Math in Focus TE Overview by Chris Johnson

Teacherâ&#x20AC;&#x2122;s Edition 1A

Consultant and Author Dr. Fong Ho Kheong Authors Chelvi Ramakrishnan and Bernice Lau Pui Wah

U.S. Consultants Dr. Richard Bisk, Andy Clark and Patsy F. Kanter

© 2009 Marshall Cavendish International (Singapore) Private Limited Published by Marshall Cavendish Education An imprint of Marshall Cavendish International (Singapore) Private Limited A member of Times Publishing Limited Marshall Cavendish International (Singapore) Private Limited Times Centre, 1 New Industrial Road Singapore 536196 Tel: +65 6411 0820 Fax: +65 6266 3677 E-mail: fps@sg.marshallcavendish.com Website: www.marshallcavendish.com/education/sg Distributed by Great Source A division of Houghton Mifflin Harcourt Publishing Company 181 Ballardvale Street P.O. Box 7050 Wilmington, MA 01887-7050 Tel: 1-800-289-4490 Website: www.greatsource.com First published 2009 All rights reserved. Permission is hereby granted to teachers to reprint or photocopy in classroom quantities, for use by one teacher and his or her students only, the pages in this work that carry the appropriate copyright notice, provided each copy made shows the copyright notice. Such copies may not be sold, and further distribution is expressly prohibited. Except as authorized above, no part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of Marshall Cavendish Education.

Math in Focus TM is a trademark of Marshall Cavendish Education. Great Source® is a registered trademark of Houghton Mifflin Harcourt Publishing Company. Math in Focus TM Grade 1 Teacher’s Edition Book A ISBN 978-0-669-01315-3 Printed in Singapore 1 2 3 4 5 6 7 8 MCI 16 15 14 13 12 11 10 09

1A ™

• Student Textbook in 2 parts • Teacher’s Edition in 2 parts • Other supporting components and teacher resources for differentiation and assessment

Math in Focus : The Singapore Approach is ™

the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards. Drawing on extensive feedback from teachers and students, this program has further strengthened mathematical concept development and introduced several features to meet the needs of educators and students. In the Student Textbook

The direct correlation of the workbook to the student’s textbook allows for practice, assessment, and development of problem-solving and thinking skills. Review pages promote long-term retention.

™

• Workbook in 2 parts

Math in Focus : The Singapore Approach

Consists of:

• Learn introduces concepts in an engaging and easy-tounderstand format • Guided Practice allows the teacher to work through exercises with students and assess understanding • Let’s Practice reinforces and enhances concepts learned through exercises that are worked and reviewed in class • Hands-On Activities and Games reinforce skills, concepts, and problem-solving strategies through cooperative learning • Let’s Explore provides opportunities to carry out investigative activities that apply to learning

Program Overview • Math Journal offers opportunities for reasoning and reflecting on mathematical concepts • Put on Your Thinking Cap! challenges students to apply thinking and reasoning skills to solve non-routine questions

Your Teacher’s Edition is key to the successful implementation of any mathematics program. The next few pages will help you understand and appreciate the unique attributes of the Math in Focus program. Distributed by

1037493

GREAT SOURCE

You will learn how your students will gain depth of understanding, fluency with skills, and confidence in problem solving. You will learn how to use the Workbook in conjunction with the Student Book, how to prepare students for formal assessments, and how to remediate and enrich to meet all your students’ needs.

The Story Behind Math in Focus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T4 Instructional Pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T8 Extensive Teacher Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T14 Program Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T18 Core Components . . . . . . Differentiation Resources . Assessment . . . . . . . . . . . Manipulatives . . . . . . . . . . Technology Resources . . .

. . . . .

.T18 .T19 .T20 .T21 .T21

Program Authors and Consultants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T22 Scope and Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T24 Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T35

The Story Behind

Math in Focus: The Singapore Approach is an elementary mathematics program for Kindergarten through Grade 5 created specifically to address the recommendations for instructional materials agreed upon by national and international panels of mathematics education specialists.

Meeting the Needs of U.S. Classrooms...

...by Drawing on Success in Singapore

Top performing countries have gained ground on and now surpass the U.S. in mathematics education, as shown by the Trends in International Math and Science Study (TIMSS)1. Efforts to reverse this trend have led to a large body of solid research. Analysis of the research base has led the National Council of Teachers of Mathematics (NCTM)2, the National Math Advisory Panel3, the American Institutes for Research4, and the National Research Council5 to make several undisputed key recommendations.

Singapore students have been top performers in the TIMSS assessment since 1995. Their success can be largely attributed to the mathematics curriculum revision implemented by the Singapore Ministry of Education6 in the 1980s. Key requirements of their instructional materials as described that parallel the recommendations of U.S. specialists are:

Precise framework of concepts and skills (specifics of what to exclude as well as what to include provides hierarchy and linkage)

1 Above all, a focused, coherent curriculum, without significant repitition year after year

Skills and concepts taught in depth to allow for mastery

2 An equal emphasis on conceptual understanding, and fluency with skills

Use of a concrete to visual to abstract development

(consolidation of concepts and skills)

3 Use of concrete and pictorial representations

of concepts using model drawings to connect visual representation to problem solving

4 Multi-step and non-routine problem-solving

Emphasis on problem solving considered central to all mathematics study

Footnotes 1. Gonzales, Patrick, Juan Carlos Guzmán, Lisette Partelow, Erin Pahlke, Leslie Jocelyn, David Kastberg, and Trevor Williams. Highlights From the Trends in International Mathematics and Science Study: TIMSS 2003. U.S. Department of Education, National Center for Education Statistics, 2004. 2. National Council of Teachers of Mathematics. Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, 2006. 3. National Mathematics Advisory Panel. Foundations for Success. U.S. Department of Education, 2008.

Math in Focus: The Singapore Approach

4. American Institutes for Research® What the United States Can Learn from Singapore’s World-Class Mathematics System. U. S. Department of Education Policy and Program Studies Services, 2005. 5. National Research Council. Adding It Up: Helping Children Learn Mathematics. Washington, DC, National Academy Press, 2001. 6. Ministry of Education, Singapore. Mathematics Syllabus: Primary, 2007.

Math in Focus is the Solution Math in Focus: The Singapore Approach uses the world-class Singaporean curriculum and instructional materials adapted to meet the unique needs of American teachers and students.

A Focused, Coherent Syllabus

Guided Practice

Answering the call for a “focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics,” Math in Focus authors created a strategic, articulated sequence of topics to be developed in depth to allow true mastery. (see Scope and

Match and compare. more or fewer. Sequence Introduction, Write p. T24) 1 Integrated Concepts and Skills

the WHY

Math in Focus helps students build a solid conceptual understanding through use of manipulative materials and visual models. Computational skills develop from this conceptual understanding and are reinforced through practice. As skills fluency increases, understanding is reinforced in turn. (see Learning and Consolidating Skills and

Concept Building

Draw on Solid Prior Knowledge

Skill Building

Foreshadow Specific Future Concepts

the HOW

Concepts, p. T8–T11)

le le

s s o n Lesson Objective

than

Extensive Problem Solving

sson

Abstract

than

2+ 1 =3

The creators of Math in Focus: The Singapore Approach believe not only that all children can learn math but that they can also enjoy math. Students learn to use model drawings to visualize and solve problems through mathematical reasoning and critical thinking.

Making number Patterns

consistently employs the Concrete 3

Pictorial

(see Applying Concepts and Skills, pp. T12–T13)

Abstract pedagogy. Clear and engaging visuals

that present concepts and model solutions allow all students regardless of language skills to focus on the math lesson. 4

Making number Patterns

• Make number patterns.

Pictorial are There

The Math in Focus:2The Singapore Approach series come next in the pattern?

Joe makes the pattern below using

Lesson Objective arn Make a pattern. • Make number patterns.

arn Make a pattern.

Concrete

Joe makes the pattern below using

How many

come next in the pattern. come next in the pattern?

1, 2, 3, 4, 5, 6

6 How many

Megan makes a pattern

come next in the pattern. Solve.

1, 2, Guided 3, 4, 5, 6 Practice

There areAbstract le to Concrete to Pictorial

More or fewer?

Vocabulary

pattern more than less than

Vocabulary

pattern

less than

. more than

Market research for Math in Focus included multiple rounds of research including focus group testing and discussions with experienced educators. Regional and national studies ensured that the student books and teacher support meet the current needs of students and teachers across the U.S. For more details, visit www.greatsource.com/mathinfocus

There are

than

. . lesson 2

Comparing Numbers

The Story Behind Math in Focus Gr1 TB A_Ch 1.indd 15

8/19/08 4:28:42 PM

The Story Behind Math in Focus

National and International Research Recommendations Focus and Depth

Interlocking Concepts and Skills

National Council of Teachers of Mathematics

National Math Advisory Panel

“A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades.” —Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics, 2006.

Math

Focus

• Knowledge is built carefully and thoroughly with both multi-page lessons and multi-day lessons. • Time is built into the program to develop understanding with hands-on activities with manipulatives as well as extensive skills practice.

Ways to Add . . . . . . . . . . . . . . . . . . . . .

Learn Add by counting on • Count to ﬁnd how many more • Add using number bonds Hands-On Activities Count on to add using connecting cubes • Use ten frames to add (Commutative Property) Game Card Fun! Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . 46–47 Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . 50–51

Grade 1, Chapter 3, Lesson 1

Math in Focus: The Singapore Approach

—Foundations for Success, 2008.

Math

addresses fewer topics in greater depth at each level.

“Use should be made of what is clearly known from rigorous research about how children learn, especially by recognizing the mutually-reinforcing benefits of conceptual understanding, procedural fluency, and automatic (i.e., quick and effortless) recall of facts.”

Focus

develops concepts and skills in tandem. • Manipulatives and visual representations provide a conceptual backbone. • Skills are connected to concepts through visual representations. • Extensive problem solving merges conceptual understanding with computational skills.

the WHY

Concept Building Skill Building the HOW

Hands-on Activity ThisActivity is aand number Hands-on Clear Visuals Use train. of Models

Emphasis on Problem Solving

Usetrain. to make number trains. This is a number Use 1

National Research Council

Singapore Ministry of Education

to makeMake number trains. number train with more than 3 . problem solving is central to “Opportunities 1should involveaconnecting symbolic “Mathematical representations and operations with physical or Howas many are in your pictorial a representations, well as translating Make number train with more than 3 between various symbolic representations.”

Make number train 2001. with fewer How —Adding many 2It Up: Helping areChildren ina your Learntrain? Mathematics, 2

mathematics learning. It involves the acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, than 3 . and real-world problems.” open-ended,

train? .

—Mathematics Syllabus: Primary, 2006.

How many are in your train? Make a number train with fewer than 3 . How many

are in your train? Math in Focus

Math

uses clear arn and engaging visuals that present

arn Use •

Use to count and compare. concepts and model solutions.

Minimalto textcount and simple, direct visuals allow all and compare. 5 students regardless of language skills to focus on the math lesson.

Focus

uses a scaffolded approach to solving word problems, focusing on model drawing to build success and confidence.

5 is greater than 3.

Chapter Wrap Up

• The visual representation of word problems leads to symbolic solutions of rich and complex problems.

5 is greater than 3. You have learned... 3 is less than 5. draw on prior knowledge as well as • Students

• The use of model drawings offer a visual 3 representation of word problems, leading to symbolic solutions of rich and complex problems.

3 is less than 5.

• Consistent use of the concrete–pictorial–abstract Guided Practice pedagogy repeatedly “models” the model-drawing problem-solving strategy. Find the missing numbers.

recently acquired and skills as they and Using Barconcepts Models: Addition combine problem-solving strategies with critical thinking skills.

Subtract

Solve using addition and subtraction.

Guided Practice

3 numbers. Find the missing 3

is greater than

Number Bonds: a visual for composing and decomposing numbers (Grade 1) 16 Chapter 1 Numbers to 10

Ch 1.indd 16

Chapter 1

How many marbles are there?

10 . is greater than is less. than is less than

42 + 21 = 63 There are 63 marbles.

Check the answer. 63 – 21 = 42 63 – 42 = 21 The answer is correct.

Numbers to 10

Gr1 TB A_Ch 1.indd 16

8/19/08 4:28:57 PM

Bar Model: a visual 82of representation a word problem (Grade 2)

68 add on

How many marbles are there in a

82 + 68 = 150 There are 150 marbles in all. Check the answer.

8/19/08 4:28:57 PM

4 Math in Focus T7 How The many Story Behind marbles? How many marbles are left?

tak

Instructional Pathway

Learning, Consolidating and Applying Grades 1–5 Math in Focus Student Books and Workbooks follow an instructional pathway of: • learning concepts and skills through visual lessons and teacher instruction • consolidating concepts and skills through practice, activities, and math journals, and • applying concepts and skills with extensive problem-solving practice and challenges

Learning Concepts and Skills Understanding the How and the Why

Abstract

3 4 whole

3 and 1 make 4. This picture shows a number bond.

part 30 Gr1 TB A_Ch 2.indd 30

Math in Focus: The Singapore Approach

Chapter 2

Number Bonds

6/16/08 5:09:15 PM

Making number Patterns

part

How many are in each part ?

Vocabulary

8/19/08 4:29:28 PM

Pictorial

s s o n Lesson Objective

into two parts.

Sam put

8/19/08 4:29:28 PM

Concrete

pattern more than less than

You can use a number train to make number bonds.

Vocabulary

part whole number bond

pattern

arn You can make number bonds with

less than

• Find different number bonds for numbers to 10.

. more than

Vocabulary

• Use connecting cubes or a math balance to find number bonds.

Making number Patterns

Lesson Objectives

• Make number patterns.

Making Number Bonds

come next in the pattern?

ssoN

Lesson Objective arn Make a pattern. • Make number patterns.

Grade 1 le

Manipulatives are used to explain abstract mathematical concepts.

Joe makes the pattern below using

arn Make a pattern.

Joe makes the pattern below using

Concrete 1

How many

come next in the pattern. come next in the pattern?

1, 2, 3, 4, 5, 6

6 How many

come next in the pattern. Solve.

Megan makes a pattern

1, 2, Guided 3, 4, 5, 6 Practice

How many beads come next in the pattern? Megan makes a pattern 20 Chapter 1 Numbers to 10 with beads.

Guided Practice with beads.

Building a Solid Foundation le at Each Level

Solve.

How many beads come next in the pattern?

Gr1 TB A_Ch 1.indd 20

Chapter 1 Numbers to 10

Scaffolded, coherent instruction promotes deep math understanding for all students with: • clearly explained thought processes • carefully selected visuals • minimal text • focus on both the how and the why

Gr1 TB A_Ch 1.indd 20

Each lesson in the Student Book is introduced with a Learn element. Mathematical concepts are presented in a straightforward visual format, with specific and structured learning tasks.

“

Increase the number, variety, and overall use of pictorial

”

representations directly tied to concepts in textbooks.

— National Math Advisory Panel

Within each lesson, from chapter to chapter, and from year to year, instruction follows the concrete to pictorial to abstract sequence.

Pictorial

Abstract

2+ 1 =3 Only numerals, mathematical notation, and symbols are used once students are familiar with the abstract representation.

Grade 2

arn You can use bar models to help you subtract. le

Pictures, models, and diagrams are used to present examples with solutions.

Will buys 24 eggs. He breaks 7 eggs. How many eggs do not break?

arn You can use bar models to solve

measurement problems in centimeters. Nikki has a cloth that is 45 centimeters long. She cuts it into three pieces. The first piece is 15 centimeters long. The second piece is 12 centimeters long.

Concrete

Pictorial

Find the total length of the first and second pieces.

What is the length of the third piece?

15 cm

12 cm

24 – 7 = 17

Abstract

17 eggs do not break.

? cm

15 + 12 = 27 The total length of the first and second pieces is 27 centimeters.

Check! 17 + 7 = 24

? cm

The answer is correct.

27 cm

45 cm

45 – 27 = 18 The length of the third piece is 18 centimeters.

MS_Gr2A_unit04.indd 98

Chapter 4

Using Bar Models: Addition and Subtraction

218 8/26/08 4:37:46 PM

MS_Gr2A_unit07.indd 218

Chapter 7 Metric Measurement of Length

8/26/08 12:17:51 PM

Instructional Pathway

arn You can use bar models to help you subtract.

Will buys 24 eggs. He breaks 7 eggs. How many eggs do not break?

Consolidating Concepts and Skills

24 – 7 = 17

for Deep Math Understanding

17 eggs do not break.

Guided Practice

Check!

Find the missing numbers. Use the bar model to help you.

Extensive Practice

Each Learn element of the lesson is followed by opportunities to develop deeper understanding through these features: • carefully crafted skills practice in the lesson using Guided Practice and Let’s Practice • real-world problems • independent practice in the Workbook

17 + 7 = 24 The answer is correct.

The second grade class has a new aquarium. There are 21 fi sh in it. 15 fi sh were given by families. The rest were bought by the school. How many fi sh did the school buy?

Guided Practice allows students to check their understanding while working with some guidance.

–

Chapter 4 Using Bar Models: Addition and Subtraction

Check!

MS_Gr2A_unit04.indd 98

The school bought

fi sh.

8/26/08 4:37:46 PM

Is the answer correct?

• additional practice problems in the Extra Practice Book Grade 2

Let’s Practice Solve. Draw bar models to help you. 1

Kevin scores 78 points in the first game he bowls. He scores 85 points in the second game. How many points does Kevin score for both games?

There are 147 fish in a pond. 49 of them are black. The rest are orange. How many fish are orange?

Jordan and Ling have 472 trading cards. Ling has 178 trading cards. How many trading cards does Jordan have?

8/26/08 4:37:47 PM

Name:

Date:

H A PTE

Using Bar Models: Addition and Subtraction

Practice 1

Using Part-Part-Whole in Addition and Subtraction

A bookstore has 179 chapter books. Solve. It has 243 picture books. Use the bar models to help you. How many chapter and picture books does the bookstore have? 1. Miss Lucy has 27 students in her morning ballet class. Lee has 528 United States and Singapore stamps. She has 39 students in her afternoon ballet class. He has 249 United States stamps. How many students does she have in both classes? How many Singapore stamps does he have? 27 39 © 2009 Marshall Cavendish International (Singapore) Private Limited

ON YOUR OWN

Go to Workbook A:

Practice 1, pages 73–76

102

Chapter 4

27 + 39 = She has

students in both classes.

Using Bar Models: Addition and Subtraction

MS_Gr2ATB_unit04.indd 102

Rani collects 365 beads in January. She collects 419 beads in April. How many beads does she collect in January and April? 8/26/08 7:01:42 PM

365

directs students to Workbook pages for independent practice.

419

ON YOUR OWN

She collects

beads in January and April. Lesson 1

G2_WB_Ch_04.indd 73

T10

Math in Focus: The Singapore Approach

Grade 2 Grade 2 Workbook

98 boys sign up for a school camp. 154 girls sign up for the camp also. How many children sign up for the camp in all?

Using Part-Part-Whole in Addition and Subtraction

MS_Gr2A_unit04.indd 99

consolidates learning and checks all prerequisite skills needed before students work independently in the Workbook.

Lesson 1

Using Part-Part-Whole in Addition and Subtraction

8/27/08 8:21:32 AM

Working together

Guided Practice Solve.

Players: 3-4 You need: •

What’s Hidden?

10 conecting are on the table. Howcubes to play: Pete takes 4 away. STEP STEP How many cubes aare left? 1 connecting Player 1 chooses number 2 Player 1 hides some of and shows them of them. = 10 − to the other players. 8 balls are on a table. 2 of the balls fall off the table. How many balls are left on the table?

Hands-On Work in Pairs and Small Groups

Game

Students develop concepts and explore connections as they practice skills and reasoning processes.

8−2=

STEP

The other players must tell the number of Count on to find out. There were 8.

Player 1 hid.

End

hands-on activity

Hands-On Activity and Game reinforce skills, concepts, and problem-solving strategies in small group or partner settings.

Use 1

P S T Eand

5, 6, 7, 8 You hid 3

4 Check their answer. 9 − 3 = ? Take turns to play! on the . Put 9 Then take away 3 . 9−3=

Correct!

Solve. 2

Now there are 5.

Lesson 1

Ways to Subtract

3 8−7=

10 − 5 = Chapter 4 Subtraction Facts to 10

Grade 2

Grade 1

Let’s Explore! provides opportunities for students to carry out investigative activities and to discus alternate solutions to open-ended questions.

Let’s Explore! Multiply each number by 5. 2

×5 Do you see any pattern in your answers? Describe the pattern. Now, multiply these numbers by 5. 1

×5

Grade 2 Workbook

Do you see any pattern in your answers? Name:

Describe the pattern.

Guided Practice

Let’s Practice Use dot paper to find the missing numbers. 3×5=

Tara is in at field day. 1. the skipping contest 36 16 She must skip 255 times without stopping. She has skipped 128 times without stopping. How many more times must she skip?

5×3=

Communication and Reflection 8×5=

5×8=

6×5=

5×6=

Students 4 9 ×communicate 5= 5 × 9 = with each other, discuss their thinking, and reflect on the math they are practicing.

1 2

Mr. Sanchez has a 835-page book. He has read 219 pages. How many more pages does he have to read?

ON YOUR OWN

Go to Workbook A:

Practice 4, pages 137–140

172

MS_Gr2A_unit06.indd 172

Chapter 6

Math Journal

Write an addition story or a subtraction story for each bar model. Then solve.

Solve. 4

Date:

Multiplication Tables of 2, 5, and 10

8/26/08 3:12:35 PM

44 ReADING AND?WRITING MATH 2.

Math Journal offers opportunities for students to reflect on mathematical learning.

Math Journal 63

732 – 218 = 516 Is the answer correct? Show how you would check it.

Tell how you could solve this problem. Then solve it. How could you check your answer? 2

There are 781 rooms in a hotel. 472 rooms are white. The rest are blue. How many rooms are blue?

Lesson 4

Real-World Problems: Two-Step Problems

G2_WB_Ch_04.indd 91

Chapter 3

Grade 2

MS_Gr2A_unit03.indd 70

8/27/08 8:21:35 AM

Subtraction up to 1,000

8/26/08 12:22:44 PM

Instructional Pathway

T11

Instructional Pathway

Applying Concepts and Skills Builds Real-World Problem Solvers

Grade 2 LE

SSON

Frequent Exposure

Comparing Two Sets

Lesson Objectives

Math in Focus: The Singapore Approach embeds problem solving throughout a lesson.

Vocabulary

• Model addition and subtraction as comparing sets.

compare

• Apply the inverse operations of addition and subtraction.

arn You can use bar models to show comparing sets to add.

Learn elements use models to explain computation concepts. Students become accustomed to seeing and using visual models to form mental images of mathematical ideas.

Keisha has 213 pins in her collection. Fran has 78 more pins in her collection. How many pins does Fran have in her collection? 78

213 Keisha Fran ?

213 + 78 = 291 Fran has 291 pins in her collection.

Check! 291 – 78 = 213 291 – 213 = 78 The answer is correct.

Lesson 3

109

Comparing Two Sets

MS_Gr2A_unit04.indd 109

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Grade 1 Workbook Name:

Date:

Practice 5

Mandy has 2.

? cm

toys in all. 450 cm

345 cm

The ag must be raised centimeters farther to reach the top.

children now.

11.

The total length of two pieces of wood is 215 centimeters. The rst piece is 135 centimeters long.

What is the length of the second piece? The length of the second piece is

12.

centimeters shorter than

Max is 135 centimeters tall. He is 18 centimeters taller than Rita. Rita is 30 centimeters shorter than Jan. How tall is Jan?

211

8/19/08 4:19:32 PM

Jan is

centimeters tall. Lesson 5

G2_WB_Ch_07.indd 181

T12

Math in Focus: The Singapore Approach

centimeters.

How much shorter is the second piece than the rst piece? The second piece is the rst piece.

marbles now.

Lesson 3 Real-World Problems: Addition and Subtraction Facts

G1_WB_Ch_08.indd 211

The top of the ag is 345 centimeters from the ground. How much farther must it be raised to reach the top?

Sam has 8 marbles. Lamont gives him 9 marbles. How many marbles does Sam have now?

Sam has

Date:

Solve. 10. A ag pole is 450 centimeters tall.

6 children are on the merry-go-round. 6 more children join them. How many children are there now? There are

Name:

Mandy has 5 toy bears. She also has 5 toy dogs. How many toys does she have in all?

• Word problems progress in complexity from 1-step to 2-step to multi-step.

• Each set of problems encompasses previous skills and concepts.

Grade 2 Workbook

Solve.

Frequent Practice Practice pages in the Workbook include both computation and problem-solving sections.

Real-World Problems: Addition and Subtraction Facts

Real-World Problems: Metric Length

181

8/27/08 8:26:26 AM

arn

Solve 3-step problems with models. Lisa had 1,750 stamps. Minah had 480 fewer stamps than Lisa. Lisa gave some stamps to Minah. Now, Minah has 3 times as many stamps as Lisa.

a How many stamps did Minah have at first?

Model-Drawing Strategies

1,750 Lisa Minah

Using bar models as a problem-solving tool is taught explicitly in Grades 2–5. Students become familiar with this systematic way to translate complex word problems into mathematical equations, and avoid the common issue with not knowing where to start. LE

SSON

Model Drawing • helps children solve simple and complex word problems • develops algebraic thinking • follows the introduction of operational skills • helps visualize the part-whole structure of the problem • develops operational sense • fosters proportional reasoning

b How many stamps does Lisa have now?

1,750 1 1,270  3,020

Find the total number of stamps Lisa and Minah had at first.

Adding On and Taking Away Sets

Lesson Objectives

Vocabulary

• Model addition as joining sets.

join

• Model subtraction as taking away.

Lisa

set

• Apply the inverse operations of addition and subtraction.

480

1,750  480  1,270 Minah had 1,270 stamps.

3,020

take away

Minah

3,020  4  755 Lisa has 755 stamps now.

arn You can use bar models to show joining sets to add.

Jenny has 87 marbles. Her friend gives her 78 more marbles. How many marbles does Jenny have now? 78

Lesson 3.5 Real- World Problems: Multiplication and Division 115

A set is a group of objects.

Grade 4

G4_TB_Ch_03-2.indd 115

5/30/08 10:54:03 AM

87 + 78 = 165 Jenny has 165 marbles now.

Check! 165 – 78 = 87 165 – 87 = 78 The answer is correct.

Lesson 2

103

Adding On and Taking Away Sets

Grade 2

MS_Gr2A_unit04.indd 103

Grade 2 Workbook

8/26/08 4:38:53 PM

Name:

Each Math in Focus chapter concludes with Put on Your Thinking Cap! which challenges students to solve nonroutine questions.

Put On Your Thinking Cap!

Grade 2

Put On Your Thinking Cap! Write the missing numbers. 1.

PROBleM SOlVING

–

2 – 8

– 3. 4

classifying comparing sequencing analyzing parts and whole identifying patterns and relationships induction (from speciﬁc to general) deduction (from general to speciﬁc) spatial visualization

9 9 – 3 2 8 2 7 1

– 2 4

4 2

5 0 0 – 3 4

7 0 – 2 5 1 Brian has a machine that changes numbers. 4 4 9 He puts one number into the machine and a different number comes out. Solve. the number 7 comes out. When he puts 12 into the machine, When he puts 20 into the machine, the number 15 comes out. The table on page 89 shows numbers. 996 7. his results 966 for 4 699

Answer the question.

Critical thinking skills students develop with Math in Focus include:

5 1 3

8 1 6 4 – 6 5 4 4 1 9 1 4

2 4 1 2 3

Find the missing numbers in each box.

These problems ask children to draw on deep prior knowledge as well as recently acquired concepts, combining problem-solving strategies with critical thinking skills.

• • • • • • • •

Challenging Practice

CRITIC Al THINK ING SKIllS

Challenging Problems

Date:

1 4 6

9 3 – 4 7 6 4 2 7

696

969

a. Write the numbers in order from greatest to least. b. Subtract the least number from the greatest number. Show your work.

Chapter 3

G2_WB_Ch_03.indd 67

MS_Gr2A_unit03.indd 88

Chapter 3

Subtraction up to 1,000

8/27/08 8:20:10 AM

Subtraction up to 1,000

8/26/08 12:23:40 PM

Instructional Pathway

T13

Extensive Teacher Support Step-by-Step Support

and Embedded Professional Development Math in Focus Teacher’s Editions provide comprehensive lesson plans with pacing suggestions, step-by-step instructional support, and embedded professional development including math background discussions and classroom management tips.

Math Background clearly outlines the mathematical significance of key concepts.

Skills Trace shows concepts and skills

APTER

learned in the previous level that this chapter is based on, as well as concepts and skills in the following level that this chapter will lead to.

Chapter Overview

Subtraction Facts to 10

Math Background

Skills Trace

Children have learned the part-whole concept and addition of numbers to 10. These two concepts are related to subtraction skills and concepts. In this chapter, children will learn different methods of subtraction, the most basic of which is the taking-away strategy. The addition concept is the inverse of subtraction, and one of the ways to subtract involves counting on. Other strategies are counting on, counting back, and using number bonds. All the subtraction strategies can be taught using the partwhole concept. If you know one part and the whole amount, and need to know the other part, you use subtraction. The subtraction strategy that builds and reinforces this concept most effectively involves the use of number bonds, which relate parts with the whole, and relate addition with subtraction. As is found in addition, there is an Identity Property of Subtraction. This property states that zero subtracted from any number is equal to that number. Another property of subtraction states that any number subtracted from itself equals zero. This chapter also requires children to use problem-solving skills to solve simple real-world word problems that involve subtraction. Children solve problems by writing subtraction sentences from number bonds.

Cross-Curricular Connections Reading/Language Arts Read aloud Subtraction Action by Loreen Leedy (Holiday House, © 2002) about Miss Prime and her students’ subtraction adventures at the fair. As a class, brainstorm subtraction story ideas. Choose one of them to be the setting for your own illustrated class book about subtraction.

Grade K

Represent subtraction stories with small whole numbers. (Chap. 18)

Grade 1

Subtract 2-digit numbers up to 100. (Chap. 4, 8, 13, 14 and 17)

Grade 2

Subtract 3-digit numbers up to 1000. (Chap. 3, 4, and10)

Every Day Counts® is

EVERY DAY COUNTS Calendar Math

FPO

an interactive bulletin board companion piece for grades K–5 to encourage classroom discussion through all the strands.

The October activities provide... Preview of geometric patterns and attributes of rectangles (skills and concepts taught at depth in Chapter 5) Review of number patterns (Chapter 1) and length comparisons using longer, shorter, and the same length as (Kindergarten skill) Practice of sums and differences involving the number 6 (see Lessons 1 and 2 of this chapter) and writing addition and subtraction sentences (see Lessons 3 and 4)

Cross-Curricular Connections provide

MIF_TG_Chp4_Overview.indd 59

T14

Math in Focus: The Singapore Approach

suggestions for tying the chapter topics to other parts of the student’s day.

C hapter 4: o VerVieW

64a

10/20/08 1:47:38 PM

Each chapter begins with a day of

guiding children to recall prior knowledge and a quick check to assess children’s readiness to proceed.

✔Quick Check CH

Recall Prior Knowledge

A PTER

Count on to ﬁnd the missing numbers in the pattern.

Subtraction Facts to 10 Counting

2, 3, 4,

5, 6,

5 7

, 8,

Complete the number bond. 3 6 six

Chapter Introduction

7 seven

Lesson 3 Real-World Problems: Subtraction

BIG

Lesson 2 Making Subtraction Stories

IDEA

Subtraction can be used to ﬁnd how many are left.

Lesson 4 Making Fact Families

a PTeR

Lesson Lesson Lesson Student Book A p. 64 Lesson

1 2 3 4

9 nine

1 less

1 less than 10 is 9. CH

A PTER

Number bonds Ch

Lesson 1 Ways to Subtract

8 eight

Subtraction Facts to 10

Recall Prior Knowledge

9 3

Subtraction Facts to 10

Counting

Solve . 4

3 8

is 1 less than 7.

Ways to Subtract Chapter 4

Making Subtraction Stories Real-World Problems: Subtraction

Subtraction Facts to 10

6 six

Chapter 4 Subtraction Facts to 10

Student Book A p. 65

Recall Prior Knowledge (page 65)

✔Quick Check (page 66)

Chapter 4 Basic subtraction facts are the main focus of this chapter.

Counting

Use this section as a diagnostic tool to assess children’s level 1 less than 10 is 9. of prerequisite knowledge before they progress to this chapter. Exercises 1 and 2 assess counting skills taught in Chapter 1. Number bonds Exercises 3 and 4 assess the part-whole concept of number bondsl taught in Chapter 2.

minus (–)

Chapter Opener (page 64)

show how many things to subtract

Lesson •1 Show children different numbers of objects, such as pencils Lesson 1

subtraction a number sentence that Lesson 1

sentence taking away The pictures illustrate the taking-away concept in subtraction usingrepresents the than 4 is less than 5 number bond 2-3-5. This is similar to work children didless in kindergarten. a word In this chapter subtraction will be extended to numberssubtraction up to 10 and will problem that is solved using a story include writing number bonds and number sentences for number stories. subtraction sentence

• Using the pictures in the Chapter Opener, have children describe what is fact family NEED DEFINITION happening. Be sure they recognize that the story is presented from left to right. • Ask: How many stickers did the boy start with? How many stickers did he drop? How many does he have left? • Explain to children that finding how many are left is called subtracting, and that they will learn many ways of subtracting in this chapter.

Definitions of key chapter Vocabulary for easy reference.

Big Idea previews what the chapter will teach and how it will be presented. 64

or crayons, and ask them to say the number. Lesson 1 Ways to Subtract

Lesson MakingaSubtraction • Use connecting cubes to2make number train. Ask: How Stories IDEA Take away 1 cube. Ask: How many is Lesson 1 many cubes are there? Lesson 3 Real-World Problems: Subtraction can be 1 less than this? Subtraction used to ﬁnd how

3 8

BIG

something

• They write subtraction sentences to represent familiar situations, to and take away, remove, subtract or compare begin to see the inverse relationship between addition and subtraction by using number bonds. the symbol used to

Number bonds64

Lesson 4 Making Fact Families

9 nine

1 less

Big Idea (page 64)

Children learned to count from 1 to 10 in Chapter 1.

8 eight

Student Book A p. 66

Making Fact Families

Vocabulary • Children use strategies, such as the take-away concept, number bonds, counting on and counting back to identify and learn take theseaway facts. to get rid of or remove

7 seven

many are left.

assessment

bonds form the fundamental concept in addition and Lesson Number 1

assessment pages subtraction. They are the basis for the formal definition of Student the Book A p. 64 to come Lesson subtraction 2 model y – x = z.

For additional assessment of children’s prior knowledge and chapter readiness,

Chapter 4

Subtraction Facts to 10

Student Book A p. 65

use the Chapter 4 Pretest on pages

Big Idea

Recall Prior Knowledge (page 65)

• Show children two groups of (page objects. Write the related 64)

00–00 of Assessments.

Lesson 4 number bond on the board.

Basic subtraction facts are the main focus of this chapter. • Help children recall other number bonds for addition. Indicate • Children use strategies, as the take-away concept, number bonds, that they can also use number bonds forsuch subtraction. counting on and counting back to identify and learn these facts.

Counting Children learned to count from 1 to 10 in Chapter 1.

• Show children different numbers of objects, such as penc or crayons, and ask them to say the number.

Assessment Book pp. 00–00

• They write subtraction sentences to represent familiar situations, and begin to see the inverse relationship between addition and subtraction by using number bonds.

Chapter Opener (page 64) The pictures illustrate the taking-away concept in subtraction using the number bond 2-3-5. This is similar to work children did in kindergarten. In this chapter subtraction will be extended to numbers up to 10 and will include writing number bonds and number sentences for number stories. • Using the pictures in the Chapter Opener, have children describe what is happening. Be sure they recognize that the story is presented from left to right. • Ask: How many stickers did the boy start with? How many stickers did he drop? How many does he have left?

C hApter

• Use connecting cubes to make a number train. Ask: How many cubes are there? Take away 1 cube. Ask: How many 1 less than this? 4: i ntrOductiOn 65–66

Number bonds

Number bonds form the fundamental concept in addition an subtraction. They are the basis for the formal definition of t subtraction model y – x = z. • Show children two groups of objects. Write the related number bond on the board.

• Help children recall other number bonds for addition. Indi that they can also use number bonds for subtraction.

• Explain to children that finding how many are left is called subtracting, and that they will learn many ways of subtracting in this chapter.

C hApter 4: i ntrOductiOn

Extensive Teacher Support

T15

Extensive Teacher Support For Deep Understanding Math in Focus: The Singapore Approach is designed for deep understanding through: • multi-page lessons • multi-day lessons

Practice and Apply

• support for learners

Count back from the greater number to subtract.

7 9

9 birds are on a wire. 6 birds ﬂy away. How many birds are still on the wire?

7 − 2 = Game 5

11 8 − 4 =

What’s Hidden?

8−5=

Ways to Subtract

3 Lesson Objectives

• Count backwards to subtract. • Use number bonds to subtract.

• Write and solve subtraction sentences.

arn You can subtract by taking away.

3 steps

Chapter 4 Subtraction Facts to 10

Count On to Subtract (page 70)

way concept in the wholeearlier part part is used to illustrate the 3 spiders are left. ess than y?’ Explain that 9 − 6 = 3 is a subtraction sentence. In the given example, a three. counting tape, show children how to count on from Read it as nine minus six• isUsing equal to 6 until they reach 9. Explain that since they took 3 steps to reach 9, the answer 3. 67 Lesson 1 Ways is to Subtract

he ‘less than’ concept. Show away 2 with 4 remaining. ide children in using this Day

Teach

10 −

8 balls onisa5table. P What less 8? 3 are S T E than 2 of the balls fall off the Check their answer. 48 table. How many balls are left Take on theturns table? to play! 8−5=

Children will count on from the subtrahend (the lesser number, 6) and stop −atisthe minuend (9). This is a second important read as minus. strategy for Itsubtraction. You will need to make a counting tape means subtract. for the numbers 1 to 10.

9−6=3

• Children may also use their fingers to count on. Have each Student Book p. 67 child show 6 fingers, and then show one more finger at a time until they reach 9. Ask how many more fingers they put up after the first 6. (3) Help children see that this is the answer to 9 – 6. Best Practices Check that children know how to identify the lesser number(page and 67) to count on from there.

hildren model ‘5 less than and then say: Take 5 The taking-away concept is used to illustrate the subtraction. Explain that in completing the missing taking-away d answer line. is one way to do subtraction.

Subtract by Taking away

Start by draw using79 connecting cubes to represent the spiders in the e the• children picture. Take away 6 cubes and count the number of cubes left. em count the circles hem •toWrite fill in the the subtraction missing sentence on the board. Explain the symbols and terms used: minus, subtract, equal to. • Explain that the group of items taken away is one part of the whole and the remaining group of items is another part. These two parts make up the whole. • The subtraction sentence reflects the relationship between the total and the two parts. • Draw children’s attention to the picture of the spiders in the Learn Box. Note that the spiders that are crossed out are taken away or subtracted.

8−2= is 5Guided less than 8.Practice 9

6−3=

9−5=

10 � 1 � ?

How to play: STEP

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9, 8, 7 10.

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12 (page 73)

Lesson 1

Ways to Subtract

9−2=?

STEP

Workbook A p. 1

G1_WB_Ch_04.indd 1

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1/21/08 11:44:07 A

G1_WB_Ch_04.indd 3

6, 7, 8, 9

5 2+?=5 Write a subtraction sentence for each picture. These exercises provide practice using the counting-back 723 Chapter 4 Subtraction Facts to 10 Lesson 1 Ways to Subtract 71 Example less than 7? 4 What is 3strategy in subtraction. Guide children in identifying the Answer: number to begin counting from and the number of steps to 3 crayons Student Book A p. 71 Student Book A p. 72 3 steps be counted. Hands-On Activity WORKING TOGETHER Game: 7−3= 4 1 � 8 9� For Struggling Learners Provide similar exercises for further 9 − 6 = Guided 3 Practice 5 to 8 (page 72) Differentiated Instruction (page 71) Use and . practice if necessary. TheseLearners exercises practice the counting-on strategy in subtraction. 4 is 3 less than 7. English Language 1 9 − 3 = ? This game helps reinforce the counting-on strategy in Lesson 1 Ways to Subtract 69 70 Chapter 4 Subtraction Facts to 10 For Struggling Learners on the . Children should recognize that the number of Put 9 A�counting tape may be useful for subtraction. 2 5 �new3meanings Count on and Count back may3. hold for (page 73) Then takeunit awaycubes 3 . displayed at the beginning (8) is the minuend (or children who have difficulty counting on. Have children point to on and back for some children. Relate these meanings Book strategies. A p. 69 Student Book A p. 70 9−3= 6 This practice reinforces Student subtraction Exercises 1 and initial number and count on from it. whole) and the number of counters covered is the answer to forward andthe backward by demonstrating with a toy 2 require children to use the taking-away strategy. Exercises Solve. 6 4. 9� 3 � to 8 – 5 = __. The number of unit cubes not covered is the car or rolling a pencil. As the car or pencil rolls forward, 3 and 4 require them to use the counting-on strategy. (page 70) 1 2 3 4 5 2 10 − 5 = subtrahend 3 (or one part). 8−7= 1 5 Exercises 5 and it goes ON to the next stop. As it rolls backward, it 6 require them to use the counting-back (page 72) 1 2 3 4 5 Children willtocount from the subtrahend (the lesser number, (page 69) • Facts Arrange children in groups of 3 or 4. goes BACK whereon it was. strategy. 68 Chapter 4 Subtraction to 10 Children will count back from the minuend (9). The subtrahend 6) and stop at the minuend5.(9). 10This is a second 6 important � 4 � This concept builds thechild taking-away the earlier • Haveonone put fromconcept 2 to 10incubes on the desk and tell (2) is the number steps count back. Explain strategy for subtraction. You willofneed toto make a counting tapethat counting Student Book A p. 68 the Learn box. The taking-away concept is used to illustrate ON YOUR OWN the group how many. This child then covers some of the back is yet for the numbers 1 to 10. another way to subtract. meaning of the cubes sentence ‘What is x less than y?’ Explain that Children practice the taking-away, counting on and counting with one hand. • Using a counting show children how to start by 2 how 8count on Check forthan’ Understanding 6. children 6 �tape, � to ‘less means ‘taken away from’. the given example, • Using a counting tape, show from activity: back strategies to In subtract in Practice 1, pp. 00–00hands-On of • The rest group tries to find out the number of hidden counting back from 9. Have children count back 2 steps to Guided Practice (page 68)of the 6 until Workbook 1A. These pages (with the answers) are shown at they reach 9. Explain that since they took 3 steps to 2 less than 6 cubes. means They can (page 68)to be subtracted is count the number of cubes that are not reach 9, the answer get an isanswer of 7. Note that the number 3. the to right. 1 Use2connecting cubes help children practice the takingis taken away from 6. activity reinforces taking-away concept. hidden, count on to the original number of cubes This and state thethe number of steps. away concept. Have themDifferentiation say the number they are taking away Options • Children may also use their fingers to count on. Have each Depending on Show students’ success the number of hidden cubes. • Using connecting cubes, model the ‘less than’ concept. Chapter 4 or Subtraction Facts to 10 2 also • This child activity can6•be done individually in groups. Each child Children may use their fingers to count and then count the remaining cubes before they complete the show fingers, and then show one more finger at a back. Have each withand the then Workbook pages, use these materials as needed. 6 connecting• cubes takeuncovers away 2 with 4 remaining. or group will need 10 counters amany TenAsk Frame (TR00). Workbook p. 2 Next, the volunteer the cubes and the group put fingers. children to they put one fingerAtwo subtraction sentence. time until theychild reach 9. up Ask9and how more fingers Struggling: Reteach pp. 00–00 Explain that 2members less than check 6 is 4.the Guide children in using this answer.pp. 00–00 times. Ask: many fingers upthis now? Guide children to up after the firstthe 6. subtraction (3)how Help children seeare that is the On Level: • Haveput children interpret sentence 73 4: lPractice essOnto1 relate 2 Useconcept ten frames (TR00) toC hApter helpExtra children the to solve problems. thethe answer to 9ten – 2frame is 7. on their to model 9 – see 6. itthat 9 – 3answer = ? and using second Haveand children take turns game. concepts of taking•away subtraction and playing to have the them copymaster and counters. Ask children to put 9 counters practice the taking-away concept. Guided Practice (page 69) Encourage children to write the subtraction sentences modeled. Best Practices thatAsk: children know Bestten Practices Check that children know howHow to identify theto identify on the frame and take away 3Check counters. manyhow Using connecting cubes, have children model lesstop than • Give3 each child a ten frame copymaster (TR00). Using‘5the the greater number andthere. how to count back from there and the lesser number and to count from counters are left? Tell them to on complete the subtraction Havehave themthem first show 8 circles counters then say:out Take ten8’. frame, draw 8 andand then cross 2. 5 number of steps to be counted. sentence. away from 8. 3the arecircles left. Guide them completing missing After they count that are notincrossed out, the guide numbers in the number sentence sentence. and answer line. • Encourage children to interpret and model Exercises C2hApter 4: l essOn 1 71–72 them in completing the subtraction and 3 using the second ten frame and counters. 4 Using the second ten frame, have the children draw 7 Bestcircles Practices Youcross may want teach this count day’s the lesson as and then out 3.toHave them circles a series three focusing each on oneinofthethe thatofare not mini-lessons, crossed out. Then ask them to fill missing threenumbers. methods of subtracting: taking away, counting on, and counting back. Two pages of independent practice in the 69–70correlate C hApterto4:each l essOn 1 Workbook method.

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Lesson 1

9−2=? Start from the greater number, 9. Count back 2 steps.

ON YOUR OWN

Differentiated 4 Instruction tips

You can count back to subtract.

7−3=

10 10 − 9 = = 6

✗✗✗✗✗

Student Book A p. 70

8−6=

Crossing out 6 spiders takes away 6 spiders.

Student Book A p. 69

5 −23taken = 2away from 6 is 4.

Solve.

9 spiders are having breakfast. 6 spiders walk away. How many spiders are left? 9−6=3

Ways to Subtract

Guided Practice

6, 7, 8, 9

You subtract one part from the whole to ﬁnd the other part. Lesson 1

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Practice and Apply Workbook pages for Chapter 4, Lesson 1

Name:

Ways To Subtract

Fill in the number bond. Complete the subtraction sentence.

Common Error alerts

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Complete the subtraction sentences.

6−1=5 5 4

e left on the plate.

subtract.

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not swim away. Lesson 1

Ways to Subtract

Student Book A p. 75

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Chapter 4 Subtraction Facts to 10

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(page 76)

This practice reinforces the subtraction strategies. Exercise 12. 1 uses the part-whole concept and number bond strategy. Exercise 2 uses the taking-away concept and number bond strategy.

ntify the two parts: the number of 2 y and the strawberries left. The Chapter 4 Subtraction Facts to 10 Chapter 4 Subtraction Facts to 10 8 10 work Best Practices You may want to have students in pairs aking away 1 gives the number of to complete the GuidedA Practice and/or Let’s Practice exercises. Workbook p. 8 e plate. Then have them share their results with the class. 76A C hApter 4: l essOn 1 1-4-5 to complete the subtraction G1_WB_Ch_04.indd 8

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page 67 for Day 2 resources.

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• Help children recognize that the picture shows two parts: the bean bags on the girl’s head and the bean bags on the floor. The number 5 represents the bean bags on the girl’s head. The total number is 9 and taking 5 away gives the number of bags on the floor. • Children can recall the number bond 4-5-9 to complete C hApter 4: l essOn 1 76 the subtraction sentence 9 – 5 = 4. In Chapter 2, children created the number bonds for 9, so they should see the connection and then complete the subtraction sentence.

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1/21/08 11:44:11 A

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Chapter 4

• As sw stu su

Common Error Some students may confuse the two R I V E R B A N K S subtraction sentences for a given number bond. If they write 5 1 4 8 5 3 10 9 7 2 the sentence 5 – 4 = 1, have them reread the question that Subtraction Facts to 10 was asked. Be sure they understand that the answer to the Workbook A p. 12 question should be the answer to the subtraction problem. 1/21/08 11:44:16 A

Use Number Bonds to Subtract (page 75) This example illustrates the use of the taking-away concept and number bond strategy in subtraction.

This 1 u Exer strat

• Ask the children to identify the two parts: the number of strawberries taken away and the strawberries left. The total number is 5 and taking away 1 gives the number of strawberries left on the plate.

Be to co Then

• Use the number bond 1-4-5 to complete the subtraction sentences.

13 This exercise provides practice using the part-whole concept and number bond strategy in subtraction.

74–75

C hApter 4: l essOn 1

Day Two of

Lesson 1 continues to develop the same topic.

Guided Practice provides ongoing assessment.

Extensive Teacher Support

T17

Program Components Grades 1–5 Core Components The direct correlation of Student Books and Workbooks provides the full program of learning, consolidating and practicing. Student Books and Workbooks are designed to work together. The Student Books focus on learning, classroom teaching, and discussion. The Workbook problems are assigned for individual work.

™ ™

Math in Focus : The Singapore Approach is ™

• Student Textbook in 2 parts • Workbook in 2 parts • Teacher’s Edition in 2 parts • Other supporting components and teacher resources for differentiation and assessment

In the Workbook • Practice reinforces essential mathematical concepts, skills, and problem-solving strategies • Put on Your Thinking Cap! Challenging Practice broadens students’ thinking skills and extends their understanding of mathematical concepts

arry out investigative

• Math Journal offers opportunities for reasoning and reflecting on mathematical concepts

soning and reflecting

• Chapter Review/Tests measure students’ mastery of concepts and skills in the chapter

Workbook

Teacher’s Edition

Workbook

Problem Solving challenges students to use relevant strategies for non-routine questions

ce skills, concepts, operative learning

™

ncepts learned ewed in class

Consists of:

Math in Focus : The Singapore Approach

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e adapted for U.S. Drawing on extensive ram has further nt and introduced s and students.

Math in Focus : The Singapore Approach

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the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards.

• Cumulative Reviews integrate concepts and topics after every two or three chapters

udents to apply outine questions

• Mid-Year and End-of-Year Reviews integrate topics and concepts to strengthen connections between strands

Distributed by

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Student Book

Name:

Teacher’s Edition

Workbook

™ ™

Math in Focus : The Singapore Approach is ™

Consists of: • Student Textbook in 2 parts • Teacher’s Edition in 2 parts • Other supporting components and teacher resources for differentiation and assessment

Math in Focus™: The Singapore Approach Workbook complements the student textbook using a variety of questions, word problems, and riddles for reinforcement, testing and consolidation of concepts. Drawing on extensive feedback from teachers and students, the Workbook includes sections such as Challenging Practice, Problem Solving, and Reviews. In the Workbook • Practice reinforces essential mathematical concepts, skills, and problem-solving strategies • Put on Your Thinking Cap! Challenging Practice broadens students’ thinking skills and extends their understanding of mathematical concepts

arry out investigative

• Math Journal offers opportunities for reasoning and reflecting on mathematical concepts

soning and reflecting

• Chapter Review/Tests measure students’ mastery of concepts and skills in the chapter

Workbook

Problem Solving challenges students to use relevant strategies for non-routine questions

ce skills, concepts, operative learning

™

• Workbook in 2 parts

the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards.

Math in Focus : The Singapore Approach

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Math in Focus : The Singapore Approach

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• Cumulative Reviews integrate concepts and topics after every two or three chapters

udents to apply outine questions

• Mid-Year and End-of-Year Reviews integrate topics and concepts to strengthen connections between strands

Distributed by

1037482

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1042514

Student Book

T18

GREAT SOURCE

Name:

Workbook

Math in Focus: The Singapore Approach

Teacher’s Edition

Differentiation Resources 1B

English Language Learners

™

Math in Focus : The Singapore Approach is

• Student Books

the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards.

™

• Reteach

The creators of Math in Focus™: The Singapore Approach are skilled educators who believe that every child has the potential to do well in mathematics. They understand that sometimes children may require additional support before mathematics activities can be a positive and rewarding experience for them.

• Extra Practice • Enrichment

• Assessments

• Teacher’s Edition and other teacher resources

• Technology and web-based resources

The exercises in this Reteach Book are specially designed to help children revisit the concepts, skills, and strategies presented in the Student Book and Workbook. Worked examples are clearly presented to provide guidance to children and mathematics vocabulary terms are explained in context. The questions are also accompanied by illustrations to visually support the learning process.

™

• Student Books • Reteach

• Extra Practice • Enrichment • Assessments

For Struggling Learners

• Teacher’s Edition and other teacher resources • Technology and web-based resources

1A ™

Reteach

™

• Workbooks

Reteach

Math in Focus : The Singapore Approach

Math in Focus : The Singapore Approach is the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards.

™

The clear drawings and visual aspect of Math in Focus: The Singapore Approach means the entire program is inherently accessible to English language learners. Additionally, the Math in Focus Teacher’s Edition provides lesson-specific suggestions for facilitating instruction for English language learners. • Workbooks

Components consist of:

Math in Focus : The Singapore Approach

Components consist of:

Reteach pages provide more exposure to concepts for those students who need more time to master new skills or concepts. Additionally, the Math in Focus Teacher’s Edition provides tips for helping struggling students at point of use.

Reteach

Distributed by The exercises in this Reteach Book are specially designed to help children revisit the concepts, skills, and strategies presented in the Student Book and Workbook. Worked examples are clearly presented to provide guidance to children and mathematics vocabulary terms are explained in context. The questions are also accompanied by illustrations to visually support the learning process.

1051078

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Distributed by

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1B ™

Math in Focus : The Singapore Approach is

• Student Books

the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards.

™

Extra Practice

™

• Workbooks

™

Math in Focus : The Singapore Approach

Components consist of:

• Reteach

Math in Focus™: The Singapore Approach Extra Practice Book is a series of practice and review tests to complement the Math in Focus™ Student Books and Workbooks. There are ample questions to reinforce all the concepts taught throughout the school year. • Teacher’s Edition and other A section of challenging questions called Put on Your Thinking ™ teacher resources Cap! is included at the end of each chapter to develop children’s • Technology and web-based critical thinking and problem-solving skills. A review test is resources also included at the end of each book to prepare children for statewide standardized assessments. This student-friendly book encourages excellence in mathematics through consistent hard ™ Componentswork consist and of: practice. Math in Focus : The Singapore Approach is the world-class math curriculum from Singapore adapted for U.S. • Student Books classrooms based on updated math standards. • Workbooks • Extra Practice • Enrichment

• Assessments

• Extra Practice • Enrichment

• Assessments

• Teacher’s Edition and other teacher resources

• Technology and web-based resources

1051043

Extra Practice

Distributed by

™

• Reteach

Extra Practice

Extra Practice pages correlate directly to the Workbook practices. Here again, Put on Your Thinking Cap! questions provide more practice on both non-routine and strategy-based questions.

Math in Focus : The Singapore Approach

For On-Level Students

GREAT SOURCE

Components consist of:

Math in Focus : The Singapore Approach is

• Student Books

the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards.

• Reteach • Extra Practice • Enrichment • Assessments 1

• Teacher’s Edition and other teacher resources

GREAT SOURCE

• Technology and web-based resources

™

The creators of Math in Focus™: The Singapore Approach are skilled educators who know that the learning of mathematics can be a positive and rewarding experience for children. This Enrichment Book is created to complement the Math in Focus™ elementary mathematics program. Each set of exercises is specially designed to extend the concepts, skills, and strategies that children have learned in the Student Book and Workbook. Filled with fun questions that involve logical reasoning and critical thinking, this is a book that will provide the challenge that children seek.

• Student Books

the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards.

• Reteach • Extra Practice • Enrichment • Assessments • Teacher’s Edition and other teacher resources

The creators of Math in Focus™: The Singapore Approach are skilled educators who know that the learning of mathematics can be a positive and rewarding experience for children. This Enrichment Book is created to complement the Math in Focus™ elementary mathematics program. Distributed by Each set of exercises is specially designed to extend the concepts, skills, and strategies that children have learned in the Student Book and Workbook. Filled with fun questions that involve logical reasoning and critical thinking, this is a book that will provide the challenge that children seek.

1051117

Enrichment

Enrichment exercises of varying complexity provide advanced students opportunities to extend the concepts, skills, and strategies they have learned in the Student Book and Workbook. • Technology and web-based resources

Enrichment

1A ™

Enrichment

™

For Advanced Students

• Workbooks

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Enrichment

Math in Focus : The Singapore Approach is

Math in Focus : The Singapore Approach

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Math in Focus : The Singapore Approach

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Distributed by

The Math in Focus Kindergarten program has a unique instructional pathway with special Kindergarten components. For more information visit www.greatsource.com/mathinfocus

1051116

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Program Components

T19

Program Components 1

1 Math in Focus : The Singapore Approach

Assessment Opportunities

Math in Focus: The Singapore Approach is the world-class math curriculum from Singapore adapted for U.S. classrooms based on updated math standards.

Components consist of: • Student Books

Grade 1 Assessments Book • Workbooks • Reteach

Math in Focus : The Singapore Approach Assessments Book is a series of tests designed to complement the Math in Focus Student Books. The assessments provide ample practice and exposure to standardized test format questions, giving children greater confidence in statewide assessment situations. Word problems and non-routine problems included throughout the Assessments provide important problem-solving practice.

• Extra Practice • Enrichment

• Assessments • Teacher’s Edition and other teacher resources • Technology and web-based resources

Name:

Assessments

Date:

T RE- ES

Number Bonds Distributed by

Name:

Vocabulary

Match the pictures to the number. 1.

Date: 1051205

T P RE ES

Assessment opportunities in Math in Focus offer a complete picture of student progress. The Student Book, the Workbook, the Assessments Book and the Teacher’s Edition all work in concert to provide both short-term and long-term assessment options.

Assessments

GREAT SOURCE

Number Bonds

Multiple Choice

25 Suggested Time: 30 min

(5 x 2 points = 10 points)

10 Fill in the circle next to the correct answer.

What is the missing number? 9 A 2 B 3 C 5

3 and

make 7.

7 What is the missing number? A 2

B 3

• Guided Practice in the Student Book: After each Learn element students work out Guided Practice examples with either peer or teacher input. Tips in the Teacher’s Edition help in assessing student understanding. • Common Errors in the Teacher’s Edition. Common Error alerts help teachers recognize and correct potential misconceptions before students practice on their own.

Formal Assessment • Chapter Review/Test in the Workbook: This can be used as either review exercises or formal assessment. • Chapter Assessment (Test Prep) in the Assessments Book: This can be used as an alternate chapter test.

• Mid-Year and End-of-Year Tests in the Assessments Book: These end-of book assessments in test-prep format provide cumulative assessment for each book.

T20

Math in Focus: The Singapore Approach

Grade 1

MS_Assess_1_Ch02_007-014.indd 7

B 4

C 5

Grade 1 Assessments Book

Grade 1 Assessments Book Name:

Date:

Benchmark Assessment 1

for Chapters 1 to 4

Suggested Time: 45 min

Multiple Choice

(10 x 2 points = 20 points)

Fill in the circle next to the correct answer. What comes just after 9? A 6

B 7

C 8

D 10

The numbers are arranged in a pattern. They are in order, beginning with the least.

What is the missing number? A 2

C 8

D 9

Which of these numbers is greater than 4 but less than 7? A 3

B 6

C 8

D 9

Benchmark Assessment 1

MS_Assess_1_BMA-1_028-037.indd 28

D 6

Chapter 2 Test Prep

MS_Assess_1_Ch02_007-014.indd 10

D 5

11/5/08 4:44:54 PM

A 3

• Cumulative and Mid-Year Assessments in the Workbook: These Assessments provide opportunities for consolidation of concepts and skills from small chunks of chapters. • Benchmark Tests in the Assessments Book: Midway through each book, these assessments provide further testprep practice combined with the opportunity to consolidate concepts and skills acquired over a period of time.

C 4

8 must you draw to show 9 whales? How many more whales Assessments

Ongoing Diagnostic

D 8

• Pre-Test in the Assessments Book: A paper and pencil pretest is also available for a more formal diagnostic assessment.

• Recall Prior Knowledge in the Student Book: At the start of each chapter, students review related prior knowledge, then try Quick Check questions to ensure they are ready for the new chapter.

3 ?

Prior Knowledge

11/5/08 4:51:51 PM

Grade 1 Assessments Book

11/5/08 4:44:55 PM

Classroom Manipulatives Kit for Grade 1 Manipulative use plays a key role in the concrete-pictorial-abstract learning sequence. The following materials are included in the Grade 1 Math in Focus Classroom Manipulatives Kit.

Grade 1 Manipulatives Kit

Suggested Alternatives

Attribute blocks, classroom kit

Seashells, pasta, buttons

Blank number cubes with labels

Number cards, spinners

Coin and bill combination set

Real coins and bills made from construction paper

Connecting cubes

Paper clips, beads and string

Counters, at least 4 colors

Buttons, coins, beans

Counting tape

Strips of paper cut and taped

Craft sticks (bag of 1000)

Marker sets, unused pencils

Demonstration clock

Cardboard clock face with hands attached with brad

Geometric solids

Cans, boxes, balls, or shapes made from modeling clay

Math balance

Virtual manipulatives math balance

Number cubes

Number cards, spinners

Pan balance

Ruler, paper clips, and string

Place value blocks

Grid paper cutouts

Transparent spinners

Construction paper, paper clip, and pencil

Technology Resources Convenient, practical, technology-based resources available online and on CD-ROMs to facilitate class instruction and discussions.

eBooks CD-ROM

(Student Book pages,) for use with projection technology Math in Focus

Teacher Resources CD-ROM

with Problem of the Lessons, Reteach, Extra Practice, Enrichment, and Assessments and additional blackline masters in printable pdf format

Virtual Manipulatives CD-ROM

for use with interactive whiteboard technology or other projection technology

Online Resources Visit www.greatsource.com/mathinfocus for additional resources.

Program Components

T21

Program Authors and Consultants Dr. Fong Ho Kheong Dr. Fong Ho Kheong is an Associate Professor and the Head of Math and Science Department of the Emirates College for Advanced Education in Abu Dhabi, United Arab Emirates. He was involved in training Mathematics teachers in the National Institute of Education, Nanyang Technological University, Singapore, for 25 years. He is the Founding President of the Association of the Mathematics Educators, Singapore. Dr. Fong specializes in teaching both high-ability children and children who have problems in mathematics. His research work includes diagnosing children with mathematical difďŹ culties, teaching thinking to solve mathematical problems, and applying psychological theories for the teaching and learning of mathematics. His experience in curriculum development has led him to innovate the use of the model-drawing approach to tackle challenging problems. He is the consultant and principal author of Marshall Cavendishâ&#x20AC;&#x2122;s My Pals are Here! math series, which is currently being used by 80% of the primary schools in Singapore.

Dr. Pamela Sharpe Dr. Pamela Sharpe has been involved in training teachers in both Singapore and the United Kingdom for 38 years and has also played a major role in setting up early childhood programs in Singapore. She was formerly an associate professor at the National Institute of Education, Nanyang Technological University, Singapore. She is currently a part time lecturer there, as well as a consultant for early childhood programs and early childhood intervention programs. Dr. Sharpe specializes in teaching both high-ability children and children who have problems in mathematics at the preschool level. Her research work includes studying the adjustment patterns of children in transition from preschool to primary school, as well as identifying and assessing preschool children with special needs. Dr. Sharpe has also been deeply involved in the development of the preschool mathematics curriculum in Singapore.

Chelvi Ramakrishnan Chelvi Ramakrishnan is currently the Head of the Mathematics Department in a primary school in Singapore. She has been teaching for 25 years and has authored primary mathematics books since 1997.

Bernice Lau Pui Wah Bernice Lau Pui Wah is currently the Head of the Mathematics Department in a primary school in Singapore. She has been teaching for 36 years in primary and secondary schools. She has authored primary mathematics books since 1997.

T22

Math in Focus: The Singapore Approach

Michelle Choo Michelle Choo has been teaching in Singapore for 20 years, including 5 years in the Gifted Education Program. She has been writing primary mathematics books for the past 12 years and also conducts math review classes and workshops on the use of problem-solving skills and strategies.

Gan Kee Soon Gan Kee Soon has been an Inspector of Schools, a Principal of a secondary school and a Lecturer at the National Institute of Education, Nanyang Technological University, Singapore. There, for 22 years, he trained and supervised primary mathematics teachers.

U.S. Consultants Andy Clark

Patsy F. Kanter

Andy Clark was the Math Coordinator for Portland Public Schools in Portland, Oregon, where he was previously an elementary and middle school teacher. Andy is coauthor of Every Day Counts® Calendar Math, Every Day Counts® Algebra Readiness, Partner Games, and Summer Success®: Math published by Great Source Education Group.

Patsy F. Kanter is an author, teacher, and math consultant. Until 1997, Patsy was the Lower School Math Coordinator and Assistant Principal at Isidore Newman School in New Orleans, Louisiana, for 13 years where she developed and implemented a hands-on activity-based math program. Patsy is the senior author of numerous supplemental math programs including Afterschool Achievers: Math Club K-5, Summer Success®: Math K-8, co-author of Every Day Counts® Calendar Math Grades K-6, and Every Day Counts® Partner Games K-6, published by Great Source Education Group.

Teacher Reviewers Judy Chambers, Educational Consultant

Lorianne Rotz, Assistant Principal

Kathryn Tobon, Curriculum Program

Fayetteville, GA

St. Margaret Mary Catholic School Winter Park, FL

Specialist Broward County Broward Country, FL

Carolyn Goodnight, Grade 4 Teacher Helen Carr Castello Elementary School Elk Grove, CA

Shelly Gufert, Grade 5 Special Education PS/MS 95X Bronx, NY

Karin Hanson, Math Curriculum Chair St. Robert School Shorewood, WI

Diane Popp, Middle School Teacher St. Rita of Cascia School Dayton, OH

Roslyn Rowley-Penk, Lead Science Teacher Maplewood Heights Elementary Renton, WA Elizabeth Sher, Curriculum Coordinator Gwyneed-Mercy Academy Elementary Spring House, PA

Nadine Solomon, Elementary Math & Science Specialist City of Arlington Arlington, MA

Jeanette Valore, Grade 4 Math and Science Teacher St. Anthony of Padua Catholic School The Woodlands, TX

Melissa Walsh, Elementary Math Coach Baldwin-Whitehall School District Pittsburgh, PA

Program Authors and Consultants

T23

Scope and Sequence Kindergarten–Grade 2 Key Differences

and Distinguishing Characteristics Articulated Sequence

Preparation for Algebra

Math in Focus answers the call for a coherent sequence of topics giving students time to master foundational topics, so that little repetition is required the next year. Thus, each grade level covers fewer topics but in more depth, and you will not find all topics in every grade level.

Math in Focus answers the call to prepare students for Algebra. As recommended by the National Math Panel, the Math in Focus sequence of topics emphasizes:

• “Missing topics” When a topic appears to be “missing,” you can be assured that it is found in either an earlier or later grade level. For example you will ﬁnd calendar concepts in grades K and 1, but not repeated in grade 2. • More advanced As a result of not repeating topics year after year, students who use Math in Focus will advance faster than students in other programs. As a result, you may ﬁnd topics that seem to be “too advanced.” However, you will find your students easily able to handle the challenge as long as they have had the appropriate preliminary instruction.

• Number sense, basic facts, and computation An early understanding of composition and decomposition of numbers is developed in tandem with mastery of basic facts and computation algorithms in Grades K–2. • Fractions and proportional reasoning Signiﬁcant time is allocated for in-depth work with fractions in Grades 3–5. • Problem-solving Challenging problem-solving is built into each chapter in every grade level.

Developmental Continuum Kindergarten

Grades 1–2

Grades 3–5

Foundational concepts through songs, rhymes, hands-on activities

View the complete K–5 Scope and Sequence at www.greatsource.com/mathinfocus

• counting • sorting • number sense

Concept and skill development through hands-on instruction and practice • • • •

basic facts place value mental math geometry concepts

Emphasis on problem-solving, skill consolidation, and a deep understanding in preparation for algebra • fractions • decimals

T24

Math in Focus: The Singapore Approach

• ratios • model drawing

• expressions, equations, and inequalities

Kindergarten

Grade 1

Grade 2

Use concrete and pictorial models to create a set with a given number of objects. (Up to 100)

Use concrete and pictorial models to create a set with a given number of objects. (Up to 1,000)

Group objects in tens and ones.

Group objects into hundreds, tens, and ones.

Numbers up to 100.

Group objects into equal sized groups.

Number and Operations Sets and Numbers

Number Representation

Count

Compare and Order

Place Value

Use concrete models to create a set with a given number of objects. (Up to 20)

Use cardinal and ordinal numbers.

Use cardinal and ordinal numbers up to 10th.

Use numbers to represent quantities up to 20.

Use number bonds to represent number combinations.

Use place value models to create equivalent representations of numbers.

Represent numbers to 100 on a number line.

Represent numbers to 1,000 on a number line.

Count up to 20 objects in a set.

Count to 100.

Count to 1,000.

Count on and back to 20. Count by 2s and 5s up to 20.

Count by 1s, 2s, 5s, and 10s forward and backward to 100.

Count by multiples of ones, tens, and hundreds.

Compare and order sets and numbers up to 20.

Compare and order whole numbers to 100.

Compare and order whole numbers to 1,000.

Compare and order using the terms fewer, more, less.

Compare and order using the terms same, more, fewer, greater than, less than, equal to, greatest, least.

Use <, >, = to compare numbers.

Use place-value models and place-value charts to represent numbers to 100.

Use base-ten models and place-value charts to represent numbers to 1,000.

Express numbers to 100 in standard and word forms.

Express numbers to 1,000 in terms of place value. Compose and decompose multi-digit numbers (including expanded form).

Scope and Sequence

T25

Scope and Sequence Kindergartenâ&#x20AC;&#x201C;Grade 2

Kindergarten

Grade 1

Grade 2

Number and Operations (continued) Fraction Concepts

Connect geometric concepts with unit fractions halves, thirds, and fourths. Understand the relationship between a fraction and a whole. Compare and order halves, thirds, and fourths using bar models.

Decimal Concepts

Money

Use the dollar sign and decimal point. Identify and relate coin values (penny, nickel, dime, quarter).

Identify and relate coin values (penny, nickel, dime, quarter).

Identify $1, $5, $10, $20 bills.

Count and make coin combinations.

Count and make combinations of coins and bills. Compare money amounts.

Whole Number Computation: Addition and Subtraction

Model joining and separating sets.

Model addition and subtraction situations.

Model addition and subtraction with place value.

Use +, -, and = to write number sentences for addition and subtraction stories.

Use models, numbers, and symbols for addition and subtraction facts to 20.

Recall addition and subtraction facts.

Use the order, grouping, and zero properties to develop addition and subtraction fact strategies.

Use different methods to develop fluency in adding and subtracting multi-digit numbers.

Add and subtract up to 2-digit numbers with and without regrouping.

Whole Number Computation: Addition and Subtraction Real-World Problems

Represent addition and subtraction stories.

Formulate addition and subtraction stories.

Solve addition and subtraction problems using basic facts.

T26

Math in Focus: The Singapore Approach

Solve multi-digit addition and subtraction problems by using a bar model.

Kindergarten

Grade 1

Grade 2

Number and Operations (continued) Whole Number Computation: Multiplication and Division Concepts

Count by 2s and 5s up to 20.

Count by 2s, 5s, and 10s.

Multiply and divide with 2, 3, 4, 5, and 10.

Add the same number to multiply.

Represent multiplication as repeated addition.

Represent sharing equally and making equal groups.

Represent division as repeated subtraction. Use the Ă&#x2014;, Ăˇ, and = symbols to represent multiplication and division situations.

Whole Number Computation: Multiplication and Division Real-World Problems

Use bar models to represent multiplication and division situations.

Fraction Computation

Add and subtract like fractions.

Solve multiplication and division fact problems.

Decimal Computation

Add and subtract money.

Solve addition and subtraction money problems.

Estimation and Mental Math

Use mental math strategies to add and subtract.

Estimate quantity by using referents.

Round to the nearest ten to estimate sums and differences.

Describe and extend repeating shape patterns.

Identify, describe and extend two- and three-dimensional shape patterns.

Describe, extend and create two-dimensional shape patterns.

Count by 2s and 5s.

Skip count by 2s, 5s, and 10s.

Skip count by 2s, 3s, 4s, 5s, and 10s.

Algebra Patterns

Identify a rule for sorting objects.

Properties

Describe a rule for sorting objects.

Identify and extend growing and repeating patterns.

Identify rules for number patterns.

Find missing terms in repeating patterns.

Find missing terms in growing and repeating patterns.

Find missing terms in table patterns.

Identify 0 as the identity element for addition and subtraction.

Understand that addition and subtraction are inverse operations.

Use the Associative and Commutative Properties of Addition.

Apply properties of addition. Use the Distributive Property as a multiplication strategy. Scope and Sequence

T27

Scope and Sequence Kindergartenâ&#x20AC;&#x201C;Grade 2

Kindergarten

Grade 1

Grade 2

Algebra (continued) Number Theory

Identify odd and even numbers.

Functional Relationships

Understand the relationships between the numbers in fact families.

Recognize how bar models show the relationship between bar models and number patterns.

Models

Use a variety of concrete, pictorial, and symbolic models for addition and subtraction.

Use a variety of concrete, pictorial, and symbolic models for addition, subtraction, multiplication, and division.

Model addition and subtraction situations by writing addition and subtraction number sentences.

Model multiplication and division situations by writing multiplication and division number sentences.

Number Sentences and Equations

Model addition and subtraction stories with addition and subtraction number sentences.

Use bar models and number sentences to represent real-world problems. Determine the value of missing quantities in number sentences.

Equality and Inequality

Understand the meaning of the = sign in number sentences.

Understand the difference between equality and inequality.

Use and create models that demonstrate equality or inequality. Use <, >, and = to write number sentences.

Geometry (continued) Size and Position

Two-Dimensional Shapes

T28

Understand big, middle-sized, and small.

Describe position with left and right.

Describe and compare objects by position.

Use positional words to describe location.

Identify similarities and differences. Name ďŹ&#x201A;at shapes that make up real-world objects.

Identify real-world twodimensional shapes.

Identify, describe, sort, and classify two-dimensional shapes.

Identify and describe attributes and properties of twodimensional shapes.

Math in Focus: The Singapore Approach

Identify, describe, sort, and classify two-dimensional shapes.

Kindergarten

Grade 1

Grade 2

Geometry (continued) Two-Dimensional Shapes (continued) Make flat shape pictures.

Sort and classify twodimensional shapes.

Identify parts of lines and curves.

Compose and decompose twodimensional shapes.

Compare areas using nonstandard units.

Three-Dimensional Shapes

Develop foundations for understanding area.

Name and sort solid shapes.

Identify real-world threedimensional shapes.

Understand that threedimensional shapes are made up of two-dimensional shapes.

Identify two-dimensional shapes in three-dimensional shapes.

Identify, describe, sort, and classify three-dimensional shapes.

Sort and classify threedimensional shapes.

Identify surfaces that slide, stack, and roll.

Recognize shapes from different perspectives. Make shape patterns.

Congruence and Symmetry

Compose and decompose three-dimensional shapes. Develop initial understanding of congruence and symmetry.

Measurement Length and Distance

Compare lengths and heights using non-standard units.

Compare two lengths by comparing each with a third length (transitivity).

Demonstrate linear measure as an iteration of units.

Compare and order lengths (long, short, longest, shortest).

Use a start line to measure length.

Use rulers to measure length.

Develop a background for measurement using nonstandard units.

Measure lengths, using nonstandard units.

Measure lengths in meters, centimeters, feet, and inches.

Explain the need for equallength units to measure. Count length units in groups of tens and ones.

Compare and measure lengths using customary and metric units.

Compare measurements made using different units.

Demonstrate partitioning and transitivity in relation to length.

Understand the inverse relationship between the size of a unit and the number of units.

Solve problems involving estimating, measuring, and computing length. Scope and Sequence

T29

Scope and Sequence Kindergartenâ&#x20AC;&#x201C;Grade 2

Kindergarten

Grade 1

Grade 2

Measurement (continued) Weight/Mass

Capacity/Volume

Order objects by weight.

Compare and measure weights using non-standard units.

Compare and measure masses.

Compare weights using nonstandard units.

Compare two massess by comparing eah with a third mass (transitivity).

Solve mass problems.

Compare capacities.

Measure volume (capacity) in liters. Solve volume problems.

Time

Name and order the days of the week and the months of the year.

Identify the days of the week and months of the year. Recognize the correct way to write the date.

Tell time to ďŹ ve minutes. Use A.M. and P.M.

Compare durations of events.

Tell time to the hour and half hour.

Find elapsed time.

Understand similarities and differences in objects and shapes.

Sort and classify geometric shapes.

Sort and classify two- and three-dimensional shapes by properties.

Sort and classify objects using one or two attributes.

Sort and classify data in order to make graphs.

Collect and organize data in picture graphs.

Collect and Organize Data

Organize data for a picture graph.

Collect and organize data in different ways.

Collect, sort, and organize data in different ways.

Represent Data

Represent data in picture graphs.

Represent measurements and data in picture graphs and bar graphs.

Represent data in picture graphs.

Interpret/Analyze Data

Interpret data in tally charts and bar graphs.

Interpret data in picture graphs, tally charts, and bar graphs.

Interpret picture graphs with scales.

Solve problems involving data.

Solve real-world problems using picture graphs.

Data Analysis Classifying and Sorting

Problem Solving Build Skills Through Problem Solving

Build skills in addition and subtraction through problem solving.

Build skills in addition, subtraction, and measurement through problem solving.

Build skills in addition, subtraction, multiplication, division, and measurement through problem solving.

Solve Real-World Problems

Solve real-world problems involving addition and subtraction.

Solve real-world problems involving addition, subtraction, multiplication, division, and measurement.

T30

Math in Focus: The Singapore Approach

Kindergarten

Grade 1

Grade 2

Problem Solving (continued) Use Appropriate Strategies and Thinking Skills to Solve Problems Apply and Explain Problem Solving

Apply problem-solving strategies in Put on Your Thinking Cap! and Problem Solving activities.

Solve real-world problems.

Apply and explain problemsolving processes in Put on Your Thinking Cap! and other activities.

Use models to explain reasoning.

Explore concepts more deeply and justify reasoning in Let’s Explore and Hands-On activities.

Apply Thinking Skills in Put on Your Thinking Cap!, Challenging Practice, and Problem Solving activities.

Reasoning and Proof Explore Concepts

Investigate Mathematical Ideas

Investigate ideas with two- and three-dimensional shapes.

Further investigate mathematical ideas by completing critical thinking skills activities.

Identify, Demonstrate, and Explain Mathematical Proof

Demonstrate that only a few big things ﬁt into small spaces and many small things ﬁt into big spaces.

Explore transitivity by comparing lengths and weights of three different objects.

Demonstrate the inverse relationship between the size of a unit and the number of units.

Describe, sort, and classify twoand three-dimensional shapes.

Identify and describe attributes and properties of two- and three-dimensional shapes.

Identify, describe, sort, and classify two- and threedimensional shapes.

Interpret data in tally charts and bar graphs.

Interpret picture graphs, tally charts, and bar graphs.

Interpret picture graphs with scales.

Identify and extend repeating shape patterns.

Identify and extend growing number patterns and repeating shape patterns.

Identify rules for number patterns.

Sort and classify using attributes.

Recognize shapes from different perspectives.

Identify surfaces that slide, stack, and roll.

Identify similarities and differences.

Use the Commutative and Associative Properties and tens and ones to solve twodigit addition and subtraction problems.

Explore the inverse relationship between addition and subtraction.

Use a Variety of Reasoning Skills

Scope and Sequence

T31

Scope and Sequence Kindergarten–Grade 2

Kindergarten

Grade 1

Grade 2

Communication Consolidate Mathematical Thinking

Consolidate thinking in independent activities.

Present mathematical thinking through Math Journal activities.

Communicate with Peers, Teachers, and Others

Discuss mathematical ideas in paired and small group activities.

Discuss mathematical ideas in Let’s Explore activities.

Work together in pairs or groups in Let’s Explore, Games, and other activities.

Share Mathematical Thinking

Share mathematical ideas in paired and small group activities.

Share mathematical ideas with others during Let’s Explore and Hands-On activities.

Express Mathematics Ideas

Express ideas in paired and small group activities.

Express ideas in Math Journal activities, using lesson vocabulary.

Use chapter and lesson vocabulary correctly.

Understand the relationship between counting and addition and subtraction.

Examine and apply the inverse relationship between addition and subtraction.

Understand the relationships between the numbers in fact families.

Connect geometric concepts with halves, thirds, and fourths.

Connect addition and multiplication (repeated addition).

Connect subtraction and division (repeated subtraction).

Recognize and apply different strategies for adding and subtracting 1-and 2-digit numbers.

Recognize and apply different strategies for multiplication and division facts.

Learn how place-value concepts apply to regrouping in addition and subtraction.

Understand how patterns can be described using numbers, operations, and data displays.

Connections Recognize Connections in Mathematical Ideas

Understand How Concepts Build on One Another

Understand the connection between quantities and written numerals.

Explore relationships among counting, ordering, and ordinal numbers.

Recognize the relationship between bar models, number sentences, and number patterns.

T32

Math in Focus: The Singapore Approach

Kindergarten

Grade 1

Grade 2

Connections (continued) Solve Real-World Problems in Contexts Outside of Mathematics

Solve real-world problems involving more and less.

Solve real-world problems involving addition, subtraction, and measurement.

Solve real-world problems involving addition, subtraction, multiplication, division, and measurement and data analysis.

Use concrete models to create a set with a given number of objects. (Up to 20)

Use concrete and pictorial models to create a set with a given number of objects. (Up to 100)

Use concrete and pictorial models to create a set with a given number of objects. (Up to 1,000)

Use numbers and numerals to represent quantities up to 20.

Represent numbers to 100 on a number line.

Represent numbers to 1,000 on a number line.

Representation Use Representations to Model, Organize, and Record

Use symbolic notation (<, >) to compare numbers.

Use picture cards to communicate understanding of comparisons (bigger, taller, smaller). Understand the meaning of the = sign in number sentences.

Use the +, −, and = symbols to represent addition and subtraction situations.

Use bar models to represent addition and subtraction situations.

Model addition and subtraction stories with addition and subtraction number sentences.

Represent numerical data using picture graphs, tally charts and bar graphs.

Represent numerical data using picture graphs with scales, tally charts, and bar graphs.

Represent addition and subtraction stories.

Represent sharing equally making equal groups.

Use the ×, ÷, and = symbols to represent multiplication and division situations. Represent multiplication with skip counting, dot paper arrays, and bar models. Represent division as repeated subtraction.

Describe and extend shape patterns.

Identify, describe and extend two- and three-dimensional shape patterns.

Describe a rule for sorting objects.

Identify a rule for sorting objects.

Describe, extend and create two-dimensional shape patterns.

Scope and Sequence

T33

Scope and Sequence Kindergartenâ&#x20AC;&#x201C;Grade 2

Kindergarten

Grade 1

Grade 2

Representation (continued) Use Representations to Model, Organize, and Record (continued) Select and Apply Representations to Model Problems

Interpret Phenomena Through Representations

T34

Identify and extend growing and repeating patterns.

Identify rules for number and table patterns.

Use number bonds to represent number combinations.

Use place-value models to create equivalent representations of numbers.

Use a variety of concrete, pictorial, and symbolic models for addition and subtraction.

Use a variety of concrete, pictorial, and symbolic models for addition, subtraction, multiplication, and division.

Show understanding of big, middle-sized, small, and same size.

Measure and compare lengths and weights using non-standard units.

Use metric and customary units to measure length, volume (capacity), weight and mass.

Describe and compare objects by position.

Use positional words to describe location.

Name ďŹ&#x201A;at shapes that make up real-world objects.

Identify real-world two- and three-dimensional shapes.

Represent measurements and data in picture graphs and bar graphs.

Represent data in picture graphs.

Represent data in bar graphs and picture graphs.

Order a number of objects according to length, height, or weight.

Solve problems about sharing equally and making equal groups.

Solve real-world problems about social phenomena.

Use one-to-one correspondence.

Use a variety of models for adding and subtracting.

Use bar models to represent addition, subtraction, multiplication, and division situations.

Use technology (virtual manipulatives and computers) to model and draw.

Represent quantities with objects, number cubes, and numerals.

Math in Focus: The Singapore Approach

Table of Contents CH

A PTER

Numbers to 10 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Recall Prior Knowledge and Quick Check Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–3

Counting to 10

DAY

Lesson

........................................... 4

Learn Point with your finger and count Hands-On Activity Show a number in ten a frame, then count Let’s Explore! Show numbers in different ways using a ten frame Game Land on 10! Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . . . . . . . 12

Comparing Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Learn Match and compare • Use cubes to count and compare • Count and compare Hands-On Activities Count and compare using cut-outs and ten frames • Make number trains using connecting cubes Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . . . . 17–18

Making Number Patterns

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Learn Make a pattern • Use connecting cubes to ﬁnd 1 more • Use connecting cubes to ﬁnd 1 less Hands-On Activity Make tower patterns using connecting cubes Let’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . . . . . . 25 Math Journal Reading and Writing Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . . 26A Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27A Assessments Book Test Prep 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27B

Table of Contents

T35

Math in Focus: The Singapore Approach CH

A PTER

Number Bonds Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Recall Prior Knowledge and Quick Check Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Making Number Bonds

DAY

Lesson

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Learn Make number bonds with connecting cubes • Make number bonds using a math balance Hands-On Activities Make number bonds using connecting cubes • Make number bonds using a math balance Let’s Explore! Number bonds with three numbers • Making number trains with connecting cubes (Associative Property) Let’s Practice and Practice and Apply Workbook A: Practice 1–3 . . . . . . . . . . . . . . . . . . . . 32–33 Math Journal Reading and Writing Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34–35 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36–37 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . . 37A Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A Assessments Book Test Prep 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A Workbook A: Cumulative Review for Chapters 1 and 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38B

Look for Assessment Opportunities Student Book A and Student Book B

Workbook A and Workbook B

• Quick Check at the beginning of every chapter to assess chapter readiness

• Chapter Review/Test in every chapter to review or test chapter material

• Guided Practice after every example or two to assess readiness to continue

• Cumulative Reviews eight times during the year • Mid-Year and End-of-Year Reviews to assess test readiness

T36

Math in Focus: The Singapore Approach

A PTER

Addition Facts to 10 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Recall Prior Knowledge and Quick Check

Ways to Add

DAY

Lesson

Counting • Number Bonds . . . . . . . . . . . . . . . . . . . . . 40–41

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Learn Add by counting on • Count on to ﬁnd how many more • Add using number bonds Hands-On Activities Count on to add using connecting cubes • Use ten frames to add (Commutative Property) Game Card Fun! Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . . . . 46–47 Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . . . . 50–51

Making Addition Stories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Learn Tell addition stories about a picture Let’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . . . . . . 56

Real-World Problems: Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Learn Read and understand a word problem Let’s Practice and Practice and Apply Workbook A: Practice 4 . . . . . . . . . . . . . . . . . . . . . . 59–60 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . . 61A

Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62–63 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63A Assessments Book Test Prep 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63B

Look for Practice and Problem Solving Student Book A and Student Book B

Workbook A and Workbook B

• Let’s Practice in every lesson

• Independent Practice for every lesson

• Put on Your Thinking Cap! in every chapter

Table of Contents

T37

Math in Focus: The Singapore Approach CH

A PTER

Subtraction Facts to 10 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Recall Prior Knowledge and Quick Check Counting • Number Bonds . . . . . . . . . . . . . . . . . . . . . 65–66

Ways to Subtract

DAY

Lesson

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Learn Subtract by taking away • Take away to ﬁnd how many less • Count on to subtract • Count back to subtract • Use number bonds to subtract Hands-On Activity Taking away using ten frames Game What’s Hidden? Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . . . . . . . 73 Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . . . . . . . 76

Making Subtraction Stories

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Learn Tell subtraction stories about a picture Hands-On Activity Zero concept Let’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . . . 79–80

Real-World Problems: Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Learn Read and understand a word problem • Subtract to solve word problems by taking away Let’s Practice and Practice and Apply Workbook A: Practice 4 . . . . . . . . . . . . . . . . . . . . . . . . . 84

Making Fact Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Learn Addition and subtraction are related • Use related addition facts to solve subtraction sentences • Use related subtraction facts to solve addition sentences Let’s Explore! Use cards to make number sentences Let’s Practice and Practice and Apply Workbook A: Practice 5 . . . . . . . . . . . . . . . . . . . . . . . . . 89 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90–91 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . . 91A

Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92–93 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93A Assessments Book Test Prep 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93B Workbook A: Cumulative Review for Chapters 3 and 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93C T38

Math in Focus: The Singapore Approach

A PTER

Shapes and Patterns Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Recall Prior Knowledge and Quick Check Shapes • Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96–97

Exploring Plane Shapes

DAY

Lesson

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Learn Get to know shapes • Sides and corners • Sort shapes in many ways • Shapes can be alike and different • Use folding to make shapes that are alike Hands-On Activities Sort shapes • Fold paper to make shapes that are alike Let’s Explore! Fold paper to make two new shapes Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . . .104–105 Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . . . . . . 109

Exploring Solid Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

110

Learn Get to know solid shapes • Name and compare solid shapes • Move solid shapes in different ways Hands-On Activity Find how to move solid shapes Let’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . .114–115

Making Pictures and Models with Shapes

DAY

Lesson

. . . . . . . . . . 116

Learn Combine plane shapes • Build models with solid shapes Hands-On Activities Combine shapes to make a picture • Make a picture with shapes on a computer • Combine shapes to make a new shape • Make a model with solid shapes Let’s Explore! Make a picture using cut-out shapes Let’s Practice and Practice and Apply Workbook A: Practice 4 . . . . . . . . . . . . . . . . . . . . . . . . 120 Let’s Practice and Practice and Apply Workbook A: Practice 5 . . . . . . . . . . . . . . . . . . . . . . . . 123

Seeing Shapes Around Us. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

124

Learn See shapes in things around you Hands-On Activities Find plane and solid shapes around you • Draw around solid shapes to ﬁnd plane shapes Let’s Practice and Practice and Apply Workbook A: Practice 6 . . . . . . . . . . . . . . . . . . . . .127–128

Table of Contents

T39

Math in Focus: The Singapore Approach

Making Patterns with Plane Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129

Learn Repeating patterns Hands-On Activity Make a repeating pattern on a computer Let’s Practice and Practice and Apply Workbook A: Practice 7 . . . . . . . . . . . . . . . . . . . . . . . . 131

Making Patterns with Solid Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

132

Learn Repeating patterns Hands-On Activity Make a repeating pattern with solid shapes Let’s Practice and Practice and Apply Workbook A: Practice 8 . . . . . . . . . . . . . . . . . . . . . . . . 134 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . 135A Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136-137 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137A Assessments Book Test Prep 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137B C

H A PTER

Ordinal Numbers and Position Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Recall Prior Knowledge and Quick Check Position numbers and words . . . . . . . . . . . . . . . . . . . . . . 139

Ordinal Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

140

Learn Use ordinals to tell order Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . . . . . . 144

Position Words

DAY

Lesson

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

Learn Use position words to tell order and position • Use left, right, and next to to tell relative position • More position words Hands-On Activities Talk about where children are in a row • Talk about where things are on your desk Let’s Explore! Use connecting cubes to describe a pattern involving the sum of number positions Game Find It First!

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Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . . .149–150 Let’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . . . . . 156 Math Journal Reading and Writing Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157–158 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . 159A Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160-161 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161A Assessments Book Test Prep 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161B Workbook A: Cumulative Review for Chapters 5 and 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161C CH

A PTER

Numbers to 20 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 Recall Prior Knowledge and Quick Check Counting • Comparing • Making patterns . . . . . . . . . 163–164

Counting to 20

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Learn Count on from 10 • Make a ten, then count on Game Roll the Number Cube! Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . . . . . . 170

Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

171

Learn Use place value to show numbers to 20 • Use models to show numbers to 20 Hands-On Activities Show numbers by grouping connecting cubes into a ten and ones and drawing place-value charts Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . . .173–174

Comparing Numbers

DAY

Lesson

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Learn Compare sets and numbers • Use place value to ﬁnd out how much greater or how much less • Use place value to compare three numbers Let’s Explore! Understand greatest and least using number trains Let’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . .179–180

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Making Patterns and Ordering Numbers

. . . . . . . . . . . . . . . . . . . . . . . . . 183

Learn Make patterns with connecting cubes • Find a number more than the number given • Find a number less than the number given • Order numbers from least to greatest Let’s Practice and Practice and Apply Workbook A: Practice 4 . . . . . . . . . . . . . . . . . . . . .187–188 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . 189A Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190–191 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191A Assessments Book Test Prep 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191B CH

A PTER

Addition and Subtraction Facts to 20 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Recall Prior Knowledge and Quick Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193-194 Fact families • Adding and subtracting 0 • Addition facts • Comparing numbers

Ways to Add

DAY

Lesson

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

Learn Add by making a 10 • Add by grouping into 10 and ones • Add using doubles facts • Add using doubles plus one facts Hands-On Activity Add using counters by first making a 10 Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . . . . . . 197 Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . . . . . . 199 Let’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . . . . . 202

Ways to Subtract

DAY

Lesson

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

Learn Subtract by grouping into a 10 and ones • Subtract using doubles facts of addition Game Spin and Subtract! Let’s Practice and Practice and Apply Workbook A: Practice 4 . . . . . . . . . . . . . . . . . . . . .207–208

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Real-World Problems: Addition and Subtraction Facts

. . . . . . . . . . 209

Learn Add to solve word problems • Subtract to solve word problems Let’s Explore! Make fact families Let’s Practice and Practice and Apply Workbook A: Practice 5 . . . . . . . . . . . . . . . . . . . . . . . . 213 Math Journal Reading and Writing Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .214–215 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . 215A Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216–217 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217A Assessments Book Test Prep 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217B C

H A PTER

Length Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218A Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218B Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218C Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218D Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 Recall Prior Knowledge and Quick Check Counting • Comparing numbers . . . . . . . . . . . . . . . . 219–220

Comparing Two Things

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Learn Compare the height of people • Compare the length of things Hands-On Activities Make towers and number trains with connecting cubes • Find a thing shorter and longer than your pencil Let’s Explore! Talk about a picture using height and length words Let’s Practice and Practice and Apply Workbook A: Practice 1 . . . . . . . . . . . . . . . . . . . . . . . . 225

Comparing More Than Two Things . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

226

Learn Compare the height of more than two people • Compare the height and length of more than two people Hands-On Activities Make towers with connecting cubes • Find the longest, tallest, and shortest things in the classroom Let’s Practice and Practice and Apply Workbook A: Practice 2 . . . . . . . . . . . . . . . . . . . . . . . . 230

Table of Contents

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Math in Focus: The Singapore Approach

Using a Start Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

231

Learn Compare the length of things with a start line Hands-On Activities Compare the lengths of strips of paper • Draw lines of different lengths on the computer Let’s Practice and Practice and Apply Workbook A: Practice 3 . . . . . . . . . . . . . . . . . . . . . . . . 233

Measuring Things

DAY

Lesson

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

Learn Measure length with objects • Use different objects to measure the same thing Hands-On Activities Measure length with craft sticks • Measure length with paper strips • Guess and measure length of paper strips with paper clips Let’s Practice and Practice and Apply Workbook A: Practice 4 . . . . . . . . . . . . . . . . . . . . .238–239

Finding Length in Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

240

Learn Measure length with units Hands-On Activity Measure things in the classroom with paper clips and craft sticks Let’s Practice and Practice and Apply Workbook A: Practice 5 . . . . . . . . . . . . . . . . . . . . . 244-245 Put on Your Thinking Cap! Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Practice and Apply Workbook A: Challenging Practice and Problem Solving . . . . . . . . . . . . . 247A Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248-249 Workbook A: Chapter Review/Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249A Assessments Book Test Prep 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249B Workbook A: Cumulative Review for Chapters 7 to 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249C Workbook A: Mid-Year Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249E

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250-264 Teacher Resources Professional Resources Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T45 Teaching Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T46 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T75

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Math in Focus: The Singapore Approach