 5 2

Step 3: Use the fraction strips to add up the fractional parts. Therefore, 4 × 5 =

8 5

155 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NF.4 (4.NF.2.4) DIRECTIONS: Find the fraction as the product of a whole number and a unit fraction. 1

4 5

1 7

2 3

1 9

DIRECTIONS: Draw fraction strips to model the equations below and solve. 5

2×

3 4

3×

5 6

DIRECTIONS: Use the fraction models below to identify the whole number and fraction being multiplied. 8

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Target PRACTICE 1 1

Sarah’s family is painting the rooms in their home. They take 16 hour to paint 4 rooms. What number could go in the box to make the statement true? Grid your answer. 4 6

1 5, 1 5,

1 10 , 2 10 ,

1 15 , 3 15 ,

1 20 , 4 20 ,

1 2 3 4 5 5, 5, 5, 5, 5

1 2 3 4 5 2, 2, 2, 2, 2

Select all of the multiplication equations that represent the number line below.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

1 7 7 1× 3 1 7× 3 4 3× 3 3×

7 3 7 = 3 7 = 3 7 = 3 =

1 3 7 3 1 7 4 3

1 2 3 5 5 5

How many liters of water will it take to fill 5 containers?

7 3 7 ×1= 3 7 ×3= 3 7 ×3= 3 ×7=

5 liters

10 liters

25 liters

35 liters

A recipe calls for 2 cups of tomato sauce. If Julia needs to add 53 cup of herbs for each cup of tomato sauce and her measuring cup holds 51 cup, how many times must Julia measure 1 11cup of herbs to have enough for 5 the recipe? Grid your answer.

Select all of the multiplication equations that represent the number line below.

1 25 5 25

One liter of water fills 5 of a container. Liter(s) 1 2 3 4 5 6 7 Amount Filled

1 6

Sandi made a list of some multiples 1 of 5. Which of the following could be Sandi’s list? A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

1 ×9= 5 4 5× = 5 4 ×5= 5 3 6× = 5

9 5 9 5 9 5 9 5

9 9 1× = 5 5 1 9 ×5= 9 5 6 9 3× = 5 5 1 9 9× = 5 5 157 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NF.4 (4.NF.2.4) DIRECTIONS: Write the fraction as the product of a whole number and a unit fraction. 1

5 = 10

3 5

8 = 12

2 8

DIRECTIONS: Draw fraction strips to model the equations below. 5

3×

3 5

2×

5 6

DIRECTIONS: Use the fraction models below to identify the whole number and fraction being multiplied. 8

158 I Smart to the Core I Educational Bootcamp

Target PRACTICE 2 Susan divided 2 pizzas among her 3 friends equally. Each of her friends got 2 of a pizza. What number could 3 go on the box to make the equation true?

2 3

3 2

Select all of the multiplication equations that represent the model below.

1 4 1 4× 6 4 6× 6 4 4× 6 6×

6 4 4 = 6 16 = 6 16 = 6 =

4 6 6 6 4 6 1 4

16 6 24 ×4= 6 24 ×6= 6 6 ×6= 4

James eats 1 of a box of chocolate 3 every day.

Number of days

1 2 3 4 5 6 7

Number of 1 2 3 4 5 6 7 3 3 3 3 3 3 3 chocolate How many boxes of chocolates will he eat in 12 days? Grid your answer.

The price of 1 pen is $2 5 . What will be the total cost of 4 pens?

A 4

1 7

B 8

4 5

D 8

4 20

×4=

Dave goes jogging every morning. He runs on a circular track that is…1 2 mile long. How many times does Dave go around the track if he runs 3 miles? Grid your answer.

1 5

Select all of the multiplication equations that represent the model below.

3 ×2= 4 3 2× = 4 1 ×2= 3 3× 2 = 2

6 4 6 4 2 3 6 2

1 3 = 2 2 1 3 ×3= 2 2 1 2 2× = 3 3 2 6 ×3= 2 2 3×

159 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NF.4 (4.NF.2.4) DIRECTIONS: Use drawings or equations to solve the problems below.

3 Brandy takes tennis lessons 4 days per week for hour. How many hours does 4 Brandy practice each week? (Show your work)

4 Justin fills 5 glasses with water for his younger siblings. He pours pint in each 5 glass. How much water does Justin pour in all? (Show your work)

8 Pablo walks of a mile to school each day. How many miles will he walk in 5 days? 12 (Show your work)

1 Yasmine uses liter of ginger ale for each pitcher of punch. What is the total 2 amount of ginger ale Yasmine uses for 8 pitchers of punch? (Show your work)

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THINK TANK QUESTION A clothing website has 15 pages for women’s apparel. Dresses are displayed on 3 of the website pages. Ladies shoes take up 3 pages, and the remaining pages 5 are used for suits, blouses, and slacks.

PART I: How many pages of the website were used to display women's dresses? (Show your work)

PART II: What fraction of the pages of the website were used to display women's shoes? (Show your work)

PART III: How many pages were used to display women’s suits, blouses, and slacks? (Show your work)

161 I Copying is strictly prohibited

FOUR-STAR CHALLENGE - 4.NF.4 (4.NF.2.4) 1

Sarah has completed a book in 5 days. She read 1 pages of the book 8 each day. What number goes in the box to make the statement true? Grid your answer. 5 8

1 2 3 4 5 6, 6, 6, 6, 6

1 2 3 4 5 6 , 16 , 26 , 36 , 46

1 6, 1 6,

2 6, 1 12 ,

3 12 , 1 18 ,

4 24 , 1 24 ,

The price of 1 liter of milk is 1 dollar. 3

Price of milk

$1 $2 $3 $4 $5 $6 $7

1 2 3 4 5 6 7 3 3 3 3 3 3 3 How much does it cost for 6 liters of milk?

Liter(s)

1 8

Royce made a list of some multiples 1 of 6 . Which of the following could be Royce’s list?

C $18

D $24

To get a custom color, Dolly needed to add 5 blue paint to the mixture, 6 but her measuring cup only holds 1 11cup. How many times must Dolly 6 measure blue paint to have enough 5 for the 6 mixture? Grid your answer.

To make 1 loaf of bread, Jessica uses 9 4 cups of flour. If Jessica made 3 loaves, select all of the phrases that tell how much flour did she used in all.

5 30 1 30

Michelle uses 56 cups of sugar to make 1 chocolate cake. If Michelle made 5 chocolate cakes, select all of the phrases that tell how much sugar did she used in all. 10

Michelle used 6 cups of sugar. 5

Jessica used 3 cups of flour. 27

Michelle used 11 cups of sugar.

Jessica used 4 cups of flour.

Jessica used 12 4 cups of flour.

Michelle used 6 cups of sugar. 1

Michelle used 4 6 cups of sugar. 10

Michelle used 11 cups of sugar. 162 I Smart to the Core I Educational Bootcamp

Jessica used 7 cups of flour. 3

Jessica used 6 4 cups of flour.

Pearl has 12 school pictures. She gives 23 of the pictures to family members and the remaining pictures to friends. How many pictures did Pearl give away to family members? Use the circles below to create a fraction model that helps to solve this problem.

Vito runs on a treadmill for 34 of an hour 5 days per week. How many hours does Vito spend on the treadmill each week?

Part I: Use models to represent the problem.

Part II: Write a number sentence to represent the models in Part I.

163 I Copying is strictly prohibited

THINK TANK QUESTION 9

Jeffrey’s tutor demonstrated a variety of ways to solve the following word problem: 3

“ Ann Marie uses 4 of a cup of sugar to bake a cake. How much will she use to bake 4 cakes?”

Part I: Select all of the examples that may be used to solve the word problem. 3 4 Method

3 3 3 3 + + + 4 4 4 4

4

Method

Method 1 3 3 3 3    4 4 4 4

1 1 1 1 1 1 1 1 1 1 1 1 + + + + + + + + + + + 4 4 4 4 4 4 4 4 4 4 4 4

Method 4

Method 5

Part II: Which method would you use to solve the problem? (Explain why)

164 I Smart to the Core I Educational Bootcamp

MISSION 17: ADDING Fractions with denominators of 10 and 100 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Bootcamp STRATEGY 1: Use division to change a number with a denominator of 100 into an equivalent fraction with a denominator of 10. Example: 30/100 Step 1: Find the common factor of the numerator and the denominator, which is 10. Step 2: Divide the numerator and the denominator by 10. 3 30 10 ÷ = 100 10 10

Therefore,

3 30 = 100 10

Bootcamp STRATEGY 2: Use multiplication to change a number with a denominator of 10 into an equivalent fraction with a denominator of 100. Example: 3/10 = ?/100

Step 1: Identify the number that can be used to multiply the numerator and the denominator. In this case, 10 times 10 equals 100. 3 10 = 100

Step 2: Multiply the numerator and the denominator by 10. 3 10 3 30 = = × 10 10 10 100

Therefore, the equivalent fraction for

3 10

= 100 .

Bootcamp STRATEGY 3: Use a tens grid to model the fraction 30/100. Step 1: Use a hundreds grid to model the fraction 30/100.

Step 2: Use a tens grid to model the fraction 3/10. Therefore, we can see that the equivalent 3 30 . fraction for = 10

100

165 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NF.5 (4.NF.3.5) DIRECTIONS: Show the equivalent fraction. 1

2 10 = 100

4 10 = 100

70 = 10 100

1 10 = 100

8 10 = 100

90 = 10 100

5 10 = 100

DIRECTIONS: Determine the numerator for the missing part of the fraction and shade in the fraction model to match. 8

9 40 = 10 100

7 10 = 100

DIRECTIONS: Shade in the fraction model for each fraction and solve each expression. 10

70 100

1 10

100

40 100

5 10

DIRECTIONS: Use the fraction model to shade in both fractional parts and solve the expression. 12 25 100

5 10

166 I Smart to the Core I Educational Bootcamp

100

Target PRACTICE 1 1

12 On her bike, Sandi rode 100 mile from 7 her house to the library and 10 mile to the market. What was the total distance Sandi rode? Grid your answer.

A package of ground beef weighs 7 10 pound. A package of ground turkey 20 pound. How much do weighs 100 the beef and turkey weigh together?

45 There were 10 fiction and 100 nonfiction books returned to the library this morning. How many books were returned this morning? Grid your answer.

Mr. Alfreds bought 100 gallon of 2 chocolate ice cream and 10 gallon of vanilla ice cream. How much ice cream did he buy in all?

90 10

9 100

1 6

60 100

9 10

1 9

60 10

6 100

Select all of the fractions that are equivalent to the model below.

40 10

40 100

50 100

55 10

50 10 4 10

50 100 4 100

55 100 5 100

50 10 5 10 167 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NF.5 (4.NF.3.5) DIRECTIONS: Show the equivalent fraction. 1

40 100 = 10

7 10 = 100

20 = 10 100

30 100 = 10

6 10 = 100

10 = 10 100

9 10 = 100

DIRECTIONS: Determine the numerator for the missing part of the fraction and shade in the fraction model to match. 8

9 20 = 10 100

3 10 = 100

DIRECTIONS: Shade in the fraction model for each fraction and solve each expression. 10

35 100

2 10

100

50 100

4 10

DIRECTIONS: Use the fraction model to shade in both fractional parts and solve the expression. 12 61 100

3 10

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100

Target PRACTICE 2 1

15 In her car, Kate drove 100 mile from 8 her house to the mall and.… 10 mile to the theater. What was the total distance Kate drove? Grid your answer.

30 A package of cheese weighs 100 pound. A package of meat weighs

6 10 pound. How much do the cheese

There were 10 horror and 100 drama DVDs returned to the kiosk this morning. How many DVDs were returned this morning? Grid your answer.

3 Mr. Jones walked 10 of a mile and 40 runs 100 of a mile. How far of a distance did he go in all?

and meat weigh in all?

90 100

1 9

7 100

70 10

9 100

90 10

1 7

7 10

Select all of the addition sentences that are equal to the fraction 48 . 100

4 100 4 10 40 10 40 10

8 + 100 8 + 10 8 + 100 80 + 100

40 100 4 10 40 100 40 100

80 + 100 8 + 100 8 + 10 8 + 100

Select all of the addition sentences that are equal to the fraction 67 . 100

6 10 6 10 6 100 60 10

7 + 10 7 + 100 7 + 100 70 + 100

60 10 60 100 40 100 40 100

7 + 10 7 + 100 70 + 100 70 + 10

169 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NF.5 (4.NF.3.5) DIRECTIONS: Use drawings or equations to solve the problems below.

1 Frankie has 100 pages to read before his next book club meeting. He has already read 30 pages. Write the number of pages he has left to read in fraction form.

Veronica runs 10 miles each morning to train for an upcoming event. She takes a break after 6 miles. Write the number of miles she left the to run after her break in fraction form.

A class of 100 students are graduating from high school. There are 20 students graduating with honors. Write the number of students that are not graduating with honors in fraction form.

Wei swept part of the sidewalk that was 30 meter in distance. The next day, he 100 swept an additional 3 meter. How much of the sidewalk did Wei sweep in 2 10 days?

170 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION Karen and her twin sister, Katie, have a competition to determine who can paint the fastest. Each girl has a wall that is the exact same size and is given 20 minutes to paint. After 20 minutes have passed, Katie and Karen stop painting. Karen believes that she has painted more of her wall than Katie. Katie, on the other hand, believes that they have painted an equal amount. The results of the paint competition are shown below.

Karen’s Wall

Katie’s Wall

Which girl do you believe painted the greatest amount in 20 minutes? Explain your answer. (Use decimal values to defend your answer)

171 I Copying is strictly prohibited

FOUR-STAR CHALLENGE - 4.NF.3.5 (4.NF.3.5) 1

Tom mixed 10 quart of red paint with 21 quart of blue paint to make 100 purple paint. How much purple paint did Tom make? Grid your answer.

40 Daniel got a score of 100 on his practice test. He got a score of 9 10 on his exam. Which of the following was the difference in score between the practice test and the exam?

Tetra uses 10 pound of strawberries 35 pound of blueberries to and 100 make jam. How many pounds of berries does Tetra use to make jam? Grid your answer.

5 Rich did 10 of his homework on 40 Friday and 100 of his homework on Saturday. How much more homework does he have to do in order to be finished?

5 100

50 100

10 10

10 1

50 10

1 5

1 10

100 100

3 Dorothy poured cup of water in 10 the container. Then she added 4 100 cup more water to the container. Select all of the statements that tell how much water the container holds. There are There are There are There are There are

30 7 + 100 100 cup of water. 77 100 cup of water. 34 100 cup of water. 70 10 cups of water. 3 4 10 + 100 cup of water.

172 I Smart to the Core I Educational Bootcamp

5 Susan poured 10 cup of flour in a bowl. She then added 8 cup more 100 flour to the bowl. Select all of the statements below that tell how much flour is in the bowl. There are There are There are There are There are

58 cups of flour. 10 58 cup of flour. 100 1 + 3 cup of flour. 100 10 50 + 8 cups of flour. 100 100 13 cups of flour. 10

Select all of the expressions that have a sum equal to

64 100

4 6 + 10 100

31 2 13 + + 100 10 100

25 7 10 + + 100 10 100

60 4 + 100 10

24 20 2 + + 100 100 10

3 24 2 + + 10 100 10

Pablo and Marianne want to plot Point K which is the halfway point of the number line. They each want to represent the same information, but using different intervals. Pablo wants his number line to have 9 points and to begin 1 with Point . Marianne wants her number line to have 9 points, but to begin 10 with Point 10 . 100

Part I: Label Pablo’s number line based on the information given. 1 10

Part II: Label Marianne’s number line based on the information given. 10 100 Part III: Point K is the point that is located at the exact halfway point of Pablo and Marianne’s number line. Plot Point K on the number lines you drew in Part I and II. What fraction is represented by Point K on Pablo’s number line? What fraction is represented by Point K on Marianne’s number line? Pablo: __________

Marianne: __________

173 I Copying is strictly prohibited

THINK TANK QUESTION 9

The fraction model below shows the scores of students on a math quiz.

Student 1

Student 2

Student 3

Part I: Record 2 equivalent fraction values for each student’s score. Student 1—> Fraction Values

100

Student 2—> Fraction Values

100

Student 3—> Fraction Values

Student 4—> Fraction Values

= =

100

Part II: Which student earned the greatest score? Part III: Explain why you believe this student has the greatest score.

174 I Smart to the Core I Educational Bootcamp

Student 4

MISSION 18: Converting Decimals and fractions Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Bootcamp STRATEGY 1: Use a hundreds grid to convert a fraction to a decimal. Example:

/100 or 54 hundredths

Example: 0.62 or 62 hundredths

= 62/100

= 0.54

Bootcamp STRATEGY 2: Use a number line to identify fractions and convert to decimal values. Example:

/100 or 54 hundredths

Step 1: Draw a number line with intervals to show hundredths. Identify the targeted fraction on the number line. 10 100

0 100

20 100

40 100

30 100

54 100 50 100

60 100

80 100

70 100

100 100

90 100

Step 2: Identify the equivalent decimal value for each fraction. Identify the decimal value for the targeted fraction on the number line. 0 100

10 100

20 100

30 100

40 100

0.0

0.1

0.2

0.3

0.4

54 100 50 100

60 100

0.5 0.6 0.54

70 100

80 100

90 100

100 100

0.7

0.8

0.9

1.0

Bootcamp STRATEGY 2: Represent money as fraction of a dollar. Step 1: Count the amount of money and record the total. = $0.41 Step 2: Convert the total amount of money to a fraction of a dollar. Note: $1.00 = 100 cents $0.41 = 41/100 175 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NF.6 (4.NF.3.6) DIRECTIONS: Use the fraction grids to determine the fractional and decimal values. 2

1 Fraction =

Fraction =

Decimal =

DIRECTIONS: Use the number line to identify the decimal value for

71 . 100

DIRECTIONS: Use the number line to identify the decimal value for 38 . 100 4

DIRECTIONS: Use the coins to determine the fractional and decimal values. 5

Fraction :

Decimal :

176 I Smart to the Core I Educational Bootcamp

Target PRACTICE 1 1

Select all of the fractions and/or decimals that could be represented by the model below.

7.0 0.7 0.70

Select all of the fractions and/or decimals that could be represented by the model below.

74 100 74 10 0.704 5

Cora found these coins in her bag:

What is the total amount of money Cora found in her bag?

70 100 7 10 0.007 3

25 110

35 100

57 100

75 100

There are 100 cents in a dollar. What fraction of a dollar is 25 cents?

25 110

35 100

57 100

25 100

0.740 0.074 0.704 2

Cambia works 210 hours each day in 2 the garden. What is 210 hours written in decimal form?

Which of the following fractions would be equivalent to 0.8?

22.0 hours

2.02 hours

8 100

17 42

2.2 hours

0.22 hour

100 8

8 10

177 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.NF.6 (4.NF.3.6) DIRECTIONS: Use the fraction grids to determine the fractional and decimal values. 2

1 Fraction =

Fraction =

Decimal =

DIRECTIONS: Use the number line to identify the decimal value for

45 . 100

DIRECTIONS: Use the number line to identify the decimal value for

64 . 100

DIRECTIONS: Use the coins to determine the fractional and decimal values. 5

Fraction :

Decimal :

178 I Smart to the Core I Educational Bootcamp

Target PRACTICE 2 1

Harry went to a theater with his 4 friends. He purchased a movie ticket and a bucket of popcorn.

Select all of the statements that are true of the number line below.

$3.45

$34.5

$30.45

$0.345

4 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Point K represents the fraction 20 . 100 3 Point L represents the fraction . 100 4 Point M represents the fraction . 10 Point N represents the fraction 60 . 10 Point O represents the fraction 9 . 100 .3 5 Lisa bought 2 pizzas. She 1 10 ate of the pizza. What part of the pizza, written in decimal form, did she eat?

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Point A represents the fraction 1 . 100 20 Point B represents the fraction . 100 5 Point C represents the fraction . 10 Point D represents the fraction 70 . 100 Point E represents the fraction 8 . 100

Select all of the statements that are true about the number line below. K

45 cents

How much did he spend in all?

Which decimal below is equivalent 10 to the fraction ? 100

0.13

13.0

1.3

0.3

0.1

1.0

0.01

D 10.0

Which fraction below is equivalent to 0.5? A B

C A

5 100 50 100 50 10 500 100

179 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NF.6 (4.NF.3.6) DIRECTIONS: Complete the word problems below. 1

Norris has 1 quarter, 2 dimes, 3 nickels, and 10 pennies. What will the fraction for sum of the coins be in terms of 1 dollar? Express the fraction in decimal form.

Nancy purchased a piece of fabric that was 0.78 of a yard long. What fraction of fabric did Nancy buy?

65 of a dollar. Express the fraction in decimal form. If she only has 4 coins, 3 Kate has 100 what coins does she possibly have?

180 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION There were 7 kids that participated in a treasure hunt to find 100 golden wrapped chocolates. The results of the treasure hunt is listed below. Marshall collected:

20 100

Jeri collected: 0.2

Shayna collected:

John collected:

Randi collected: 6

Christy collected:

0.09

Paola collected:

1 10

10 100

1 4

Part I: Who found the greatest amount of golden wrapped chocolates?

Part II: Which kids found an equal number of golden wrapped chocolates.

Part III: How many chocolates did Randi, Shayna, and John collect in all? Randi: __________

Shayna: __________ John: __________

181 I Copying is strictly prohibited

FOUR-STAR CHALLENGE - 4.NF.6 (4.NF.3.6) 1

Which decimal below is equivalent to the fraction 60 ? 100

0.06

0.6

6.0

60.0

Veronica got some coins from her brother.

How much money did Veronica get as a fraction in terms of a dollar? 75 49 C A 110 100 B

A box contains 100 crayons. Of the crayons, 24 are red crayons. Select all of the statements that are true. 0.024 of the crayons are red. 0.24 of the crayons are red. 0.204 of the crayons are red. 24 of the crayons are red. 10 24 100 of the crayons are red. 24 1,000 of the crayons are red. 2 Dane jogged 5 10 miles this morning.

What is the distance written as a decimal? A

5.2 miles

52.0 miles

0.52 miles

5.02 mile

182 I Smart to the Core I Educational Bootcamp

50 100

25 100

A case of water contains 100 bottles. What fraction of a case is 48 bottles?

48 100

50 100

48 110

75 100

A bag contains 10 marbles. Of all the marbles, 9 are blue. Select all of the statements that are true. 9 100 of the marbles are blue. 90 10 of the marbles are blue. 9 of the marbles are blue. 1,000 1 of the marbles are not blue. 10 0.009 of the marbles are blue. 0.90 of the marbles are blue.

Part I: Create 2 fractions that are equivalent to 0.3.

100

Part II: Explain how you know that the 2 fractions are equivalent.

Part I: Identify the fraction and the decimal value for both of the models listed below.

Decimal = ___________ Fraction =

100 Part II: Compare the decimal values for the models above.

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THINK TANK QUESTION 9

Part I: Use the number line below to plot the following points: Point A =

4 10

Point B =

30 100

Point C =

0.75

Point D =

7 10

Part II: Explain how you determined where to place each point.

184 I Smart to the Core I Educational Bootcamp

MISSION 19:Comparing Decimals and fractions to The Hundredths Place Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Bootcamp STRATEGY 1: Use grids to compare 2 decimals. Example: Compare 0.54 to 0.5.

54 of 100 parts are shaded

50 of 100 parts are shaded

NOTE: 54 is greater than 50. Therefore, we add a greater (>) than symbol above.

Bootcamp STRATEGY 2: Use a place value chart to compare 2 decimals. Example: Compare 0.54 to 0.5. Ones

Tenths

Hundredths

Step 1: Compare the digits under the greatest place value (“Ones”). If they are the same, continue comparing the numbers in order of decreasing place value (“Tenths”, “Hundredths”, etc.). Step 2: When the place value is different, determine which number is the greatest. The largest digit will indicate that this is the number with the greatest value. NOTE: 4 is greater than 0 in the hundredths place and therefore, 0.54 is greater than 0.5.

Bootcamp STRATEGY 3: Use a number line to compare 2 decimals. Example: Compare 0.54 to 0.5. 0.50

0.51

0.52

0.53

0.54

0.55

0.56

NOTE: 0.54 is to the right of 0.5 (0.50). Therefore, 0.54 is greater. 185 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 1 4.NF.7 (4.NF.3.7) DIRECTIONS: Use the grids below to compare the decimals.

0.36

0.3

0.19

0.91

DIRECTIONS: Use the place value tables below to compare the decimals.

0.71

Ones

0.7

Tenths

0.87

Hundredths

Ones

0.77

Tenths

Hundredths

DIRECTIONS: Use the number line below to compare the decimals and write the decimals each letter represents. 5

11.1

8.5

S 8

T 9

DECIMAL:

186 I Smart to the Core I Educational Bootcamp

12.7

9.7

U 10

V 12

Target PRACTICE 1 1

Jessica needs to write a two-digit decimal that is between 0.1 and 0.15. What is one decimal she can write? Grid your answer.

Leon needs to write a two-digit decimal that is between 0.2 and 0.3. What is one decimal he can write? Grid your answer.

Select all of the decimal comparisons that are true.

0.07 > 0.70

0.17 < 0.71

1.14 < 1.04

5.43 > 3.45

0.96 > 0.69

0.67 < 0.76

2.34 < 2.43

3.50 > 3.05

0.13 > 0.14

0.12 < 0.21

3.61 < 3.16

1.87 > 1.78

0.34 > 0.23

0.59 < 0.39

4.87 < 8.47

2.96 > 2.69

0.55 > 0.45

0.23 < 0.20

6.66 < 6.96

4.15 > 5.14

Andrew made a mosaic design. He used 0.6 inch blue tiles and 0.59 inch green tiles. Which of the following statements is true?

Jami uses 0.06 pound of strawberries and 0.6 pound of blueberries to make jelly. Which statement below is true?

0.59 > 0.6

0.6 > 0.06

0.59 = 0.6

0.6 = 0.06

0.6 < 0.59

0.6 < 0.06

0.6 > 0.59

0.06 > 0.6

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TRAIN THE BRAIN PRACTICE 2 4.NF.7 (4.NF.3.7) DIRECTIONS: Use the grids below to compare the decimals.

0.75

0.7

0.24

0.42

DIRECTIONS: Use the place value tables below to compare the decimals.

0.07

Ones

0.7

Tenths

0.65

Hundredths

Ones

0.6

Tenths

Hundredths

DIRECTIONS: Use the number line below to compare the decimals and write the decimals each letter represents. 5

23.5

22.3

E 22

F 23

DECIMAL:

188 I Smart to the Core I Educational Bootcamp

24.8

26.4

.G 24

H 25

Target PRACTICE 2 What is a one or two-digit decimal greater than 0.29 that will make the comparison statement below true? Grid your answer.

What is a one or two-digit decimal greater than 1.0 that will make the comparison statement below true? Grid your answer.

0.5 > ?

Select all of the statements about the number line below that are true.

3 E

1.09 > ?

Select all of the statements about the number line below that are true.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Point E is greater than Point F.

Point U is less than Point V.

Point F is less than Point H.

Point S is greater than Point T.

Point H is greater than Point G.

Point T is greater than Point S.

Point G is less than Point I.

Point V is greater than Point W.

Point I is greater than Point E.

Point W is less than Point U.

Lupe has 0.9 yards of fabric and Dole has 0.7 yards to make a tablecloth. Which of the following statements is true? A

0.7 > 0.9

0.9 = 0.7

0.9 < 0.7

0.9 > 0.7

Kitty’s classroom has 2 tables of differing lengths. There is 1 table that has a length of 0.89 feet and the other has a length of 0.98 feet. Which statement below is true? A 0.98 > 0.89 B

0.89 = 0.98

0.98 < 0.89

0.89 > 0.98 189 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 3 4.NF.7 (4.NF.3.7) DIRECTIONS: Use the number lines to solve the problems below. 1

Mr. Davids drew the number line below on the board. A 1

1.5

2.5

3.5

4.5

5.5

What decimal could name the location of point A?

Luis sprinted more than 13 2 meters at a marathon. He plotted point J on the number line below to show how many meters he sprinted.

J 13

What decimal shows how far Luis sprinted?

Mrs. Perez drew the number line below on the board. H 6

6.25

6.5

6.75

7.25

7.5

7.75

What decimal could name the location of point H?

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THINK TANK QUESTION PART I: There are 3 pies that were split between 4 friends. Mike ate 0.75 of 1 pie, Gayle ate 0.5 of another, and Chris ate 0.25 of the last pie. How much pie was left for Paul in fraction form? Use the circles below to model the problem.

Paul = PART II: Write your answer as a decimal. Explain how you got your answer.

191 I Copying is strictly prohibited

Four-STAR CHALLENGE - 4.NF.7 (4.NF.3.7) 1

What is a two-digit decimal less than 1.0 that will make the comparison statement below true? Grid your answer.

What is a one or two-digit decimal less than 3.6 that will make the comparison statement below true? Grid your answer.

0.91 < ?

Select all of the sets of numbers that correctly compare the numbers below. 0.32

3.49 < ?

0.43

0.23

0.34

Select all of the sets of numbers that correctly compare the numbers below. 2.67

2.56

2.76

2.45

0.32 > 0.34 > 0.23 > 0.43

2.67 < 2.56 < 2.76 < 2.45

0.23 < 0.34 < 0.32 < 0.43

2.76 > 2.67 > 2.56 > 2.45

0.23 < 0.32 < 0.34 < 0.43

2.45 > 2.56 > 2.67 > 2.76

0.23 < 0.32 < 0.43 < 0.34

2.76 > 2.56 > 2.67 > 2.45

0.43 > 0.34 > 0.32 > 0.23

2.45 < 2.56 < 2.67 < 2.76

Lourdes has 0.7 yards of cloth and Maylin has 0.5 yards of cloth to make a costume. Which of the following statements is true? A

0.5 > 0.7

0.5 = 0.70

C D

Ann’s bedroom has 2 bookshelves of different lengths. There is 1 that has a length of 0.99 feet and the other has a length of 0.90 feet. Which of the following statements is true? A 0.90 > 0.99 B

0.99 = 0.90

0.5 < 0.7

0.90 < 0.99

0.7 > 0.70

0.90 > 0.90

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Use the number line below to help compare (>, <, or =) the following numbers:

31.7

31.07

Part I: Use the hundreds grids below to compare (>, <, or =) 0.8 to 0.88.

0.8

0.88

Part II: Explain how you got your answer.

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THINK TANK QUESTION 9

Jennifer ran 2.5 miles on Monday, 2.25 miles on Tuesday, and forgot to record the distance she ran on Wednesday. Part I: .On Wednesday, Jennifer ran a greater distance than she ran on Tuesday, but less than she ran on Monday. Find 3 difference possibilities for the number of miles that Jennifer may have run on Wednesday. miles Possibility # 1

miles Possibility # 2

miles Possibility # 3

Part II: Place the numbers you created on the number line below.

2.25

2.5

Part III: Explain how you determined where to place each value on the number line.

194 I Smart to the Core I Educational Bootcamp

MISSION 20: Using customary and metric measureKnow relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Bootcamp STRATEGY 1: Use the knowledge of the conversion units of measurements to express a larger unit in terms of a smaller unit. Weight

Time

1 lb. = 16 oz 1 ton = 2,000 lb

Length

Mass

1 ft = 12 in. 1 minute = 60 seconds 1 yd = 3 ft 1 hour = 60 minutes 1 mile = 5,280 ft 1 day = 24 hours 1 week = 7 days 1 meter (m) = 1,000 mm 1 month = 28 to 31 days 1 meter = 100 cm 1 month = 4 weeks 1 meter = 10 dm 1 year = 12 months 1 cm = 10 mm 1 year = 52 weeks 1 dm = 10 cm 1 year = 365 days 1 km = 1,000 m

Examples: Convert Years to Months

Capacity 1 L = 1,000 mL

1 g = 1,000 mg 1 kg = 1,000 g

Examples: Convert Tons to Pounds

TABLE 1 Multiply each year YEARS 1 × 2 × 3 × 4 ×

1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts

TABLE 2

MONTHS

Multiply each ton × 2,000 × 2,000 × 2,000 × 2,000

12 24 36 48

TONS

POUNDS

1 2 3 4

2,000 4,000 6,000 8,000

Bootcamp STRATEGY 2: Use your knowledge of conversion units to build a conversion equation. 20 years =

Example:

20 years 1

months

12 months

1 year

20 × 12 months 1×1

= 240 months

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TRAIN THE BRAIN PRACTICE 1 4.MD.1 (4.MD.1.1) DIRECTIONS: Solve for the equivalent of each of the following measurements.

Weight

1 lb. = 16 oz 1 ton = 2,000 lb

Time

Length

Mass

Capacity 1 L = 1,000 mL

1 g = 1,000 mg 1 kg = 1,000 g

1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts

1 100 centimeters = ______ meters

5 meters = ______ centimeters

2 2 tons = ______ pounds

2 miles = ______ feet

3 3 kilometers = ______ meters

3 feet = ______ inches

196 I Smart to the Core I Educational Bootcamp

Target PRACTICE 1 1

Coach Shaw has a bag of softballs that weigh 3 pounds. How many ounces does the bag of softballs weigh? Grid your answer.

Which of the following units is most likely to be used when measuring the weight of a basket of apples?

1 lb = 16 oz 3

Andy’s driveway is 300 centimeters long, and his garage is 8 meters long. How long are Andy’s driveway and garage together in meters? Grid your answer.

1 m = 100 cm 5

A piece of wood is 21 feet long. Select all of the statements that are true.

grams

kilograms

meters

milliliters

Which of the following shows the weight of a 5 pound fish in ounces?

16 ounces

80 ounces

32 ounces

160 ounces

1 lb = 16 oz 6

The curtain is 300 centimeters long. Select all of the statements that are true.

The piece of wood is 8 yards long.

It is 3 meters long.

The piece of wood is 142 inches long.

It is 30 meters long.

The piece of wood is 7 yards long.

It is 0.3 meters long.

The piece of wood is 154 inches long.

It is 300,000 millimeters long.

The piece of wood is 6 yards long.

It is 30,000 millimeters long.

The piece of wood is 252 inches long.

It is 3,000 millimeters long.

1 yd = 3 ft 1 ft = 12 in.

1 m = 100 cm 1 cm = 10 mm

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TRAIN THE BRAIN PRACTICE 2 4.MD.1 (4.MD.1.1) DIRECTIONS: Solve for the equivalent of each of the following measurements.

Weight

1 lb. = 16 oz 1 ton = 2,000 lb

Time

Length

Mass

Capacity 1 L = 1,000 mL

1 g = 1,000 mg 1 kg = 1,000 g

1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts

1 10 yards = ______ inches

4 6 pints = ______ quarts

2 3 hours = ______ minutes

5 3 kilograms = ______ grams

3 6 miles = ______ feet

6 7 kilometers = ______ meters

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Target PRACTICE 2 1

Leanne received a package that weighed 160 ounces. How many pounds did the package weigh? Grid your answer.

1 lb = 16 oz 3

Zoe has 400 centimeters of red thread and 6 meters of yellow thread. How much thread does Zoe have in all? Grid your answer.

Which of the following units of measurement is most likely to be used when measuring the height of a building? A

meters

centimeters

inches

millimeters

Jeff wants to measure the mass of a large bag of dog food. What is the best unit of measurement for him to use? A

grams

kilograms

liters

milliliters

1 m = 100 cm 5

A crate weighs 4,000 pounds. Select all of the statements that are true.

A box weighs 6,000 grams. Select all of the statements that are true.

The crate weighs 4 tons.

The box weighs 6 kilograms.

The crate weighs 64,000 ounces.

The box weighs 600,000 milligrams.

The crate weighs 2 tons.

The box weighs 60,000 milligrams.

The crate weighs 6,400 ounces.

The box weighs 6,000,000 milligrams.

The crate weighs 640 ounces.

The box weighs 0.6 kilograms.

The crate weighs 40 tons.

The box weighs 60 kilograms.

1 ton = 2,000 lb 1 lb = 16 oz

1 kg = 1,000 g 1 g = 1,000 mg

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TRAIN THE BRAIN PRACTICE 3 4.MD.1 (4.MD.1.1) DIRECTIONS: Solve the following word problems. 1 A flagpole is 25 feet high. How tall is the flagpole in inches?

1 ft = 12 in.

2 A book weighs 12 pounds. How heavy is the book in ounces?

1 lb = 16 oz

3 Mark studied for 2 hours and 20 minutes. How many seconds did Mark study? 1 hr = 60 min 1 min = 60 sec

4 A man is 72 inches tall. How tall is the man in feet?

1 ft = 12 in.

5 A box weighs 3 kilograms. How heavy is the box in grams?

1 kg = 1,000 g

6 A bus traveled for 4 hours. How many minutes did the bus travel?

1 hr = 60 min

200 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION Dr. Henderson delivered 3 babies in 1 hour. The 1st-baby born was 7 pounds 12 ounces, the 2nd-baby weighed 116 ounces, and the 3rd-baby was 8 pounds 3 ounces.

1st-baby

2nd-baby

7 pounds 12 ounces

116 ounces

3rd-baby

8 pounds 3 ounces

Place the babies (1st-baby, 2nd-baby, 3rd-baby) in order from least to greatest weight. (Show your work) 1 lb = 16 oz

Least to greatest

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FOUR-STAR CHALLENGE - 4.MD.1 (4.MD.1.1) 1

Mr. Kilgore has a box of wooden toy planes that weighs 672 ounces. How many pounds does the box of planes weigh? Grid your answer.

Which of the following units is most likely used when measuring the weight of a turkey?

1 lb = 16 oz 3

Which of the following shows the height of a 240-inch ladder in feet? Grid your answer.

tons

pounds

ounces

milligrams

Mrs. Larson wants to measure the volume of a soda bottle. What is the best unit of measurement for her to use? A

grams

kilograms

liters

milliliters

1 ft = 12 in. 5

Select all of the values that will complete the table correctly.

Pounds

Feet

Ounces

112

160

Inches

A=2

A=3

M=2

M=4

B=7

B=8

N=6

N=7

C = 80

C = 64

O = 60

O = 72

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Rainforests are where some of the tallest trees are found. Below is a table of some trees found in the rain forest. Complete the chart to show the length of each tree in feet. 1 yd = 3 ft Tree

Yards

Feet

Brazil Nut Tree Kapok Tree Samauma Tree Redwood Tree

44 38 51 125

132 114 153 375

Describe the relationship between the trees’ length in yards and their length in feet.

A team of carpenters measured the height of a building to be renovated. The height of the east side of the building is 500 feet. The height on the west side is 210 yards. Which side of the building has the greater height? Explain your answer. 1 yd = 3 ft

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THINK TANK QUESTION 9

Part I: A doctor’s office provides water to patients in the waiting room. The water dispenser can hold 5 gallons. Normally, the water bottle is replaced with a new bottle every three days. This week, the water bottle is empty at the end of the first day. The office staff decides to refill the bottle using 16-ounce water bottles. 1 g = 4 qt 1 qt = 2 pt 1 pt = 2 c 1 c = 8 oz How many 16-ounce water bottles will it take to fill the water dispenser? ________ (Show your work)

Part II: A staff member wants to order the exact number of plastic cups necessary to fill a 10-gallon water dispenser. If the dispenser is completely filled and each plastic cup is completely filled with exactly 1 cup of water, how many plastic cups does the staff member need to order? (Show your work) 1 g = 4 qt 1 qt = 2 pt 1 pt = 2 c 1 c = 8 oz

204 I Smart to the Core I Educational Bootcamp

MISSION 21: Solving Problems involving Measurement Use the four operations to solve word problems involving distances, intervals of time, and money, including problems involving simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models.

Bootcamp STRATEGY 1: Use the clock to count the amount of time elapsed. IDENTIFYING THE STARTING TIME Example: It took 35 minutes for Carlton to cut the grass. He finished cutting the grass at 2:10. At what time did Carlton start cutting the grass? Step 1: Identify 2:10 on the clock. Step 2: Count backwards in 5 minute intervals up to 35 minutes.

15 20

Step 3: Identify the starting time. Remember to subtract 1 hour when passing the 12. STARTING TIME: 1:35

30 35

IDENTIFYING THE FINISHING TIME Example: It took 35 minutes for Carlton to cut the grass. He started cutting the grass at 2:10. At what time did Carlton finish cutting the grass? Step 1: Identify 2:10 on the clock.

5 min

Step 2: Count forward in 5 minute intervals up to 35 minutes.

Step 3: Identify the finishing time. FINISHING TIME: 2:45

15 20 min

Bootcamp Strategy 2: Use an elapsed timeline to find the elapsed time. Example: Start time: 8:45 End time: 11:30

Elapsed Time: 2 hours and

Step 1: Draw a linear model.

1 hr + 1 hr + 15 min + 15 min + 15 min

Step 2: Start the intervals in hour increments just before your end time. Step 3: Continue the time line in 15 minute intervals just before your end time.

9:45 10:45 11:00 11:15 11:30

8:45

Step 4: Determine the number of hours and minutes passed.

Bootcamp STRATEGY 3: Use a number line to represent fractional quantities of distance and time. Example: Rick ran 4

1 1 miles on Saturday and 3 on Sunday. How many miles did Rick run on both days? 4 2

Step 1: Identify 4 4 on the number line. Step 2: Count forward by 4

1 4

. 3.Count forward by an additional 2

3 7 4

1 2

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TRAIN THE BRAIN PRACTICE 1 4.MD.2 (4.MD.1.2) DIRECTIONS: Use the number line to help solve the following problems. 1

1 1 2 4 +3 2 =

3 1 4 4 ‒1 2 =

$4.25

$1.50 =

DIRECTIONS: Record the new time on each clock after 1 hour and 30 minutes have passed. 5

DIRECTIONS: Record the new time on each clock 2 hours and 45 minutes before the time shown. 9

: 206 I Smart to the Core I Educational Bootcamp

Target PRACTICE 1 1

What time will it be 45 minutes after the time listed on the clock?

1:30

2:30

2:15

1:15

Jamie delivered newspapers for 416 weeks. What is the best estimate for the number of years Jamie delivered newspapers? Grid your answer.

There are 2 pipes connected end-toend. The first pipe is 4 feet long, while the second pipe is 24 inches long. Select all of the statements that tell how long the pipes are together. 1 foot = 12 inches

3 hours and 5 minutes

3 hours and 15 minutes

3 hours and 30 minutes

4 hours and 15 minutes

At an ice cream parlor, 1 serving of ice cream costs $6, and each dessert topping costs $2. How much does a customer pay for 1 serving of ice cream and 4 toppings in dollars? Grid your answer.

There are 2 ribbons connected end-to -end. The red ribbon is 108 inches long, while the yellow ribbon is 5 feet long. Select all of the statements that tell how long the ribbons are together.

1 year = 52 weeks

Damien started cutting the grass at 8:30 AM. He finished at 11:45 AM. How long did it take Damien to cut the grass?

1 foot = 12 inches

The 2 pipes are 65 inches long.

The 2 ribbons are 100 inches long.

The 2 pipes are 72 inches long.

The 2 ribbons are 10 feet long.

The 2 pipes are 6 feet long.

The 2 ribbons are 168 inches long.

The 2 pipes are 5 feet long.

The 2 ribbons are 8 feet long.

The 2 pipes are 70 inches long.

The 2 ribbons are 14 feet long.

The 2 pipes are 7 feet long.

The 2 ribbons are 95 inches long.

207 I Copying is strictly prohibited

TRAIN THE BRAIN PRACTICE 2 4.MD.2 (4.MD.1.2) DIRECTIONS: Use the number line to help solve the problems below. 1

3 1 3 4 + 3 2

1 1 5 4 ‒2 4 =

$5.75

$1.25 =

DIRECTIONS: Record the new time on each clock after 2:45 minutes have passed. 5

DIRECTIONS: Record the new time on each clock 1:15 minutes before the time shown. 9

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Target PRACTICE 2 1

Kevin wants to split a $66.00 tip between the 3 waiters that served his party. How much will each of the 3 waiters get in dollars? Grid your answer.

Pizza is delivered at the time shown on the watch below. The pizza took 1 hour and 10 minutes to arrive. What time was the order placed? A

7:00

7:10

9:20

9:30

There are 2 boxes that weigh 10 pounds together. The first box weighs 64 ounces. Select all of the statements that could be true of the second box. 1 lb = 16 ounces

What time will be shown on the watch below in 3 hours and 55 minutes?

8:00

9:15

8:55

9:25

Candice paid a fee of $50 to become a pass holder for an amusement park so that each time she visited the park, she was only charged $15. Candice visited the park 5 times. How much did she pay in all including the membership fee in dollars? Grid your answer.

There are 2 baskets that weigh 112 ounces together. The first basket weighs 2 pounds. Select all of the statements that could be true of the second basket. 1 lb = 16 ounces

The second box weighs 86 ounces.

The second basket weighs 5 pounds.

The second box weighs 6 pounds.

The second basket weighs 4 pounds.

The second box weighs 106 ounces. The second box weighs 96 ounces.

The second basket weighs 3 pounds. The second basket weighs 76 ounces.

The second box weighs 16 pounds.

The second basket weighs 80 ounces.

The second box weighs 4 pounds.

The second basket weighs 92 ounces.

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TRAIN THE BRAIN PRACTICE 3 4.MD.2 (4.MD.1.2) DIRECTIONS: Use drawings or equations to solve the problems below.

1 Brian saw a movie that lasted 1 hour and 45 minutes. How many seconds long was the movie? 1 hr = 60 min 1 min = 60 sec

2 A train traveled for 6 hours. How long, in minutes, did the train travel? 1 hr = 60 min

1 3 Andy’s driveway is 367 2 centimeters long, and his garage is 8 meters long. How long are Andy’s driveway and garage together? 1 m = 100 cm

2 4 Leanne has 305 10 centimeters of red thread and 6 meters of yellow thread. How much thread does Leanne have in all? 1 m = 100 cm

5 Uma has $5.85 and Tahir has $4.87. The girls put their money together to buy a set of beach balls. The beach balls cost $14.15. How much more money do Uma and Tahir need in order to buy the beach balls?

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THINK TANK QUESTION Thorpe and his friends measured the distance earthworms traveled before burying themselves in the ground. The chart below shows the distance traveled by 3 earthworms. Earth Worm

Worm 1

Distance Traveled

1 2

feet

Worm 2

Worm 3

48 inches

1 yard and 8 feet

1 yd = 3 ft 1 ft = 12 in. Place the 3 earth worms in order from the greatest to the least distance traveled.

(Show your work)

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Four-STAR CHALLENGE - 4.MD.2 (4.MD.1.2) 1

Deidra had a piece of string that was 6 yards and 3 feet long. How long is the ribbon in feet? Grid your answer.

Emma ate 2 of the chocolate bar. Dave ate 1 of the same chocolate 4 bar. What decimal is equivalent to the amount of the chocolate bar that is left? Grid your answer.

At a bakery, a large loaf of bread costs $20, and each sandwich spread costs $8. Which of the following represents the total cost of a loaf of bread and 2 sandwich spreads?

1 yard = 3 feet

Julie’s dance rehearsal lasted for 1 hour and 30 minutes. The rehearsal ended at the time shown on the clock below. What time did the rehearsal begin?

3:15

5:15

3:45

6:45

Josephine worked for 3.5 hours on her school project. Select all of the statements that are true.

$36.00

$28.00

$48.00

$56.00

It takes Vivian 120 minutes to commute to work. Select all of the statements that are true.

1 hr = 60 min

1 hr = 60 min 1 min = 60 sec

She worked 3 hours and 60 minutes.

She commutes 1 hour.

She worked 3 hours and 30 minutes.

She commutes 2 hours.

She worked 3 hours and 50 minutes.

She commutes 3 hours.

She worked 180 minutes.

She commutes 3,600 seconds.

She worked 210 minutes.

She commutes 7,200 seconds.

She worked 240 minutes.

She commutes 10,800 seconds.

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Kincaid rides his bike 50 kilometers each morning. His friend, Bruce, rides his bike 45,000 meters. The men try to decide which of the 2 of them ride the furthest each morning. 1 km = 1,000 m

Part I: Help Kincaid and Bruce determine who rides the furthest. (Show your work)

Part II: How much further does one of the men ride than the other in kilometers? (Show your work)

Mr. Henderson is planning to have a fireworks show for his son’s 16th birthday. He purchases 2 of each of the firework packages listed in the table below. He also uses a coupon that gives him a 15¢ discount off of every item. The table below was set up to show the total that Mr. Henderson would need to spend on fireworks. Part I: Complete the table to determine Mr. Henderson’s total. Fireworks

Cost

Cherry Bombs

$7.69

Fire Crackers

$8.51

Sky Rockets

$7.09

Sparklers

$4.00

Cost with discount

Cost for 2

Part II: Mr. Henderson has $50.00. Does he have enough money? If so, how much change will he receive? If not, how much more money does he need?

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THINK TANK QUESTION 9

The scores of the top competitors in the Family Fun Day races were posted for each event. The competitors were awarded medals based on the posted scores. Use the table of scores to assign medals for each category as listed below. COMPETITOR Cat Run

Competitor 1 420 seconds

Competitor 2

Competitor 3

7 min 3 sec

8 minutes

Mad Relay

1 hour 6 min

63 min

70 min

Distance Hike

4 hours 6 min

4 hours

245 min

1 hr = 60 min 1 min = 60 sec

CAT RUN (least to greatest times) 1st Place (GOLD MEDAL)

2nd Place (SILVER MEDAL)

3rd Place (BRONZE MEDAL)

MAD RELAY RACE (least to greatest times) 1st Place (GOLD MEDAL)

2nd Place (SILVER MEDAL)

3rd Place (BRONZE MEDAL)

DISTANCE HIKE (least to greatest times) 1st Place (GOLD MEDAL)

2nd Place (SILVER MEDAL)

214 I Smart to the Core I Educational Bootcamp

3rd Place (BRONZE MEDAL)

MISSION 22: CALCULATING Area and perimeter Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Bootcamp STRATEGY 1: Find the perimeter of a rectangle by counting the outer boundary of a two-dimensional figure. Perimeter is defined as the total distance around the edge of the figure. To calculate the perimeter: Step 1: Mark the side of each unit as the figure is counted.

Perimeter = 6 + 3 + 6 + 3 = 18 6

Step 2: Add the length of each side to find the perimeter of the rectangle.

3 6

Bootcamp STRATEGY 2: Find the area of a rectangle by counting the units inside the figure. Area is defined as the inside space measured in square units.

To calculate the area: Step 1: Dot the middle of each individual unit as the inside space of the figure.

Area = 18 dots = 18 square units

Step 2: Add the number of dots in the figure to find the area of the rectangle.

Bootcamp STRATEGY 3: Find the area of a rectangle by multiplying the length of the rectangle by its width. The Area of a rectangle is calculated by using the formula length × width. To calculate the area: Step 1: Mark each unit as the length of the rectangle is counted. Step 1: Mark each unit as the width of the rectangle is counted. Step 3: Multiply the length by the width to find the area of the rectangle. Area = length × width = 6 units × 3 units = 18 square units 6 3

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TRAIN THE BRAIN PRACTICE 1 4.MD.3 (4.MD.1.3) DIRECTIONS: Calculate the area and perimeter for each of the shapes below. (Show your work) Area =

Perimeter =

Area =

Perimeter =

4 4 ft 25 m 14 ft

Area =

Perimeter =

Area = Perimeter = 20 ft

20 ft 12 ft 10 ft 216 I Smart to the Core I Educational Bootcamp

Area =

Perimeter =

Target PRACTICE 1 The width of a front porch is 5 feet. The length is twice as long as its width. What is the perimeter of the porch in feet? Grid your answer.

Eduardo has a canvas that is 8 by 30 inches. He colored a rectangle in the middle of the canvas that is 7 inches by 5 inches. What is the area of the canvas that is not covered with the rectangle in inches squared? Grid your answer.

Denise is making a sign in the shape of a square. The perimeter of the sign is 280 inches. What is the area of the sign?

5 feet

Matt traced the following image on grid paper:

Which of the following is true?

area = 11 square units

area = 22 square units

280 in2.

2 . 4,900 in.

area = 27 square units

2 . 1,120 in.

78,400. in.2

area = 30 square units Select all of the statements that are true of a rectangle.

Select all of the statements that are true of a rectangle.

If l = 10 and w = 10, perimeter is 40

If l = 11 and w = 23, perimeter is 68

If l = 12 and w = 11, perimeter is 132

If l = 4 and w = 7, perimeter is 22

If l = 15 and w = 22, perimeter is 74

If l = 15 and w = 5, perimeter is 75

If l = 30 and w = 3, perimeter is 90

If l = 25 and w = 15, perimeter is 80

If l = 55 and w = 33, perimeter is 176

If l = 38 and w = 29, perimeter is 134

If l = 14 and w = 41, perimeter is 110

If l = 12 and w = 3, perimeter is 30

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TRAIN THE BRAIN PRACTICE 2 4.MD.3 (4.MD.1.3) DIRECTIONS: Calculate the area and perimeter for each of the shapes below. (Show your work) Area =

Perimeter =

Area =

Perimeter =

4 5 ft 20 m 18 ft

Area =

Perimeter =

Area = Perimeter =

8 cm

12 cm 20 cm

18 cm

Area = 218 I Smart to the Core I Educational Bootcamp

Perimeter =

Target PRACTICE 2 1

Jane’s room has an area of 375 feet2. The length of her room is 25 feet. What is the perimeter of the room? A 100 feet B

225 feet

80 feet

625 feet

Tom needs to determine if his rectangular frame will fit on the free space of his wall. The dimensions of the frame are 3 feet by 2 feet. The area of the space is 9 feet2. The frame will fit on his wall.

John knows that the area of his wallpaper is 120 square inches.

True

False

Ms. Dawson wants to rent a condo unit. She uses the floor plans below and the formula for area to decide which condo unit she will rent.

area = 120 square in.

What could be the dimensions of the wallpaper?

What piece of information does Ms. Dawson most likely find using the area formula?

10 feet long by 5 inches wide

20 feet long by 6 inches wide

12 feet long by 8 inches wide

Distance around each unit

16 feet long by 5 inches wide

Price per square meter of each unit

Amount of floor space in each unit Distance between floor and ceiling in D each unit C

Select all of the statements that are true of a rectangle. If l = 15 and w = 20 , area is 300 units2 If l = 53 and w = 2, area is 96 units2 If l = 17 and w = 15, area is 255 units

Select all of the statements that are true of a rectangle. If l = 7 and w = 45, area is 315 units2

If l = 40 and w = 14, area is 540 units

If l = 10 and w = 10, area is 100 units2

If l = 22 and w = 31, area is 682 units

If l = 37 and w = 5, area is 185 units2

If l = 7 and w = 28, area is 266 units

If l = 24 and w = 13, area is 412 units2 If l = 12 and w = 40, area is 480 units2 If l = 42 and w = 21, area is 862 units2

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TRAIN THE BRAIN PRACTICE 3 4.MD.3 (4.MD.1.3) 1

Eva’s rectangular pool is 250 square feet with a width of 10 feet. She wants to make a fence around her pool. How many feet of fence does she need? Draw a diagram to help you solve.

2 Jeff wants to place a boarder around a square garden he wants to make. The side lengths will be 9 feet. He wants to first put grass inside of it. How many square feet of grass does he need? Draw a diagram to help you solve.

Justine built a square sandbox for her daughter. It is 49 square feet. She wants to build a wooden boarder along the edges. How many feet of wood does she need? Draw a diagram to help you solve.

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THINK TANK QUESTION DIRECTIONS: Use the dimensions from the floor plan to find the area of all of the rooms in the home below. Note: The dimensions of the hall are 5 ft × 3 ft. 50 feet

18 feet

Bedroom 3 15 ft × 9 ft

Bedroom 1 15 ft × 9 ft

Living Room 20 ft × 12 ft Hall

Bedroom 4 15 ft × 9 ft

Living Room (Area)

Kitchen (Area)

Bathroom (Area)

Kitchen 18 ft × 6 ft

Bedroom 1 (Area)

Bathroom 7 ft × 6 ft

Bedroom 2

Bedroom 2 (Area)

Bedroom 3 (Area)

Bedroom 4 (Area)

Hall (Area)

TOTAL AREA

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Four-STAR CHALLENGE - 4.MD.3 (4.MD.1.3) 1

Celeste wants to build a boarder around her rectangular koi pond that has a length of 2 feet. The area of the pond is 6 feet2. How many feet of material will she need to make the boarder? Grid your answer.

Select all of the statements that are true of the floor plan below.

Aiden has a rectangular piece of fabric that has the dimensions of 9 yards by 5 yards. He wants to cut out a square from it that has a perimeter of 12 yards. What is the area of the fabric he has left in square yards? Grid your answer.

The area of a rectangle is 120 square feet. If the length of the rectangle is 12 feet, what is the width? A

10 feet

20 feet

Room 1 has a perimeter of 10 feet.

30 feet

Room 2 has an area of 20 square feet.

40 feet

Room 3 has a perimeter of 12 feet. Room 4 has an area of 10 square feet.

Select all of the statements that are true of the floor plan below.

Room 1 has an area of 10 square feet. 5

Jeff wants to carpet the floor of a bedroom and a dining room. 10 feet 20 feet

Bedroom

Dining room 10 feet

30 feet

How much carpet does he need to cover the floor in both areas? 400 square feet C 600 square feet

500 square feet

D 700 square feet

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Room 1 has an area of 10 square feet. Room 2 has a perimeter of 9 feet. Room 3 has an area of 30 square feet. Room 1 has a perimeter of 7 feet. Room 2 has an area of 20 square feet.

Part I: Draw 3 different rectangles that each have an area of 40 square units. Show the dimensions for each rectangle on your drawing.

Part II: Which rectangle has the greatest perimeter? (Show your work)

City planners have a budget to cover 270 feet of fencing to completely enclose 4 playgrounds in the community. Help the planners determine the missing dimensions, perimeter, and/or missing area based on the information given about the playgrounds. Draw pictures to help you solve.

North End Playground Width: 25 feet Area: 250 feet2 What is the PERIMETER? What is the LENGTH?

South End Playground Length: 15 feet Width: 20 feet What is the PERIMETER? What is the AREA?

West End Playground

East End Playground

Length: 30 feet Perimeter: 80 feet What is the AREA? What is the WIDTH?

Perimeter: 50 feet Area: 150 feet2 What is the WIDTH? What is the LENGTH?

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THINK TANK QUESTION 9

DIRECTIONS: Use the dimensions from the floor plan to find the area of all of the rooms in the home below. Note: The dimensions of the hall are 4 ft × 4 ft. 44 feet

20 feet

Bedroom 3 12 ft × 10 ft

Bedroom 1 12 ft × 10 ft

Living Room 20 ft × 14 ft Hall

Bedroom 4 12 ft × 10 ft

Kitchen 16 ft × 6 ft

Living Room (Area)

Bedroom 1 (Area)

Kitchen (Area)

Bedroom 3 (Area)

Bathroom 8 ft × 6 ft

Bedroom 2

Bedroom 2 (Area)

Hall (Area) Bathroom (Area)

TOTAL AREA

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Bedroom 4 (Area)

MISSION 23: SOLVING PROBLEMS PRESENTED IN LINE PLOTS Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4,1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot, find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Bootcamp STRATEGY 1: Organize a set of data involving fractions into a tally table to be used to make a line plot. 5 8

3 8

5 3 1 1 5 1 7 1 8 8 8 8 8 8 8 8

Step 1: Organize the data in order from least to greatest. 1 1 1 1 3 8 8 8 8 8

3 5 8 8

5 5 7 8 8 8

Step 2: Set up a tally table to include the frequency of each fraction. Fraction

Tally

1 8

3 8 5 8

7 8

Bootcamp STRATEGY 2: Make a line plot to display a data set of measurements in fractions of a unit. X X

0 8

1 8

2 8

3 8

4 8

5 8

X 6 8

7 8

8 8

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TRAIN THE BRAIN PRACTICE 1 4.MD.4 (4.MD.2.4) DIRECTIONS: Organize the sets of data involving fractions into a tally table and a line plot. 1

1 4

3 4

4 4

1 4

4 4

Fraction

5 8

3 8

2 4

1 4

3 4

4 4

5 8

2 8

Tally

1 8

Fraction

4 4

3 8

1 8

5 8

1 8

Tally

1 1 1 1 1 1 1 2 12 1 2 12 2 2 12 2 1

Fraction

Tally

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Target PRACTICE 1 Use the line plot for questions 1 and 2. Use the line plot for questions 4 and 5. The line plot shows the lengths of straws The line plot shows the height of newly cut by students. sprouted bean seeds.

× ×1 4

× × × ×3

2 4 4 Length (foot)

× × × × × ×× × ×× × × × × × × × ×× × ×× × × × × × × 1 2 3 4 5 6 7

× × × × ×4 4

8 8 8 Growth (foot)

How many straws were cut to 34 foot? Grid your answer.

What is the difference between the longest and shortest growth in feet? Grid your answer.

What is the total length of straws that were cut? 2 46 A C 11 4 4 B D 10 1 46 4

How many more bean 6 4 sprouted at 8 than 8 ?

Joan made a line plot based on the tally table below. Select all of the lengths that would have the same number of X’s placed on the line

× × × × ××

RIBBON LENGTH

FREQUENCY

1 2 2 5 and 5 1 3 2 5 and 2 5 2 3 2 5 and 2 5

C D

4 8 2 8

Sally made a line plot based on the tally table below. Select all of the widths that would have the same number of X’s placed on the line

RIBBON LENGTH

FREQUENCY

2 1 8 3 1 8 4 1 8 5 1 8

1 5 2 2 5 3 2 5 4 2 5 2

seeds

3 4 2 5 and 5

1 and 2 45 5 2 4 2 and 2 5 5 2

2 4 1 8 and 1 8 4 5 plot. 1 and 1 8 8 2 5 1 8 and 1 8

3 4 1 8 and 1 8 2 3 1 and 1 8 8 3 5 1 8 and 1 8

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TRAIN THE BRAIN PRACTICE 2 4.MD.4 (4.MD.2.4) DIRECTIONS: Organize the sets of data involving fractions into a tally table and a line plot.

1 4

3 4

4 4

2 4

1 4

Fraction

3 4

1 4

7 8

2 4

Tally

1 4 2 4 3 4 4 4

7 8

5 8

Fraction

3 8

1 8

3 8

1 8

Tally

1 1 1 1 1 1 12 2 2 2 1 2 2 2 12 2 2 1

Fraction

Tally

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Target PRACTICE 2 Use the line plot for questions 1 and 2. Use the line plot for questions 4 and 5. The line plot shows the lengths of stickers The line plot shows the distance students used by students. rode their bikes to mall.

× ×1

× × × ×2

× × × × ×3

× ×× 4

× × × × × × × × × ×1 ×2 ×3 ×4 ×5 8

Length (inches)

A B

How many stickers had a length greater than 24 ? Grid your answer.

What is difference in length between the longest sticker and the shortest? 4

2 4 3 4

C D

Study the line plot below. Select all of the lengths of the crayons that occurred 5 times.

1 1 8 8 8 Distance (mile)

× × × ×3

What is the difference between the longest and shortest distance

How many more students rode 1….. 8 4 mile than 1 8 mile?

A B

1 8 2 8

Number of Pipes

× × × × × × × × × × × × ×1 ×1 ×3 ×7 ×1 ×1

× × × ×3

1 4 inches 1 4 2 inches 3 inches 4 4 4

Study the line plot below. Select all of the lengths of the pipes that occurred 4 times.

× × × ×3

64 62 64 74 7 2 7 4 Pipe Length (in feet)

3 44 4 2 4 4 2 4 Crayon Length (in inches)

1 4 inches 1 3 inches 2 3 3 inches 4

× × × × × × × × × ×4 ×1 ×1

Number of Crayons

× × × × × × ×1 ×1

1 2 feet 1 6 feet 4 3 6 feet 4

1 7 4 feet 1 7 feet 2 3 7 feet 4

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TRAIN THE BRAIN PRACTICE 3 4.MD.4 (4.MD.2.4) DIRECTIONS: Use the in formation given to solve the following problems. Sam wants to record the distances he ran in miles on a line plot. He ran 4 times this week. The total distance he ran was 29 miles. Use the number line below to create a line plot that shows the possible distances Sam ran this week. Show your work below. Be sure to label the line plot.

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7 12

THINK TANK QUESTION A party planner cut streamers to attach to balloons. The streamers were cut at varying lengths. The data below shows the measurements of the streamers to the nearest one-eighth of an inch. 5

34 8 in. 35 8 in. 5

34 8 in.

34 8 in. 1

35 8 in.

35 8 in. 7

34 8 in.

35 8 in. 7

34 8 in.

35 8 in.

34 8 in.

35 8 in.

Part I: .Create a data table to display the various lengths of the streamers. Label with a title and the appropriate headers for the data table.

Part II: Create a line plot to display the various lengths of the streamers. Label with a title for the line plot .

Part III: Find the length of the longest streamer and the shortest streamer. How many streamers have the longest length? How many streamers have the shortest length? What is the difference between the measurement of longest and shortest streamers?

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FOUR-STAR CHALLENGE - 4.MD.4 (4.MD.2.4) Use the line plot for questions 1 and 2. Use the line plot for questions 4 and 5. The line plot shows the fraction of pizza The line plot shows the distance fourth each kid ate at a party. grade students ran in a team competition.

× × × × × × × × × ×1 ×2 ×3 ×4 ×5 8

8 8 8 Pizza Eaten (each kid)

× ×1

2 6

× × × × × × × × × ×× × ×3 ×4 ×5 × ×1 ×2

1 1 2 6 6 6 Distance (mile)

How many kids ate 38 and less slices of pizza? Grid your answer.

What is the difference in miles between the most run length and least run length? Grid your answer.

How much pizza was eaten in all?

What is the total distance traveled in miles by the students?

1 8 4 38

Select all of the statements that could be true of the line plot below.

× × × × × ×1

Number of Curtains

× × × × × × × × × × × ×2 ×3 ×4 ×5

5 5 56 6 6 6 Curtain Length (in yards) 1

5 curtains have a length of 5 6 yards. 5 curtains have a length of 5 26 yards.

3 curtains have a length of 5 36 yards. 3 curtains have a length of 5 46 yards. 4 curtains have a length of 5 5 yards. 6 232 I Smart to the Core I Educational Bootcamp

18 6

34 6

35 6

Select all of the statements that could be true of the line plot below. Number of Chairs

× × × × × × × × × × × ×2 ×3 ×4 ×5 ×6

48 48 8 Chair Height (in feet)

2 2 chairs have a height of 4 8 feet. 3 3 chairs have a height of 4 8 feet.

6 chairs have a height of 4 48 feet. 3 chairs have a height of 4 58 feet. 4 chairs have a height of 4 68 feet.

Robert weighed several pieces of precious gems to be sold by weight in grams. Robert recorded the weight of the gems on a line plot to the nearest one-fourth of a gram. When Robert went to review the line plot, he noticed that the paper that he recorded his measurements on had been ripped apart. Part I: Help Robert determine the missing measurements he previously recorded.

X X X X 2

1 4

X X

X X X X X 3

X X X 1 2

Part II: Explain how you determined the missing measurements.

Part III: What was the weight that the least number of gems weighed?

Part IV: What is the total weight of all of the gems that weighed 3 1 grams? 2

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THINK TANK QUESTION 8

The teacher’s helper sharpened pencils each day at the end of the class. The length of the pencils that have been sharpened today are shown below. 3 3 inches 4 2 3 inches 4 3 1 inches 2 3 3 inches 4 3 3 inches 4 4 inches 2 3 inches 4 2 3 inches 4 4 inches 4 inches

Part I: Make a line plot to display the various lengths of the pencils. Create a title and intervals for the line plot.

Part II: Determine the difference between the longest lengths and the shortest pencil lengths.

234 I Smart to the Core I Educational Bootcamp

MISSION 24: RECOGNIZING angles Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: (a) An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular are between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles. (b) An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Bootcamp STRATEGY 1: Determine how many turns make a complete circle. 1 8

1 8 1 8

1 8

Note: In this example the circle is divided in oneeighth angles. Therefore, there are 8 turns that can be made.

1 8

Step 2: Count the total number of turns that are made to complete the circle.

1 8

Step 1: Determine the fractional amount being represented in the circle.

1 8

Bootcamp STRATEGY 2: Determine the angle measure of each turn. Step 1: Once the 8 fractions of the circle have been determined, multiply the fractioned part by 360°. This number will give the number of degrees in each turn. In this case, multiply one-eight by 360° to get the measure of each angle. 1 360 × 360 = = 45° angle 8 8 Step 2: Count the number of turns made. Multiply this number by the number of degrees for each turn. 3 × 45° = 135°

Note: The 3 shaded parts represent 3 turns. Therefore, 45° is multiplied by 3 turns to determine the measure of the angle. The angle measure is equal to 135°.

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TRAIN THE BRAIN PRACTICE 1 4.MD.5 (4.MD.3.5) DIRECTIONS: Identify the following angles as >, <, or = to 90 degrees. 1

2 D

4 X R

C 90°

ABC

DEF

90°

Y XYZ

Z 90°

90°

RST

DIRECTIONS: Identify the fraction of the circle the shaded angle represents. Classify the type of angle given. 5

DIRECTIONS: Identify the measure of the angle in degrees. Classify the type of angle given. 8

1 4

236 I Smart to the Core I Educational Bootcamp

9 1 8

3 8

Target PRACTICE 1 1

Which of the statements below best describes the shaded turn?

A B C D

1 8 1 8 1 4 1 4

Jessica started cooking at 12:00 P.M. and finished at 12:20 P.M. What fraction of a circle did the minute hand turn?

turn counterclockwise turn clockwise turn counterclockwise

1 turn 3

1 turn 4

turn clockwise

1 turn 8

3 turn 4

Identify all of the acute angles in the figure.

4 Identify all of the obtuse angles in the figure.

Angle AOB

Angle DOE

Angle ROS

Angle POS

Angle BOC

Angle AOE

Angle QOT

Angle QOR

Angle COD

Angle COE

Angle POQ

Angle SOT

How many degrees are in an angle that turns through 12 of a circle? Grid your answer.

What is the angle measure of the shaded region below? Grid your answer. 1 8

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TRAIN THE BRAIN PRACTICE 2 4.MD.5 (4.MD.3.5) DIRECTIONS: Identify the following angles as >, <, or = to 90 degrees. 1

T S

Y E

B CAB

90°

F 90°

DFE

Z XYZ

90°

RST

DIRECTIONS: Identify the fraction of the circle the shaded angle represents. Classify the type of angle given. 5

DIRECTIONS: Identify the measure of the angle in degrees. Classify the type of angle given. 8

9 3 4

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1 2

5 8

Target PRACTICE 2 1

Which of the statements below best describe the shaded turn?

A B C D

1 8 1 8 1 4 1 4

Jess started cooking at 6:00 P.M and finished at 6:30 P.M. What fraction of a circle did the minute hand turn?

turn counterclockwise turn clockwise turn counterclockwise

1 turn 3

1 turn 2

turn clockwise

1 turn 8

3 turn 4

3 Identify all of the obtuse angles in the figure.

Identify all of the acute angles in the figure.

Angle POQ

Angle QOR

Angle AOB

Angle DOE

Angle ROS

Angle SOT

Angle BOC

Angle AOE

Angle POT

Angle POS

Angle COD

Angle AOD

How many degrees are in an angle that turns through 44 of a circle? Grid your answer.

What is the angle measure of the shaded region below? Grid your answer. 1 12

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TRAIN THE BRAIN PRACTICE 3 4.MD.5 (4.MD.3.5) 1

How many degrees equal the shaded portion of the circle below?

___________ degrees

How many degrees equal the shaded portion of the circle below?

___________ degrees 240 I Smart to the Core I Educational Bootcamp

THINK TANK QUESTION DIRECTIONS: Use the information below to solve the word problem. Be sure to use the circle given to support your answer. Brandon had baseball practice from 6:00 PM to 6:45PM. How many degrees did the minute hand make on the clock during the length of his practice? Draw a picture to support your answer. If he stayed after practice another 10 minutes, how many more degrees did the minute hand turn?

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FOUR-STAR CHALLENGE - 4.MD.5 (4.MD.3.5) 1

Which of the statements below best describe the shaded turn?

A B C D

3 4 3 4 1 4 1 4

Each morning, Danny leaves home at 8:00 A.M and arrives at school by 8:45 A.M. What fraction of a circle did the minute hand turn?

turn counterclockwise turn clockwise turn counterclockwise turn clockwise

Select all of the statements that could be true of the angle below.

1 turn 3

1 turn 4

1 turn 8

3 turn 4

Select all of the statements that could be true of the angle below.

The angle is a right angle.

The angle is greater than 90°.

The angle is an acute angle.

The angle is less than 90°.

The angle is an obtuse angle.

The angle is an acute angle.

The angle is greater than 90°.

The angle is an obtuse angle.

The angle is less than 90°.

The angle is a right angle.

How many degrees are in an angle that turns through 3 of a circle? Grid 4 your answer.

Jack started jogging at 6:55 A.M and finished at 7:15 A.M. How many degrees did the minute hand turn? Grid your answer. 1 3

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Draw a circle that has 8 equal parts and determine the angle measure for each part. (Show your work)

Part I: Describe the shaded area of the circle shown below. B

A X

C Part II: Calculate the angle measure for AXB . (Show your work)

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THINK TANK QUESTION 9

DIRECTIONS: For each partially shaded circle, tell what fraction the shaded area represents and determine the measure of the angle in degrees. A.

B. C.

G. F.

Fraction:

Degree Measure:

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MISSION 25: USING A PROTRACTOR TO MEASURE angles Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Bootcamp STRATEGY 1: Measuring angles using a protractor.

STEP 1: Place the center point of the flat side of the protractor over the vertex of the angle being measured. NOTE: The vertex is where the 2 lines of the angle meet. STEP 2: Align the protractor so that it is flush with the zero mark of the first ray on either side. STEP 3: Locate the point at which the second ray intersects the curved portion of the protractor.

STEP 4: Read the measurement that is aligned with the point of intersection. If aligned to the side of the angle with the zero on the left side of the protractor, read the top number as the angle measurement. If aligned to the side of the angle with the zero on the right side of the protractor, read the bottom number as the measurement. The acute angle depicted has a measure of 40°.

Bootcamp STRATEGY 2: Sketching angles of a specified measure. STEP 1: Use the protractor to draw a straight line. STEP 2: Draw a point in the center of the line to represent the vertex. STEP 3: Place the center of the flat side of the protractor over the vertex of the line. STEP 4: Align the zero mark (on either side of the protractor) with the line. STEP 5: Locate the measurement of the angle that must be drawn. Make a small mark at this measurement. STEP 6: Line up the vertex of the angle with the mark made. STEP 7: Use the straight edge of the protractor to draw a line connecting the two points.

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TRAIN THE BRAIN PRACTICE 1 4.MD.6 (4.MD.3.6) DIRECTIONS: Use the protractor below to identify 2 of each of the angles listed below. C B

E F

right angle =

acute angle =

obtuse angle =

straight angle =

DIRECTIONS: Draw the following angles: 30°, 45°, 105°, and 135°. Label each angle measure with the appropriate angle measure.

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Target PRACTICE 1 1

Use a protractor. What is the measure of ABC? Grid your answer.

What is the measure of the angle formed by the hands of the clock? Grid your answer.

Use a protractor. What is the measure of the smallest angle in the triangle?

Use a protractor. What is the measure of the largest angle in the triangle?

80 ͦ

100 ͦ

90 ͦ

110 ͦ

Use a protractor to measure the angle below. Select all of the statements below that are true.

30 ͦ

50 ͦ

40 ͦ

90 ͦ

Use a protractor to measure the angle below. Select all of the statements below that are true.

Angle is obtuse

Angle is 80º

Angle is 30º

Angle is obtuse

Angle is right

Angle is 145º

Angle is 125º

Angle is right

Angle is acute

Angle is 40º

Angle is 170º

Angle is acute

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TRAIN THE BRAIN PRACTICE 2 4.MD.6 (4.MD.3.6) DIRECTIONS: Use the protractor below to identify 2 of each of the angles listed below. C

E B

F G

right angle =

acute angle =

obtuse angle =

straight angle =

DIRECTIONS: Draw the following angles: 60°, 95°, 115°, and 165°. Label each angle with the appropriate angle measure.

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Target PRACTICE 2 1

Use a protractor. What is the measure of ABC? Grid your answer.

Use a protractor. What is the measure of the angle formed? Grid your answer.

Use a protractor. What is the measure of the smallest angle in the triangle?

C A

Use a protractor. What is the measure of each of the angles in the equilateral triangle below?

59 ͦ

100 ͦ

30 ͦ

50 ͦ

75 ͦ

145 ͦ

40 ͦ

90 ͦ

Use a protractor to find the 45º angle. Select the statements that are true of that angle. B

Use a protractor to find the 75º angle. Select the statements that are true of that angle. B C

A Angle AOB

D O 45° is an obtuse angle

A Angle AOD

D O 75° is an obtuse angle

Angle BOC

45° is a right angle

Angle AOC

75° is a right angle

Angle COD

45° is an acute angle

Angle BOC

75° is an acute angle

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TRAIN THE BRAIN PRACTICE 3 4.MD.6 (4.MD.3.6) DIRECTIONS: Use a protractor to measure the following angles.

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THINK TANK QUESTION Part I: Find the measure of the angels based on the measure given.

C A

1 =

5 =

2 =

6 =

3 =

7 =

4 =

8 =

Part II: Explain some similarities and differences between angles. Explain why some angle measures are the same.

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FOUR-STAR CHALLENGE - 4.MD.6 (4.MD.3.6) 1

Use a protractor. What is the measure of ABC? Grid your answer.

Use a protractor. What is the measure of the angle formed by the hands of the clock? Grid your answer.

Use a protractor. What is the measure of the largest angle in the triangle?

Use a protractor. What is the measure of the smallest angle in the triangle?

70 ͦ

90 ͦ

30 ͦ

60 ͦ

80 ͦ

100 ͦ

40 ͦ

90 ͦ

Select all of the statements that are true. B

Select all of the statements that are C true. B

Angle AOB: 130º

Angle COD: 45º

Angle BOC: 30º

Angle AOC: 85º

Angle AOC: 45º

Angle BOC: 90º

Angle AOB: 70º

Angle BOD: 100º

Angle BOD: 130º

Angle AOD: 180º

Angle COD: 75º

Angle AOD: 0º

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Use a protractor to measure the angle below.

Use a protractor to draw a 45 °angle.

Use a protractor to draw a 165 °angle.

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THINK TANK QUESTION 11 Part I: Use a protractor to determine the measure of Angle K. (Show your work)

K m

Part II: Explain how you determined the measure of angle K.

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MISSION 26: adding and subtracting angles Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Bootcamp STRATEGY 1: Recognize angle measures as additive. STEP 1: Measure and/or record the existing angles. DCE = 67 ͦ

ECF = 55 ͦ STEP 2: Calculate the sum of the measures. DCE +

ECF =

DCF

67 ͦ

F ͦ

Bootcamp STRATEGY 2: Solve addition problems to find unknown angles. STEP 1: Record the measure of the existing angles.

ADB = 87 ͦ

BDC = 55 ͦ

STEP 2: Calculate the sum of the measures to find the unknown. ADB +

BDC =

ADC

C ͦ

87 ͦ + 55 ͦ = X ͦ 142 ͦ = X ͦ

Bootcamp STRATEGY 3: Solve subtraction problems to find unknown angles. STEP 1: Record the measure of the existing angles. KNM = 122 ͦ LNM = 55 ͦ

STEP 2: Calculate the difference between the measures. KNM ‒

LNM =

122 ͦ ‒ 55 ͦ = X ͦ 67 ͦ = X ͦ

KNL

122 X

ͦ ͦ

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TRAIN THE BRAIN PRACTICE 1 4.MD.7 (4.MD.3.7) DIRECTIONS: Determine what the measure of the angle is in each problem. (Show your work) 1 A

33 ͦ

51 ͦ

65 ͦ

25 ͦ B

ABC =

118 ͦ

I G

27 ͦ

EFG =

IJK =

DIRECTIONS: Determine what the measure of the missing angle is in each problem. (Show your work)

20 ͦ

35 ͦ

X B

Q M

65 ͦ 58 ͦ R

LMN = 78°

ABC = 180° X=

QRS = 163° X=

DIRECTIONS: Calculate the sum of the unknown angles. (Show your work) 7

180 ͦ = x + 45 ͦ

90 ͦ = x + 15 ͦ

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180 ͦ = x + 127 ͦ

90 ͦ = x + 84 ͦ

Target PRACTICE 1 What is the measure of the unknown angle in the figure?

X 65 ͦ A B

45 ͦ 130 ͦ

C D

Which equation below shows the sum of the measures of 4 right angles?

115 ͦ

45 ͦ + 45 ͦ + 45 ͦ + 45 ͦ = 180 ͦ

180 ͦ + 180 ͦ + 180 ͦ + 180 ͦ= 720 ͦ

90 ͦ + 90 ͦ + 90 ͦ + 90 ͦ = 360 ͦ

100 ͦ + 100 ͦ + 100 ͦ + 100 ͦ= 400 ͦ

220 ͦ

Study the figure below. Select all of the statements that are true.

Angle HFG = 44º

Angle HFG = 58º

Angle KOM = 128º

Angle MON = 38º

Angle HFG = 148º

Angle HFG = 112º

Angle KOM = 134º

Angle MON = 46º

Angle EFG = 90º

Angle EFG = 180º

Angle KON = 0º

Angle KON = 180º

Wyatt has a piece of cloth that is 4 of a large circle. He cuts the piece of cloth in half from the point that would be the center of the circle. What is the angle measure of each part? Grid your answer.

Irina is making a design using wedgeshaped paper. Each paper wedge has an angle measure of 60 ͦ. How many sheets of wedge-shaped paper would she need to form an 180 ͦ angle? Grid your answer.

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TRAIN THE BRAIN PRACTICE 2 4.MD.7 (4.MD.3.7) DIRECTIONS: Determine what the measure of the angle is in each problem. (Show your work) 1

2 B

22 ͦ

Y X

45 ͦ

111 ͦ

25 ͦ Z

133 ͦ

22 ͦ

W W

YAS =

BDW =

XYZ=

DIRECTIONS: Determine what the measure of the missing angle is in each problem. (Show your work) 4

5 D

X 30 ͦ 36 ͦ B

T Q

16 ͦ

X C

ABC = 90° X=

X 35 ͦ N

LMN = 131°

QRS = 73°

DIRECTIONS: Calculate the sum of the unknown angles. (Show your work) 7

176 ͦ = x + 67 ͦ

110 ͦ = x + 29 ͦ

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145 ͦ = x + 133 ͦ

89 ͦ = x + 71 ͦ

Target PRACTICE 2 What could be the possible sum of <1, <2, <3, <4, <5, and <6?

Which of the given equation shows the sum of the measures of 5 right angles?

<3 <2

A 60 ͦ+ 60 ͦ+ 60 ͦ+ 60 ͦ+ 60 ͦ= 60 ͦ

B 90 ͦ+ 90 ͦ+ 90 ͦ+ 90 ͦ+ 90 ͦ= 450 ͦ

90 ͦ

360 ͦ

C 180 ͦ+ 180 ͦ+ 180 ͦ+ 180 ͦ+ 180 ͦ= 360°

180 ͦ

270 ͦ

D 70 ͦ+ 70 ͦ+ 70 ͦ+ 70 ͦ+ 70 ͦ= 350 ͦ

Select all of the angle combinations that have a difference of 20º.

Select all of the angle combinations that have a sum over 150º.

L and M

L and O

T and U

T and W

N and O

P and M

S and V

U and V

P and N

O and P

W and V

S and W

Molly is making a circular figure using different colored papers. The shape of each equal piece is shown in the diagram. If each equal piece measures 30 ͦ, how many pieces will be needed? Grid your answer.

Lisa bought a large half circle-shaped cake from the shop to celebrate her birthday. She invited 10 of her friends. If she cuts the cake into 10 identical slices, what is the angle measure of each slice? Grid your answer.

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TRAIN THE BRAIN PRACTICE 3 4.MD.7 (4.MD.3.7) DIRECTIONS: Use drawings or equations to solve the problems below.

1 The

BAD measures 93°. Calculate the measure of

CAD.

Show your work. B

C 49 ͦ

2 The

CAD = __________

WYZ measures 133°. Calculate the measure of

XYW.

Show your work.

133 ͦ Y

3 The

XYW = __________

KMO measures 32°. Calculate the measure of

KMN.

Show your work. K

M O

100 ͦ

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KMN= __________

THINK TANK QUESTION Patti and Tammy are on the Independence Day festival committee that will be organizing an event to be held on the Fourth of July. They need to send invitations to all of the guests. Tammy decides they should create their own envelopes for the invitations.

Patti’s Envelope

88°

Patti creates a red envelope with a white flap and decorates it with blue stars. Tammy decides to create a white envelope with a flap that has red on one side and blue on the other. Patti’s envelope has a measure of 88° at the seal line. Tammy has the exact same-sized flaps however, the red part of the flap has an angle measure of 51°. Part I: Calculate the blue (b) portion of Tammy’s envelope. (Show your work)

Tammy’s Envelope

51°

Part II: The girls come to a decision to make the envelopes based on Tammy’s design. They decide to make 1 small change to the blue and red flaps. Help the girls determine the measure for both the red and blue flaps if they want to make them exactly the same sized-angle measure. (Show your work)

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FOUR-STAR CHALLENGE - 4.MD.7 (4.MD.3.7) What is the measure of the unknown angle in the figure?

60 ͦ X 55 ͦ

45 ͦ

65 ͦ

55 ͦ

75 ͦ

Study the figure below. Angle RST is a right angle. If angle RSU = 19º, select all of the equations that can be used to find the measure of x.

Which equation below shows the sum of the measures of 2 right angles? A

45 ͦ + 45 ͦ = 90 ͦ

50 ͦ + 50 ͦ = 100 ͦ

90 ͦ + 90 ͦ = 180 ͦ

180 ͦ + 180 ͦ = 360 ͦ

Study the figure below. Angle LON is a right angle. If angle MON = 28º, select all of the equations that can be used to find the measure of y.

x = 180º − 19º

x + 19º = 180º

y = 360º − 28º

y + 28º = 90º

x = 360º − 19º

x = 90º − 19º

y = 180º − 28º

y + 28º = 180º

x + 19º = 90º

x + 19º = 360º

y = 90º − 28º

y + 28º = 360º

Nicole has a piece of paper that is….3 of a large circle. She cuts the paper into 3 equal parts from the center point of the circle. What is the angle measure for each part? Grid your answer.

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Mona baked wedge-shaped cakes. The wedge of each cake has an angle measure of 40 ͦ. How many cakes would she need to put together to form an 360 ͦ angle? Grid your answer.

Part I: Angle X has a measure of 58°. What is the measure of Angle Y?

Part II: If angle X is increased by 20°, what would be the new angle measure for Angle Y?

Larry wants to share a slice of pizza with his sister. Larry wants to keep the larger part of the pizza for himself. He measures the total angle as 52°. If Larry keeps an angle measure of 30° for himself, what will be the angle measure of his sister’s part of the pizza?

30°

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THINK TANK QUESTION 9

Claire cut the first slice of pie at an angle of 40°. The second slice was cut half of the angle of the first slice and the third slice was twice the first. Part I: What are the angle measures for the 3 pieces of pie that were cut? (Show your work)

40°

Part II: If the whole pie is equal to 360°, what is the angle measure for the remaining pie? (Show your work)

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MISSION 27: IDENTIFYING LINES AND ANGLES Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Bootcamp STRATEGY 1: Distinguish between points, lines, line segments, rays, and angles. A

point A A point is an exact location in space.

line AB or AB

B B A Ray AB or AB Ray BA or BA

line segment AB or AB line BA or BA

line BA or BA

A line extends in both directions without an end.

Angle ABC or

ABC

Angle CBA or

CBA

A ray is part of a line that begins at an exact location and extends without end in the opposite direction.

Angle

A line segment is part of a line that has 2 distinct end points.

An angle is a figure formed by 2 rays sharing a common end point, commonly called the vertex.

Bootcamp STRATEGY 2: Identifying types of angles using the right angle as a guide.

A right angle forms a 90 degree angle.

An acute angle is an angle less than 90 degrees.

An obtuse angle is an angle greater than 90 degrees.

A straight angle forms a line that is 180 degrees.

Bootcamp STRATEGY 3: Distinguish between parallel and perpendicular lines. Parallel lines are lines which never meet. A

Line AB is parallel to line CD AB II CD

Perpendicular lines are lines which cross at a 90 degree angle. C

B D

Line AB is perpendicular to line CD AB CD

Line AB is parallel to line CD Line AB is perpendicular to line AC and BD

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TRAIN THE BRAIN PRACTICE 1 4.G.1 (4.G.1.1) DIRECTIONS: Identify the angles as acute, obtuse, right, or a straight angle. 1

DIRECTIONS: Identify the number of each type of interior angle in the shapes below. 5

acute angles

obtuse angles

right angles

number of sides

DIRECTIONS: Identify the lines below as parallel, perpendicular, or intersecting. 9

DIRECTIONS: Identify all of the acute angles in the shapes below. U

U W

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Target PRACTICE 1 Which set of lines listed below will eventually intersect?

Which of the following best describes the figure below?

point Y

line segment XY

ray XY

line XY

How many right angles are in the figure below? Grid your answer.

How many acute angles are in the figure below? Grid your answer.

Jessica connected 2 rays together to create acute angles. Identify all of he angles below she could have made.

Sylvia connected 2 rays together to create a right angle. Identify all of the angles below she could have made.

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TRAIN THE BRAIN PRACTICE 2 4.G.1 (4.G.1.1) DIRECTIONS: Identify the angles as acute, obtuse, right, or a straight angle. 1

DIRECTIONS: Identify the number of each type of interior angle in the shapes below. 7

acute angles

obtuse angles

right angles

number of sides

DIRECTIONS: Identify the lines below as parallel, perpendicular, or intersecting. 9

DIRECTIONS: Identify all of the obtuse angles in the shapes below. J

A D

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Target PRACTICE 2 Which of the figures below show AB CD?

1 A

What degree angle of the figure below is shaded? Grid your answer.

A map of the bike path at the local park is drawn below.

B C

D B

How many acute angles are in the figure below? Grid your answer.

What 2 paths of the park are perpendicular?

Select all of the figures that show parallel lines.

EF and GH

C EF and FH

EG and FH

D EG and GH

Select all of the figures that show perpendicular lines.

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TRAIN THE BRAIN PRACTICE 3 4.G.1 (4.G.1.1) DIRECTIONS: Use a ruler to complete the following problems.

1 Use a ruler to draw AB at 3 inches.

2 Draw point C.

3 Draw

MNO to form an acute angle.

4 Draw

H to form an obtuse angle.

5 Use a ruler to draw 2 parallel lines AB and CD.

6 Use a ruler to draw 2 perpendicular lines EF and GH.

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THINK TANK QUESTION DIRECTIONS: Use a ruler to complete the following problems.

Draw and label right angle BAD.

Draw and label acute angle CAD.

Draw and label obtuse angle EAD.

4 Draw and label straight line FAD.

Draw a shape that has at least 2 right angles.

6 Draw a shape that has 3 acute angles.

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Four-STAR CHALLENGE - 4.G.1 (4.G.1.1) 1

Which of the lines below form a right angle?

The picture below shows a magnet of the letter “A.”

What type of angle is  U? B

acute angle

right angle

straight angle

obtuse angle

Veronica drew the shape below. How many obtuse angles does this shape have? Grid your answer.

Karen drew the shape below. How many acute angles does this shape have? Grid your answer.

Select all of the statements that are always true of parallel lines.

Select all of the statements that are always true of perpendicular lines.

They are straight lines.

They intersect at a right angle.

They intersect at an acute angle.

They intersect at a straight angle.

They intersect at an obtuse angle.

They intersect at an acute angle.

They intersect at a right angle.

They intersect at an obtuse angle.

They do not intersect.

They are intersecting lines.

They intersect at a straight angle.

They do not intersect.

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Use the figure below to compare and contrast intersecting and perpendicular lines. Give examples using the diagram below. A

F C E

Use the protractor below to identify 2 of each of the angles as indicated below. S

right angle =

acute angle =

obtuse angle =

straight angle =

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THINK TANK QUESTION 9

Part I: Identify KLM illustrated in the figure below as either a right, acute, or obtuse angle. K L

right angle

acute angle

obtuse angle

Part II: Explain the difference between KLM and LMN.

Part III: Identify N as either a right, acute, or obtuse angle. right angle

acute angle

obtuse angle

Part IV: Describe the number of sets of parallel and/or perpendicular lines found in the closed figure you created in Part I. (Use the figure to give examples)

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MISSION 28: classifying two---dimensional figures Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Bootcamp STRATEGY 1: Identify figures based on the number of sides and the number of angles.

A triangle has 3 sides and 3 angles.

A quadrilateral has 4 sides and 4 angles.

A pentagon has 5 sides and 5 angles.

A hexagon has 6 sides and 6 angles.

Bootcamp STRATEGY 2: Classify triangles based on the size of the angle. acute acute

acute acute

acute obtuse

acute

right

A right triangle has 1 right angle.

An obtuse triangle has 1 obtuse angle.

An acute triangle has 3 acute angles.

Bootcamp STRATEGY 3: Classify quadrilaterals by the number of sides, types of lines, and the size of its angles. A trapezoid has 1 pair of parallel sides. A square has 4 right angles, 4 equal sides, and 2 pairs of parallel sides.

A rectangle has 4 right angles and 2 pairs of parallel sides.

A quadrilateral has 4 sides and 4 angles. A parallelogram has 2 pairs of parallel sides.

A rhombus has 4 equal sides and 2 pairs of parallel sides.

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TRAIN THE BRAIN PRACTICE 1 4.G.2 (4.G.1.2) DIRECTIONS: Identify the two-dimensional figures below and their properties. Number of angles: _________________________________

Number of sets of parallel lines: ______________________ Name of shape: ___________________________________

Number of angles: _________________________________ Number of sets of parallel lines: ______________________ Name of shape: ___________________________________

DIRECTIONS: Identify the triangles below based on the measures of the angles. 4

Number of acute angles: _____

Number of obtuse angles: _____

Number of right angles: _____

Type of triangle: _____________

DIRECTIONS: Circle all of the quadrilaterals below. 7

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Target PRACTICE 1 1

A picture of a stop sign is shown below. How many obtuse angles are there in the stop sign? Grid your answer.

How many pairs of parallel lines does the figure below have? Grid your answer.

Tim made a sign for a garage sale as shown below.

Maia drew a shape of an obtuse triangle. Which of the following could be the shape of the triangle?

What is the best name for the shape of the sign? C triangle parallelogram

trapezoid

square

Select all of the figures that have 2 pairs of parallel sides.

Select all of the figures that have 2 pairs of perpendicular sides.

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TRAIN THE BRAIN PRACTICE 2 4.G.2 (4.G.1.2) DIRECTIONS: Identify the two-dimensional figures below and their properties. Number of angles: _________________________________

Number of sets of parallel lines: ______________________ Name of shape: ___________________________________

Number of angles: _________________________________ Number of sets of parallel lines: ______________________ Name of shape: ___________________________________

DIRECTIONS: Identify the triangles below based on the measures of the angles. 4

Number of acute angles: _____

Number of obtuse angles: _____

Number of obtuse angles: _____ Number of obtuse angles: _____

Number of right angles: _____

Type of triangle: _____________ Type of triangle: _____________ Type of triangle: _____________

DIRECTIONS: Circle all of the quadrilaterals below. 7

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Target PRACTICE 2 1

Allie’s swimming pool looks like the quadrilateral below.

How many right angles does the figure below have? Grid your answer.

How many perpendicular lines does the figure below have? Grid your answer.

Identify all of the obtuse triangles.

What type of quadrilateral is it?

square

trapezoid

rectangle

rhombus

Liam has a drawing book in the shape of a square. Which figure could be the shape of Liam’s drawing book?

Identify all of the acute triangles.

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TRAIN THE BRAIN PRACTICE 3 4.G.2 (4.G.1.2) DIRECTIONS: Use drawings to solve the following problems. 1 Draw a quadrilateral that has 1 pair of parallel lines, 2 right angles, 1 obtuse angle, and 1 acute angle.

Name of the two-dimensional shape: _________________________ 2 Draw a quadrilateral that has 2 pairs of parallel lines, 2 obtuse angles, and 2 acute angles.

Name of the two-dimensional shape: _________________________ 3 How many acute angles can be identified in the shape below?

Number of acute angles: _______________

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THINK TANK QUESTION Draw a house using the following properties: (1) FACE OF THE HOUSE: Draw a quadrilateral that has 4 right angles and 2 pairs of parallel sides. (2) ROOF OF THE HOUSE: Draw 2 right triangles that when placed together form an acute triangle. (3) DOOR TO THE HOUSE: Draw a quadrilateral that has 4 right angles, 4 equal sides, and 2 pairs of parallel sides. (4) WINDOW ON THE HOUSE: Draw a polygon that has 6 equal sides and 6 obtuse angles. Make your drawing here.

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Four-STAR CHALLENGE - 4.G.2 (4.G.1.2) 1

Jenny is counting the number of acute angles in a obtuse triangle. How many acute angles does the triangle have? 0 A B

Linda drew a parallelogram on a piece of paper. Select all of the statements that can be true of the shape she drew.

A sign is in the shape of an acute triangle. Which of the following could be the shape of the sign?

How many acute angles does a right triangle have? Grid your answer.

Jericho drew a trapezoid on a piece of paper. Select all of the statements that can be true of the shape he drew.

It could have 1 perpendicular side. It could have 2 perpendicular sides.

It could have 1 pair of parallel sides. It could have 2 pairs of parallel sides. It could have 4 acute angles. It could have 1 pair of obtuse angles. It could have 4 right angles.

Mrs. Smith drew a shape on the board as shown below.

It could have 2 obtuse angles. It could have 1 pair of right angles. It could have 2 acute angles. It could have 1 pair of parallel sides.

How many sides does Mrs. Smith’s shape have? Grid your answer.

It could have 2 pairs of parallel sides.

It could have 1 perpendicular side. It could have 2 perpendicular sides.

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Use the Venn diagram below to compare and contrast the two-dimensional figures below. Figure 2

Figure 1

Draw 3 different quadrilaterals and describe how they are similar and different. Quadrilaterals 1

Quadrilaterals 2

Quadrilaterals 3

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THINK TANK QUESTION 9

Part I: Explain how each of the groups below could have been sorted. Group 1

Group 2 D

Group 3

Group 4

H E

C I

Group 1:

Group 2:

Group 3:

Group 4:

Part II: Compare and contrast Figure “C ” and Figure “G”.

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MISSION 29: IDENTIFYING LINES of symmetry Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Bootcamp STRATEGY 1: Identify a line of symmetry by determining if the 2 halves are equal when folded along a line. A trapezoid has 1 line of symmetry.

The letter “A” has 1 line of symmetry.

The number “3” has 1 line of symmetry.

Bootcamp STRATEGY 2: Identify shapes with multiple lines of symmetry by drawing lines through the center vertically, horizontally, and diagonally.

A square has 4 lines of symmetry.

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TRAIN THE BRAIN PRACTICE 1 4.G.3 (4.G.1.3) DIRECTIONS: Draw the lines of symmetry that exist for each shape below. 1

DIRECTIONS: Draw the second half of the shape to make it symmetrical. 5

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Target PRACTICE 1 1

Vita drew a line of symmetry on a happy face. Which of the following could be Vita’s line of symmetry? A

Ursula slowed her car down as she came closer the sign shown below.

Which number listed below has at least 1 line of symmetry? Grid your answer.

Which figure shown below is not symmetrical?

How many lines of symmetry does the street sign have? Grid your answer.

Select all of the letters that have at least 1 line of symmetry.

F P Q

M G V

Select all of the numbers that have no lines of symmetry.

1 8 9

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TRAIN THE BRAIN PRACTICE 2 4.G.3 (4.G.1.3) DIRECTIONS: Draw the lines of symmetry that exist for each shape below.

DIRECTIONS: Draw the second half of the shape to make it symmetrical. 5

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Target PRACTICE 2 Which of the letters below does not have at least 1 line of symmetry?

How many lines of symmetry does the figure below have? Grid your answer.

Letter “O”

Letter “H”

Letter “L”

Letter “D”

Mattie has a sticker. She drew a line of symmetry through the sticker. Which of the following shows Mattie’s sticker?

Jason had pizza for lunch. The slice of pizza he had was shaped like the triangle as shown below.

How many lines of symmetry does this triangle have? Grid your answer. C

Select all of the figures that do not show the correct line of symmetry.

Select all of the figures that show the correct line of symmetry.

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TRAIN THE BRAIN PRACTICE 3 4.G.3 (4.G.1.3) DIRECTIONS: Use the letters of the alphabet to answer the questions below.

Which letter(s) have 1 line of symmetry? ____________________________

Which letter(s) have 2 lines of symmetry? ____________________________

Which letter(s) have no lines of symmetry? ___________________________

DIRECTIONS: Use the numbers below to answer the questions below.

Which number(s) has 1 line of symmetry? ____________________________

Which number(s) have 2 lines of symmetry? ____________________________

Which number(s) have no lines of symmetry? ___________________________

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THINK TANK QUESTION DIRECTIONS: Jimmy drew a diagram of a house and explained to the class that the house is symmetrical. Is the diagram of the house below symmetrical? Draw lines of symmetry to support your answer.

Part I: Is Jimmy correct or incorrect?

Part II: If you believe the house to be symmetrical, explain why. If you believe the house to not be symmetrical, explain what could be changed to make it so.

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Four-STAR CHALLENGE - 4.G.3 (4.G.1.3) 1

How many lines of symmetry does the figure below have? Grid your answer.

How many lines of symmetry does the figure below appear to have? Grid your answer.

Which of the following shows exactly 1 line of symmetry?

Carol drew a rhombus with 1 line of symmetry. Which of the following shows Carol’s rhombus?

Identify all of the lines that do not show a line of symmetry for the figure.

Study the figure below. Identify all of the lines of symmetry for the figure.

Line A is a line of symmetry.

Line E is a line of symmetry.

Line B is a line of symmetry.

Line D is a line of symmetry.

Line C is a line of symmetry.

Line D is a line of symmetry.

Line B is a line of symmetry.

Line E is a line of symmetry.

Line A is a line of symmetry.

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Does the diagonal line drawn on the rectangle below represent a line of symmetry?

YES

Explain why or why not.

Each student in Ms. Rodriquez’s class was given a cut-out of a shape and asked to describe the number of lines of symmetry the shape has. There was 1 student that described a circle as having 2 lines of symmetry and demonstrated the symmetry by making the 2 folds shown below.

Is the student correct or incorrect? Explain your answer.

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THINK TANK QUESTION 10 Part I: Use the triangles below to determine if all triangles have the same number of lines of symmetry. (Show your work)

Triangle A has ________ line(s) of symmetry.

Identify the triangle: _____________

Triangle B has ________ line(s) of symmetry.

Identify the triangle: _____________

Triangle C has ________ line(s) of symmetry.

Identify the triangle: _____________

Part II: Explain how you arrived at your answer.

294 I Smart to the Core I Educational Bootcamp

Grade 4

Lesson Number:

Target Practice

Name: Target Practice 1

Question #:

Target Practice 2

Question #:

Four-Star Challenge Question #:

NOTE: For mixed numbers, write the whole number, leave a space, and write the fraction. Do not fill in a bubble for the empty space. 295 I Copying is strictly prohibited

NOTES

296 I Smart to the Core I Educational Bootcamp

Grade 4 - Smart to the Core (Student Booklet) - FULL

Articles inside

times as many as 15 is 45