Teacher s Resource€¦ · Look for Assessment Opportunities Student Book • Quick Check at the...

3A

3ATeacher’s Resource

The My Math Path 3 components work together to support student success and mathematical mastery.

The Teacher’s Resource includes the following:

• Chapter Overviews and Planning Guides for easy lesson preparation

• Math Background, outlining the mathematical significance of key concepts

• Cross-Curricular Connections that tie chapter topics to other subjects

• Differentiating Instruction opportunities for all learners

• Built-in assessment opportunities to check for student understanding

• Access to the Online Teaching Centre, which includes a Program Overview; Online Workbook, Revisit, and Enrichment; Blackline Masters; Virtual Manipulatives; Games; and activities that support Indigenous ways of knowing

My Math Path 3 components:

Teacher’s ResourceStudent BooksTeach

er’s Reso

urce

MY

MA

TH PA

TH 3

A

B

C

Teacher’s Resource

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SAMPLE LESSONS

INSIDE

ACCESS THE DEMO VERSION OF THE MY MATHPATH GRADE 3 ONLINE TEACHING CENTRE (OTC)

FOR FREE!Features include:• Additional teaching materials that support the detailed lessons

found in the print Teacher’s Resource

• Indigenous Connections through meaningful and authentic activities

• Extra practice Blackline Masters to reinforce lesson concepts and allow independent practice

• Revisit and Enrichment Blackline Masters to differentiate instruction

• Virtual Manipulatives and Games to model concepts and enhance instruction

Access your demo now!Please visit nelson.com/mmp3_OTCdemo_BC

For assistance contact Customer Support atE-mail: [email protected]: 1-800-268-222

3A











Teacher’s ResourceStudent Books

Teacher’s R

esou

rceM

Y M

ATH

PATH

3

A

B

C



My Math Path 3 at a Glance iii

My Math Path 3 at a Glance

Book A

1 Numbers to 1000

2 Addition to 1000

3 Subtraction to 1000

4 Addition and Subtraction Strategies

5 Rounding and Estimating

6 Using Bar Models: Addition and Subtraction

Book B

7 Multiplication and Division

8 Multiplication Facts for 2, 5, and 10

9 Multiplication Facts for 3 and 4

10 Length

11 Mass

12 Capacity

Book C

13 Area and Perimeter

14 Fractions

15 Money

16 Calendar and Time

17 2-D and 3-D Geometry

18 Graphs and Probability

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nelson.com/MMPCanadianReport

Learn about the research and efficacy behind Singapore Math®

and Nelson’s My Math Path3A


Consultant and AuthorDr. Fong Ho Kheong

AuthorsChelvi Ramakrishnan, Michelle Choo,

Bernice Lau Pui Wah, and Gan Kee Soon

Canadian Curriculum Advisor Dr. Douglas Edge

Canadian Program AdvisorJean Ford

Canadian Indigenous ReviewersMelissa Flynn

Nadine McSpadden

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Table of Contents

Numbers to 1000Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1A

Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1B

Assessment and Remediation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1C

Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1E

Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Recall Prior Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2–3

Quick Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4–5

1 Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Learn Read and Write Numbers to 100 in Word Form • Use Base 10 Blocks to Show Numbers • Use Base 10 Blocks to Count Forward by 1 • Use Base 10 Blocks to Count Forward by 10 • Use Base 10 Blocks to Count Forward by 100

2 Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Learn Use Base 10 Blocks and a Place-Value Chart to Show a Number • Write Numbers in Standard Form and Expanded Form

Hands-On Activity Estimating Large Quantities Using Benchmarks

Game Show the Number!

3 Comparing Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Learn Use Base 10 Blocks to Compare Numbers • Use Number Lines to Compare Numbers

Game Roll and Show!

1Chapter

Please visit the Online Teaching Centre for Program Overview, Scope and Sequence, and Planning Chart.

iv My Math Path Teacher’s Resource 3A

Look for Assessment Opportunities

Student Book

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

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

Online Workbook

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

• Cumulative Reviews seven times during the year

• Mid-Year and End-of-Year Reviews

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Table of Contents v

Addition to 1000Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47A

Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47B

Assessment and Remediation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47C

Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47E

Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47

Recall Prior Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48–49

Quick Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50–51

1 Addition and Subtraction Facts within 20 . . . . . . . . . . . . . . . . . . . . . . . . . . .53

Learn Add by Using the Make 10 Strategy • Add by Using a Doubles Fact • Subtract by Using Number Bonds

2 Addition without Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Learn Add Ones to a 3-Digit Number without Regrouping • Add a 2-Digit Number to a 3-Digit Number without Regrouping • Add a 3-Digit Number to a 3-Digit Number without Regrouping

2Chapter

ABook

4 Ordering and Patterning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Learn Use Place-Value Charts to Order Numbers • Use a Number Line to Find the Missing Number in a Pattern • Use a Number Line or a Calculator to Find the Missing Numbers in a Pattern

Math Journal

Game Roll and Count!

Let’s Explore Number Patterns

Put on Your Thinking Cap! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Look for Practice and Problem Solving

Student Book

• Let’s Practise in every lesson

• Put on Your Thinking Cap! in every chapter

Online Workbook

• Independent Practice for every lesson

• Put on Your Thinking Cap! in every chapter

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vi My Math Path Teacher’s Resource 3A

3 Addition with Regrouping in Ones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Learn Add to a 3-Digit Number with Regrouping in Ones

Game Make a Hundred!

4 Addition with Regrouping in Tens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Learn Add to a 3-Digit Number with Regrouping in Tens

5 Addition with Regrouping in Ones and Tens . . . . . . . . . . . . . . . . . . . . . 68

Learn Add to a 3-Digit Number with Regrouping in Ones and Tens

Game Go for the Greatest!

Let’s Explore Investigate the Relationship between Addition and Subtraction

Math Journal

6 Addition Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Learn Make Number Patterns Using Addition • Describe Geometric Patterns Using Numbers

Hands-On Activity Representing Geometric Patterns Using a Number Sequence

Math Journal

Put on Your Thinking Cap! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79–80

Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81–82

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ABook

Table of Contents vii

Subtraction to 1000Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83A

Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83B

Assessment and Remediation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83C

Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83E

Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83

Recall Prior Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84–85

Quick Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86–87

1 Subtraction without Regrouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

Learn Subtract a 1-Digit Number from a 3-Digit Number • Subtract a 2-Digit Number from a 3-Digit Number • Subtract a 3-Digit Number from a 3-Digit Number

Math Journal

2 Subtraction with Regrouping in Tens and Ones . . . . . . . . . . . . . . . . . . 96

Learn Subtract from a 3-Digit Number with Regrouping in Tens and Ones

Math Journal

3 Subtraction with Regrouping in Hundred and Tens . . . . . . . . . . . . . 101

Learn Subtract from a 3-Digit Number with Regrouping in Hundreds and Tens

Game Break a Hundred!

4 Subtraction with Regrouping in Hundreds, Tens, and Ones . . . 107

Learn Subtract from a 3-Digit Number with Regrouping in Hundreds, Tens, and Ones

5 Subtraction across Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Learn Subtract from Numbers with Zeros

Math Journal

6 Subtraction Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Learn Make Number Patterns Using Subtraction

Put on Your Thinking Cap! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120–121

Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122–123

3Chapter

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viii My Math Path Teacher’s Resource 3A

Addition and Subtraction StrategiesChapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124A

Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124B

Assessment and Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124C

Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124D

Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Recall Prior Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125–126

Quick Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130–131

1 Addition Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Learn Add Mentally Using the Add the Ones or Add the Tens Strategy • Add Using the Add the Ones Then Add the Tens Strategy • Add Using the Add the Tens Then Subtract the Extra Ones Strategy • Add Using the Add 100 Then Subtract the Extra Tens or Ones Strategy

2 Subtraction Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Learn Subtract Mentally Using the Subtract the Ones or Subtract the Tens Strategy • Subtract Using the Subtract from the Tens and Add the Ones Strategy • Subtract Mentally Using the Subtract the Ones Then Subtract the Tens Strategy • Subtract Using the Subtract the Tens Then Add the Extra Ones Strategy • Subtract Using the Subtract 100 Then Add the Extra Tens or Ones Strategy

3 More Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Learn Find an Unknown Result in an Addition Sentence • Find an Unknown Start Number in an Addition Sentence • Find an Unknown Change in an Addition Sentence • Find an Unknown Result in a Subtraction Sentence • Find an Unknown Start Number in a Subtraction Sentence • Find an Unknown Change in a Subtraction Sentence

Hands-On Activity Writing Problems in Different Ways

Math Journal

Put on Your Thinking Cap! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

4Chapter

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Book A

Table of Contents ix

Rounding and EstimatingChapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157A

Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157B

Assessment and Remediation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157C

Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157D

Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157

Recall Prior Knowledge and Quick Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158–159

1 Rounding Numbers to Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Learn Round a 3-Digit Number to the Nearest Ten • Round a 3-Digit Number to the Nearest Hundred • Decide Whether to Find an Estimate or an Exact Amount • Round to Estimate Sums and Check That the Answers Are Reasonable • Round to Estimate Differences and Check That the Answers Are Reasonable

2 Front-End Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Learn Identify the Leading Digit in a Number • Use Front-End Estimation to Estimate Sums and Differences • Use Front-End Estimation to Check the Reasonableness of Sums and Differences

Math Journal


Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Using Bar Models: Addition and SubtractionChapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175A

Differentiation Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175B

Assessment and Remediation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175C

Chapter Planning Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175D

Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175

Recall Prior Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176–177

Quick Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178–179

1 Real-World Problems: Two-Step Problems . . . . . . . . . . . . . . . . . . . . . . . . .180

Learn Use Bar Models to Solve 2-Step Problems

Math Journal


Chapter Wrap Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

5Chapter

6Chapter

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Chapter Overview

Addition and Subtraction Strategies4Chapter

Math BackgroundChildren learned addition and subtraction of whole numbers to 100 in My Math Path 2 by applying the concept of number bonds. Using number bonds, children were taught the strategy of grouping numbers into tens and ones and then adding or subtracting the tens and ones. With this knowledge, children learned various strategies and applied these to deal with 2-digit numbers. Additionally, children were introduced to the bar model as a way of representing addition and subtraction to 100 to apply the regrouping concept in more complex problems.

In this chapter, children apply known and new strategies to 1000. They will perform addition and subtraction using the basic add or subtract the ones or tens strategy, as well as the more advanced addtens, and then subtract the extra ones and subtract from tens and then add ones strategies. Children learn to decompose, compose, and regroup numbers in various ways, and learn how and when to apply these strategies. The concept of number bonds is integral to the mental addition and subtraction strategies.

Cross-Curricular ConnectionsScience and Technology Using natural materials gathered outside, have children work in pairs to demonstrate how to add and subtract up to 2-digit numbers concretely and pictorially. Have children make up a story about their addition or subtraction, using examples taken from the world around them.

The Arts: Drama Put children in groups of five. Have each child choose an addition strategy to act out or model for the group. Remind them to include each step they take when they add.

Skills Trace

Grade 2

• Describe a change in quantity using pictorial and symbolic representation.

• Develop a variety of strategies to add and subtract 2-digit numbers with and without regrouping.

Grade 3

• Determine the unknown number in one-step addition and subtraction equations.

• Develop a variety of strategies to add and subtract 2- and 3-digit numbers with and without regrouping.

Grade 4

• Represent and explain one-step equations with an unknown number.

• Determine the unknown number in one-step equations for all operations.

• Develop a variety of strategies to add and subtract 2-, 3-, and 4-digit numbers with and without regrouping.

CHAPTER 4: OVERVIEW 124A

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Differentiation Resources

Differentiating InstructionEnglish-Language

LearnersExtra Support

Revisit 3AAt Level

Online Workbook 3AExtension

Enrichment 3A

Lesson 1 p. 133 Worksheet 1 Practice 1

Chapter 4Lesson 2 p. 140 Worksheet 2 Practice 2

Lesson 3 p. 148 Worksheet 3 Practice 3

Additional SupportFor English-Language LearnersSelect activities that reinforce the chapter vocabulary and the connections among these words, such as having children

• add terms, definitions, and examples to the Word Wall

• draw pictures to illustrate addition and subtraction

• create posters to show the many words and symbols that can represent addition and subtraction

• discuss the Chapter Wrap Up

For Extra Support Select activities that go back to the appropriate stage of the Concrete–Pictorial–Abstract spectrum, such as having children

• regroup with manipulatives

• create number bonds

• use paper strips for bar models

See also pages 129, 133, 136, and 140.

If necessary, review

• Chapter 2 (Addition to 1000) or

• Chapter 3 (Subtraction to 1000)

For ExtensionSee suggestions on pages 136 and 137–138.

124B CHAPTER 4: DIFFERENTIATION RESOURCES



CHAPTER 4: ASSESSMENT AND REMEDIATION 124C

Assessment and Remediation

Chapter 4 AssessmentPrior Knowledge

Resource Page Numbers

Quick Check Student Book 3A p. 130–131

Formative Assessment

Guided Learning Student Book 3A pp. 133, 134, 135, 137, 140, 141, 142, 143, 145, 147, 148, 149, 150, 151, 152

Misconceptions Teacher’s Resource 3A pp. 141–142, 146

Math Journal Student Book 3A p. 155

Summative Assessment

Chapter Review/Test Online Workbook 3A Chapter 4

Math Pre-assessment 3

Number

Addition Adding Mentally

Subtraction Subtracting Mentally

Review/Test Questions Revisit Student Book

Workbook 1AGoals Online Workbook 3A Revisit 3A Student Book 3A

Add 2-digit or 3-digit numbers with and without regrouping.

1–6, 13 Worksheet 1 Lesson 1

Subtract 2-digit or 3-digit numbers with and without regrouping.

7–12, 14–15 Worksheet 2 Lesson 2

Find the missing number in addition and subtraction sentences.

13–15 Worksheet 3 Lesson 3

Remediation OptionsProblems with ... Can be remediated with ...

Additional Assessment Resources



Chapter Planning Guide

Addition and Subtraction Strategies4Chapter

124D CHAPTER 4: PLANNING GUIDE

Lesson Pacing Goals Vocabulary Resources

Chapter Openerpp. 124–131

Recall Prior KnowledgeQuick Check

*1 day Key Idea Different strategies can be used to add and subtract numbers.

Student Book 3A, pp. 124–131

Lesson 1, pp. 132–138

Addition Strategies2 days • Add 2-digit or 3-digit numbers

with and without regrouping using different strategies.

Student Book 3A, pp. 132–138Online Workbook 3A, Practice 1Revisit 3A, Worksheet 1

Lesson 2, pp. 139–146

Subtraction Strategies2 days • Subtract 2-digit or 3-digit

numbers with and without regrouping using different strategies.


Lesson 3, pp. 147–155

More Addition and Subtraction

1 day • Find the missing number in addition and subtraction sentences.


Problem Solving p. 155

Put on Your Thinking Cap!

12 day Curricular Competencies

• Understanding and Solving • Connecting and Refl ectingProblem-Solving Strategies• Work Backwards

Student Book 3A, p. 155Online Workbook 3A, Put on Your Thinking Cap!Enrichment 3A, Chapter 4

Chapter Wrap Up pp. 156

12 day • Reinforce and consolidate

chapter skills and concepts.Student Book 3A, p. 156Online Workbook 3A, Chapter Review/Test

*Assume that 1 day is a 60-minute period.



Materials Curricular Competencies

• 3 copies of Number Bonds (TR08) per child

• 3 copies of Ten Frames (TR09) per child

• a set of 50 counters in 2 different colours per child

• a pair of scissors per child

• Number Bonds (TR08) per child R & A: p. 133, Q1, 4; p. 134, Q7; p. 135, Q10; p. 137, Q13, 16; p. 138, Q1–24U & S: p. 133, Q1–6; p. 134, Q7–9; p. 135, Q10–12; p. 137, Q13–18; p. 138, Q1–24Com & Rep: p. 133, Q1, 4; p. 134, Q7; p. 135, Q10; p. 137, Q13, 16

• 6 copies of Number Bonds (TR08) per child

R & A: p. 140, Q1, 4; p. 141, Q7; p. 142, Q10; p. 143, Q13; p. 145, Q16, 19; p. 146, Q1–24U & S: p. 140, Q1–6; p. 141, Q7–9; p. 142, Q10–12; p. 143, Q13–15; p. 145, Q16–21; p. 146, Q1–24Com & Rep: p. 140, Q1, 4; p. 141, Q7; p. 142, Q10; p. 143, Q13; p. 145, Q16, 19

• 20 linking cubes per pair R & A: p. 147, Q1; p. 148, Q2; p. 149, Q3; p. 150, Q4; p. 151, Q5; p. 152, Q6U & S: p. 154, Q1–6Com & Rep: p. 153, Hands-On ActivityCon & Ref: p. 155, Math Journal

CHAPTER 4: PLANNING GUIDE 124E

Curricular Competencies LegendReasoning and Analyzing: R & AUnderstanding and Solving: U & SCommunicating and Representing:

Com & RepConnecting and Refl ecting: Con & Ref

Online Teaching Centre

• Selected Student Book pages* • Teacher’s Resource • Indigenous Connections • Blackline Masters • Problem of the Lesson • Online Workbook and Answers • Revisit and Answers • Enrichment and Answers • Virtual Manipulatives • Games

*These pages have been identifi ed for

projection or reproduction purposes.



Chapter Introduction

Student Book 3A p. 124

Addition and Subtraction Strategies4

Chapter

Different strategies can be used to add and subtract numbers.

KEY IDEA

Lessons1 Addition Strategies2 Subtraction Strategies3 More Addition and Subtraction

124

Addition and Subtraction Strategies

BIG IDEA• Development of computational fl uency in

addition, subtraction, multiplication, and division of whole numbers requires fl exible decomposing and composing.

Lesson 1 Addition Strategies

Lesson 2 Subtraction Strategies

Lesson 3 More Addition and Subtraction

4Chapter

124 CHAPTER 4: INTRODUCTION

Key Idea (page 124)

Developing strategies to add and subtract is the main focus of this chapter.

• Children use fl exible computation strategies involving taking apart and combining numbers in a variety of ways.

Chapter Opener (page 124)

This picture shows two children looking at a scoreboard at a basketball game. It models the use of math strategies in a real-world context.

• Have children look at the picture and invite them to share what they see.

• Read the boy’s speech bubble and have children consider the scores on the scoreboard. Ask: What are you trying to fi nd? (the difference between the two scores) What operation would you use? (subtraction)

• Write 107 – 80 on the board.

• Now direct children to the girl’s thought bubble. Explain the girl’s strategy. Say: The girl knows the number fact 80 + 20 = 100. So, to subtract 80, she subtracts 100 and then adds 20.

• Write 107 – 100 = 7 and 7 + 20 = 27 on the board. Ask: Is the girl’s answer correct? (yes)

• Have children discuss strategies they could use to answer the boy’s question. Guide children to check the subtraction using another math strategy they know.

As you go through this chapter with children, you may choose to enhance your lesson by using the interactive tools in the Online Teaching Centre.

Selected Student Book pages are available in the Online Teaching Centre for projection or reproduction. These pages are provided to help children record their answers.




Adding ones using the “add the ones” strategy

Adding tens mentally using the “add the tens” strategy

RECALL PRIOR KNOWLEDGE

Find 14 � 7.Group 14 into tens and ones.

Step 1 Add the ones.

Step 2 Add the result tothe tens.

So, 14 � 7 � 21.

4 � 7 � 11

10 � 11 � 214

14

10


Step 1 Add the tens.

Step 2 Add the result tothe ones.

So, 15 � 30 � 45.

10 � 30 � 40

5 � 40 � 4510

15

5

Chapter 4 Addition and Subtraction Strategies 125


Adding ones using the “add 10 then subtractthe extra ones” strategy

Adding ones mentally using the “add the ones then addthe tens” strategyFind 23 � 25.

3 � 5 � 8

20 � 20 � 40

40 � 8 � 48

20

23

3

20

25

5

Find 38 � 8.

Step 1 Add 10 to 38.

Step 2 Subtract 2from the result.

So, 38 � 8 � 46.

38 � 10 � 48

48 � 2 � 468

10

2



Step 3 Add the tensand the ones.

So, 23 � 25 � 48.

126 Chapter 4 Addition and Subtraction Strategies

CHAPTER 4: INTRODUCTION 125–126

Recall Prior Knowledge (pages 125 to 130)

Children learned various addition and subtraction strategies in My Math Path 1 and My Math Path 2, using number bonds to group 2-digit numbers in different ways. Provide children with a copy of Number Bonds (TR08) to help them work through the examples in Recall Prior Knowledge.

Adding Ones Using the Add the Ones Strategy:Children learned to apply the concept of number bonds in addition in My Math Path 1 and My Math Path 2.

• Show children the number bond that groups 14 into 1 ten and 4 ones.

• Have them add the ones separately before adding the result to the tens to get the fi nal answer.

Adding Tens Mentally Using the Add the Tens Strategy: Children learned to add tens and ones in My Math Path 2.

• Show children the number bond that groups 15 into 1 ten and 5 ones.

• Have children add the 10 and 30 separately before adding the result to the ones to get the fi nal answer.

Adding Ones Mentally Using the Add the Ones Then Add the Tens Strategy: Children learned to use number bonds to decompose 2-digit numbers into tens and ones, and then apply to addition of two 2-digit numbers in My Math Path 2.

• Have children use number bonds to group both 23 and 25 into tens and ones.

• Have them add the ones and add the tens separately before adding the results together to get the fi nal answer.

Adding Ones Using the Add 10 Then Subtract the Extra Ones Strategy: Children learned ways to make 10 in My Math Path 1, and then applied this knowledge to addition strategies of numbers to 50 in My Math Path 2.

• Have children recall how to make 10. (1 + 9; 2 + 8; 3 + 7; 4 + 6; 5 + 5)

• Have them add 8 to 38 by adding 10 and then subtracting 2 to get the fi nal answer.

Best Practices As children work through the Recall Prior Knowledge, encourage them to make a list of the different strategies. Have them write an example for each strategy. Children may refer to this as they select the best strategy to use for the addition and subtraction problems they encounter.

• Explain to the children that they will be learning strategies in this chapter to work out addition and subtraction problems.



127–128 CHAPTER 4: INTRODUCTION


Subtracting ones from 2-digit numbers using the“subtract 10 then add the extra ones” strategy

Subtracting ones from 2-digit numbers using the“subtract from the tens then add the ones” strategy

Subtracting 2-digit numbers from 2-digit numbersmentally using the “subtract the ones then subtractthe tens” strategy

Find 42 � 9.

Step 1 Subtract 10 from 42.

Step 2 Add 1 to the result.

So, 42 � 9 � 33.

42 � 10 � 32

32 � 1 � 339

10

1

Find 46 � 8.



So, 46 � 8 � 38.

40 � 8 � 32

32 � 6 � 3840

46

6

Find 37 � 16.


7 � 6 � 1


30 � 10 � 20

Step 3 Add the tens and ones.

20 � 1 � 21

So, 37 � 16 � 21.

30

37

7

10

16

6



Adding two 2-digit numbers using the “add the tensthen subtract the extra ones” strategy

Subtracting ones mentally using the “subtract theones” strategy

Subtracting tens mentally using the “subtract thetens” strategy

Find 14 � 38.


Step 2 Subtract 2from the result.

So, 14 � 38 � 52.

14 � 40 � 54

54 � 2 � 5238

40

2


Step 1 Subtract the ones.

Step 2 Add the result tothe tens.

So, 27 � 4 � 23.

7 � 4 � 3

20 � 3 � 2320

27

7


Step 1 Subtract the tens.

Step 2 Add the result tothe ones.

So, 39 � 20 � 19.

30 � 20 � 10

9 � 10 � 1930

39

9


Adding Two 2-Digit Numbers Using the Add the Tens Then Subtract the Extra Ones Strategy: Children learned to look for friendly numbers, such as multiples of 10, in My Math Path 2when performing addition mentally.

• Have children consider the numbers 14 and 38.

• Explain that 38 + 2 = 40.

• Have children add 40 and 14, before subtracting the extra 2.

Subtracting Ones Mentally Using the Subtract the OnesStrategy: Children learned to apply the concept of number bonds in subtraction in My Math Path 2.

• Have them group 27 into 2 tens and 7 ones.

• Have them subtract the ones separately before adding the result to the tens to get the fi nal answer.

Subtracting Tens Mentally Using the Subtract the TensStrategy: Children learned to subtract tens and ones in My Math Path 2.

• Have children group 39 into 3 tens and 9 ones.

• Have children subtract the tens separately before adding the result to the ones to get the fi nal answer.

Subtracting Ones from 2-Digit Numbers Using the Subtract 10 Then Add the Extra Ones Strategy: Children learned ways to make 10 in My Math Path 1, and then applied this knowledge to subtraction strategies of numbers within 50 in My Math Path 2.


• Point out that 1 more than 9 is 10.

• Have children subtract 10 from 42 and then add the extra 1.

Subtracting Ones from 2-Digit Numbers Using the Subtract from the Tens Then Add the Ones Strategy: Children learned to apply the concept of number bonds in subtraction from 2-digit numbers in My Math Path 2.

• Have children group 46 into 4 tens and 6 ones using a number bond.

• Have them subtract 8 from the tens (40), and then add the ones (6) to the result to get the fi nal answer.




Subtracting 2-digit numbers from 2-digit numbers usingthe “subtract the tens then add the extra ones” strategy

Using part-whole bar models to solve real-worldaddition problems.

10

?

12

Nyla has 10 game pieces. Her friend gives her 12 more game pieces.How many game pieces does Nyla have altogether?

10 � 12 � 22Nyla has 22 game pieces altogether.

Find 47 � 29.


47 � 30 � 17


17 � 1 � 18

So, 47 � 29 � 18.

29

30

1

I can subtract inanother way.

Step 1 47 � 27 � 20Step 2 20 � 2 � 18

27

292


Subtracting 2-Digit Numbers from 2-Digit Numbers Mentally Using the Subtract the Ones Then Subtract the Tens Strategy: Children learned to use number bonds to decompose 2-digit numbers into tens and ones and apply to subtraction involving two 2-digit numbers in My Math Path 2.

• Have children group both 37 and 16 into tens and ones using number bonds.

• Have them subtract the ones and subtract the tens separately before adding the results together to get the fi nal answer.

Subtracting 2-Digit Numbers from 2-Digit Numbers Using the Subtract the Tens Then Add the Extra Ones Strategy:Children learned to subtract 2-digit numbers from 2-digit numbers in My Math Path 2.


• Point out that 1 more than 29 is 30.

• Have children subtract 30 from 47, and then add the extra 1.

• Direct their attention to the thought bubble in the Student Book and discuss the alternate strategy shown. Explain that there are various ways to solve problems.

+ =

For Extra Support If children are struggling to apply the various strategies to add and subtract, a more concrete approach may be benefi cial. Help children to visualize decomposing and combining numbers in different ways using counters and Ten Frames (TR09). Guide children to move the counters to demonstrate the strategy being applied.For example, 23 + 25 = 20 + 20 + 3 + 5 = 40 + 8 = 48

CHAPTER 4: INTRODUCTION 129




Using part-whole bar models to solve real-worldsubtraction problems.

24

7 ?

Add. Use number bonds to help you.

1 32 � 7 � 2 41 � 8 �

3 16 � 6 � 4 23 � 7 �

5 33 � 14 � 6 24 � 15 �

7 17 � 10 � 8 13 � 20 �

9 25 � 16 � 10 19 � 21 �

Subtract.Use number bonds to help you.

11 35 � 4 � 12 48 � 5 �

13 43 � 7 � 14 31 � 9 �

15 26 � 10 � 16 33 � 20 �

17 36 � 18 � 18 45 � 29 �

Quick Check

Raphael baked 24 cookies. He and his friends ate 7 cookies. How many cookies are left?

24 � 7 � 17There are 17 cookies left.


39 49

22 30

47 39

27 33

41 40

31

36

16

18

43

22

13

16

Using Part-Whole Bar Models to Solve Real-World Addition Problems: Children learned to use part-whole bar models to solve real-world addition problems in My Math Path 2.

• Have children note how to use a part-whole bar model.

• Draw the model on the board.

• Help children relate the model to the problem by explaining how each number is represented by a bar of proportionate length.

• Lead children to see that addition is used to solve the problem.

Using Part-Whole Bar Models to Solve Real-World Subtraction Problems: Children learned to use part-whole bar models to solve real-world subtraction problems in My Math Path 2.

• Review how the subtraction part-whole model is different from the addition model.

• Point out that 24 represents the whole and that 7 represents a part of the whole.

• Remind children that they need to subtract to fi nd the other part of the whole.

Quick Check (pages 130 and 131)

Use this section as a diagnostic tool to assess children’s level of prerequisite knowledge before they progress to this chapter.

130–131 CHAPTER 4: INTRODUCTION


Solve.Use bar models to help you.19 Aurbal donated 14 hats to a local charity for the winter.

Her sister donated 17 hats.How many hats did they donate altogether?

14 � 17 �

Aurbal and her sister donated hats altogether.

20 Malik borrowed 21 books from the library.He returned 15 books to the library.How many books does he have left to return to the library?

21 � 15 �

Malik has books left to return to the library.

14 17

?

15 ?

21


31

31

6

6

Exercises 1 to 10 assess children’s ability to use math strategies to add.

Exercises 11 to 18 assess children’s ability to use math strategies to subtract.

Exercises 19 and 20 assess children’s ability to solve addition and subtraction real-world problems using part-whole bar models.



Chapter 4

Addition Strategies

LESSON OBJECTIVES• Add 2-digit or 3-digit numbers with and

without regrouping using different strategies.

DAY

1 Student Book 3A, pp. 132–134

DAY


Online Workbook 3A, Practice 1

MATERIALS• Number Bonds (TR08) per child

DIFFERENTIATION RESOURCES• Revisit 3A, Worksheet 1

5 5-minute Warm Up

• Have children work in pairs. One child picks a 2-digit number at random, while the other child picks a 1-digit number at random.

• Partners add the numbers mentally using the add the ones strategy.

• Partners switch roles and repeat.

CHAPTER 4: LESSON 1 132


LEARN You can add mentally using the “add the ones”or “add the tens” strategy.

Find 253 � 6.Group 253 into ones, and hundreds and tens.

Step 1 Add the ones. 3 � 6 � 9

Step 2 Add the result to the 250 � 9 � 259 hundreds and tens.

So, 253 � 6 � 259.

Find 213 � 50.Group 213 into tens, and hundreds and ones.

Step 1 Add the tens. 10 � 50 � 60

Step 2 Add the result to the 203 � 60 � 263hundreds and ones.

So, 213 � 50 � 263.

Goals• Add 2-digit and 3-digit numbers with and without

regrouping using different strategies.

1Lesson

Addition Strategies

3

253

250

10

213

203


TeachDAY

1

LEARN Add Mentally Using the Add the Ones or Add the Tens Strategy (page 132)

Children learn to mentally add ones or tens to a 3-digit number without regrouping.

• Review addition of a 1-digit number and a 3-digit number without regrouping in vertical form, for example, 132 + 2 and 910 + 4.

• Next show children a few number bonds for numbers less than 10, for example, 5—3–2, 8—5–3, and 9—7–2.

• Write: 253 + 6. Write the number bond 253—3–250 to separate the ones from the hundreds and tens. Ask: What is the sum of 3 and 6? (9) Write: 3 + 6 = 9. Say: Add 9 to the remaining hundreds and tens. What is the sum? (259) Write: 250 + 9 = 259. Say: So, 253 + 6 = 259.

Curricular Competencies

R & A: p. 133, Q1, 4; p. 134, Q7; p. 135, Q10; p. 137, Q13, 16; p. 138, Q1–24

U & S: p. 133, Q1–6; p. 134, Q7–9; p. 135, Q10–12; p. 137, Q13–18; p. 138, Q1–24

Com & Rep: p. 133, Q1, 4; p. 134, Q7; p. 135, Q10; p. 137, Q13, 16

1Lesson



133 CHAPTER 4: LESSON 1


Add.Use number bonds to help you.

1 Find 472 � 5. Group 472 into ones, and hundreds and tens.

2 322 � 7 �

3 414 � 5 �

4 Find 351 � 40. Group 351 into tens, and hundreds and ones.

?

351

301

5 237 � 50 �

6 613 � 70 �

Step 1 Add the tens. + 40 =

Step 2 Add the result to the hundreds and ones.

301 + =

So, 351 + 40 = .

GUIDED LEARNING

?

472

470

Step 1 Add the ones. � 5 �

Step 2 Add the result to thehundreds and tens.

470 � �

So, 472 � 5 � .

Lesson 1 Addition Strategies 133

2 7

50 90

90 391

391287

683

7 477

477

329

419

Differentiating InstructionEnglish-Language Learners

Have children repeat the words add mentally as you touch your head. Explain that when you add mentally, you do the addition in your head, not on paper.

The term strategy may be new vocabulary. Have children repeat the word strategy as you use your index fi ngers to point to your temples. Explain that when you use a strategy, you determine one way to solve a problem.

Problem of the Lesson

Complete each sentence.

(a) The sum of 684 and 135 is ___.

(b) The sum of 329 and 555 is ___.

(c) The sum of 268 and 493 is ___.

Answers:(a) 819(b) 884(c) 761

Best Practices You can teach this lesson as a series of mini-lessons, each focusing on one of the addition strategies:add the ones, add tens, then subtract the extra ones, add the tens, and add 100, then subtract the extra tens or ones.

For Extra Support You may want to assess children’s understanding in Exercises 4 to 6 by having them explain which strategy they used to add.

• Now read the second example.

• Review adding 3-digit numbers and tens without regrouping in vertical form, for example, 350 + 20 and 420 + 30.

• Next show a few examples of number bonds in tens, for example, 80—50–30, 80—60–20, and 70—40–30.

• Write: 213 + 50. Write the number bond 213—10–203 to separate the tens from the hundreds and ones. Ask: What is the sum of 10 and 50? (60) Write: 10 + 50 = 60. Say: Add 60 to the remaining hundreds and ones. What is the sum? (263) Write: 203 + 60 = 263. Say: So, 213 + 50 = 263.

Check for Understanding

Guided Learning (page 133)

1 to 3 These exercises provide practice with mental addition

using the add the ones strategy.

4 to 6 These exercises provide practice adding tens to a 3-digit number by using the add the tens strategy.



Student Book 3A p. 134 Student Book 3A p. 135

LEARN You can add using the “add the ones then add the tens” strategy.


7 Find 67 � 58.

60

67

?

50

58

?



Step 3 Add the results.

So, 67 � 58 � .

8 49 � 84 � 9 76 � 37 �

GUIDED LEARNING

Find 43 � 69.



Step 3 Add the results.

So, 43 � 69 � 112.

3 � 9 � 12

40 � 60 � 100

100 � 12 � 112

40

43

3

60

69

9

� �

� �

� �


7 8 1560 50 110110 15 125

133 113

125

LEARN You can add using the “add the tens thensubtract the extra ones” strategy.

Add.Use number bonds to help you.

10 Find 347 � 46.

46

50

?

Step 1 Add to 347.

Step 2 Subtract from the result.

So, 347 � 46 � .

11 156 � 39 � 12 223 � 57 �

GUIDED LEARNING

70 is the nearest ten to68.

Adding 68 is the sameas adding 70 andsubtracting 2.

347 � �

397 � �

Find 117 � 68.


Step 2 Subtract 2 from the result.

So, 117 � 68 � 185.

117 � 70 � 187

187 � 2 � 185

68

70

2


195 280

504

393

50 397

4 393

CHAPTER 4: LESSON 1 134–135

See the Lesson Organizer on page 132 for Day 2resources.

DAY

2 TeachLEARN Add Using the Add the Tens Then Subtract the Extra OnesStrategy (page 135)

Children learn to add the nearest tens to a 3-digit number and subtract the extra ones.

• Children learn to add two 2-digit numbers using the add the ones then add the tens strategy. You may use virtual number bonds to represent numbers to 100 to guide children to group numbers into tens and ones.

• Remind children of fi nding the nearest ten. Ask: What is the nearest ten to 68? (70) Point out that 70 is 2 more than 68.

• Write: 117 + 68 = 117 + 70 – 2. Show children the number bond grouping 70 into 68 and 2. Say: Adding 68 is the same as adding 70 and subtracting 2.

• Ask: What do you get when you add 117 and 70? (187) Write: 117 + 70 = 187. Say: Since 68 is 2 less than 70, subtract 2 from 187. Children may choose to count back in ones to do this. What is the difference? (185) Write:187 – 2 = 185. Say: So, 117 + 68 = 185.

LEARN Add Using the Add the Ones Then Add the Tens Strategy (page 134)

Children learn to group two numbers into tens and ones, and then add the tens and ones separately before adding the results to get the fi nal answer.

• Review adding 1- and 2-digit numbers with regrouping in vertical form. For example, 8 + 4 and 30 + 70.

• Write the question on the board: 43 + 69 = .

• Draw the number bonds for both numbers and point out the ones in each bond and the tens in each bond.

• Ask: What do you get when you add the ones? (3 + 9 = 12) What do you get when you add the tens? (40 + 60 = 100)

• Next say: Now add the tens and ones. What is the sum? (112) Write: 12 + 100 = 112. Say: So, 43 + 69 = 112.


7 to 9 These exercises provide practice in addition using the add the ones then add the tens strategy.




LEARN You can add using the “add 100 then subtractthe extra tens or ones” strategy.

Adding 97 is the sameas adding 100 andsubtracting 3.

Find 345 � 80.

Step 1 Add 100 to 345. 345 � 100 � 445

Step 2 Subtract 20 from 445 � 20 � 425the result.

So, 345 � 80 � 425.

80 � 100 � 20

80

100

20

Adding 80 is the same as adding100 and subtracting 20.

Find 269 � 97.


Step 2 Subtract 3 from the result.

So, 269 � 97 � 366.

269 � 100 � 369

369 � 3 � 366

97

100

3


For Extra Support Some children may struggle to fi nd the nearest ten. Recall fi nding the nearest ten on a number line. Draw a number line on the board with tens labelled and tick marks to show 10 intervals. Have children mark the number on the line. Then have them say which tens the number is between before supporting children to identify the nearest ten.


10 to 12 These exercises provide practice with addition using the add the tens then subtract the extra ones strategy.

For Extension Have children work in pairs. One child says a 3-digit number. The partner then says a multiple of 10 so that the sum of the tens of both numbers is 90 or less. The fi rst child adds the numbers using the add the tens strategy. The partner checks. For example, 437 + 40: 30 + 40 = 70, 407 + 70 = 477. Switch roles and repeat.


LEARN Add Using the Add 100 Then Subtract the Extra Tens or OnesStrategy (page 136)

Children learn to add tens to a 3-digit number with regrouping.

• Review addition of a 3-digit number and tens with regrouping in tens in vertical form. For example, 280 + 30 and 420 + 80.

• Show children a few examples of number bonds for 100 in tens. For example, 100—30–70, 100—20–80, and 100—40–60.

• Write: 345 + 80. Ask: What is the sum of 100 and 345? (445) Write: 345 + 100 = 445. Say: Since 80 = 100 – 20, subtract 20 from 445. Children may choose to count back in tens to do this. Ask: What is the difference? (425) Write:445 – 20 = 425. Say: So, 345 + 80 = 425.





13 Find 568 � 90.

90

100

?

Step 1 Add to 568.


So, 568 � 90 � .

14 465 � 70 �

15 795 � 40 �

16 Find 179 � 95.

95

100

?

Step 1 Add to 179.


So, 179 � 95 � .

17 254 � 99 �

18 384 � 98 �

GUIDED LEARNING

90 � 100 �

568 � �

� �

179 � �

279 � �


535

835

10010658

100 66810 658668

1005

274

353

482

5100 279

274

10

LET’S PRACTISEAdd. Use number bonds to help you.

1 325 � 4 � 2 734 � 3 �

3 247 � 5 � 4 8 � 339 �

5 446 � 30 � 6 628 � 20 �

7 337 � 50 � 8 421 � 60 �

9 59 � 56 � 10 76 � 65 �

11 28 � 85 � 12 93 � 27 �

13 125 � 39 � 14 214 � 67 �

15 434 � 58 � 16 88 � 309 �

17 582 � 60 � 18 675 � 70 �

19 80 � 499 � 20 747 � 90 �

21 198 � 98 � 22 359 � 96 �

23 468 � 99 � 24 593 � 97 �


329

252

476

387

115

113

164

492

642

579

296

567

737

347

648

481

141

120

281

397

745

837

455

690

Let’s Practise (page 138)

These exercises provide more practice in addition. Provide children with a copy of Number Bonds (TR08) to help them group numbers required in the different strategies.

Exercises 1 to 8 reinforce strategies used when adding without regrouping.

Exercises 9 to 24 reinforce strategies used when adding with regrouping.

Children practise addition in Practice 1 of Online Workbook 3A. These pages (with the answers) are available online.

Differentiation Options Depending on children’s success with the Online Workbook pages, use these materials as needed.Extra Support: Revisit 3A, Worksheet 1


13 to 18 These exercises provide practice with addition using the add 100 then subtract the extra tens or ones strategy.

For Extension Have children work in pairs. The fi rst child says a 3-digit number. The partner then says a multiple of ten such that the sum of the tens of both numbers is 90 or more. The fi rst child mentally adds the numbers using the add 100 then subtract the extra tens strategy. The partner checks. For example, 437 + 70: 70 = 100 – 30; 437 + 100 = 537, 537 – 30 = 507. Switch roles and repeat.

CHAPTER 4: LESSON 1 137–138



Chapter 4

More Addition and Subtraction

LESSON OBJECTIVES• Find the missing number in addition and

subtraction sentences.

DAY


Online Workbook 3A, Practice 3

MATERIALS• 20 linking cubes per pair

DIFFERENTIATION RESOURCES• Revisit 3A, Worksheet 3

5 5-minute Warm Up

• Have children work in pairs. Give each pair a set of 20 linking cubes.

• Have children use the linking cubes to show pairs of numbers. Then get them to write the fact families of these pairs of numbers. For example, 14 + 6 = 20, 6 + 14 = 20; 20 – 6 = 14, 20 – 14 = 6.

3Lesson


Goals• Find the missing number in addition and subtraction

sentences.

3 More Addition and Subtraction Lesson

LEARN You can find an unknown result in an additionsentence.

15 birds are on a tree. 5 more birds join the birds on the tree. How many birds are there on the tree in all?

We can write an addition sentence to represent the story.15 � 5 � ?

15 and 5 make 20. So, the missing number is 20. 15 � 5 � 20

There are 20 birds on the tree in all.

15

?

5

GUIDED LEARNINGis the missing number?

1 23 � 9 �

23

?

9

What is the sumof 23 and 9?

What is the result of15 and 5?

How do wefind the wholegiven 2 parts?

Lesson 3 More Addition and Subtraction 147

32

TeachDAY

1

LEARN Find an Unknown Result in an Addition Sentence (page 147)

Children learn to translate a problem into an addition sentence with an unknown result.

• Have children read the problem aloud.

• As they read the problem, draw the bar model on the board to model the given information in each line of the problem.

• Ask: What do we have to fi nd? (The total number of birds on the tree.) What do we have to do to fi nd the total number? (Add 15 and 5.)

• Have children look at the bar model. Have them identify that the unknown is the total number of birds.

• Using the bar model, guide children to write the addition sentence with the unknown result on the board. The result in this case is the total number of birds.

• Have children add 15 and 5 to fi nd the unknown result, 20.



R & A: p. 147, Q1; p. 148, Q2; p. 149, Q3; p. 150, Q4; p. 151, Q5; p. 152, Q6;

U & S: p. 154, Q1–6

Com & Rep: p. 153, Hands-On Activity

Con & Ref: p. 155, Math Journal



Problem of the Lesson

Write the given problem in different ways. One problem with an unknown start number and another with an unknown change. Then write the addition or subtraction sentence and solve for the unknown number.

There were 26 students in a classroom. 8 more students entered the classroom. How many students are there in the class now?

Solution:Answers vary. Example: There were some students in a classroom. 8 more students entered the classroom. There are 34 students altogether in the classroom. How many students were there in the classroom at fi rst?? + 8 = 34. So, 34 – 8 = 26.

Answers:The unknown start number is 26.

Check for Understanding


1 This exercise provides practice in fi nding an unknown result in an addition sentence.


LEARN You can find an unknown start number in anaddition sentence.

There were some birds on a tree. 5 more birds joined the birds on the tree. There are now 20 birds altogether on the tree. How many birds were on the tree at first?

We can write an addition sentence to represent the story. ? � 5 � 20


There were 15 birds on the tree at first.


2 � 7 � 18

?

20

5

?

18

7

What makes 20 with 5?Think of a related subtraction sentence.20 � 5 � 15

What makes 18 with 7?18 � 7 � ?


11

Differentiating InstructionEnglish-Language Learners

Children may have diffi culties differentiating among the terms result, start, and change. Tell them an addition story and relate each part of the story to the terms. For example, Tom has 5 pencils (start). He buys 7 more pencils (change). He has 12 pencils now (result).

LEARN Find an Unknown Start Number in an Addition Sentence (page 148)

Children learn to translate a problem into an addition sentence with an unknown start number.


• Point out that this problem has the same context as the one in the earlier Learn. Ask: What has changed in the problem this time? (The number of birds on the tree at the beginning is not given; the number of birds on the tree in the end is given.)

• Have children read the problem aloud again. As they read the problem, draw the bar model on the board to model the given information in each line of the problem.

• Draw children’s attention to the bar model. Ask: What do we have to fi nd? (How many birds were on the tree at fi rst.) What do we have to do to fi nd the start number? (Answers vary. Example: Subtract 5 from 20.)

• Have children identify that the unknown is the number of birds at fi rst, which is the start number.

• Using the bar model, guide children to write the addition sentence with the unknown start number on the board.

• Tell children that in this addition sentence, the start number is unknown. The start number in this case is the number of birds on the tree at fi rst.

• Have children subtract 5 from 20 to fi nd the unknown start number, 15.


2 This exercise provides practice in fi nding an unknown start number in an addition sentence.





LEARN You can find an unknown change in an additionsentence.

15 birds were on the tree. More birds joined the birds on the tree. There are now 20 birds altogether on the tree. How many birds joined the first 15 birds on the tree?

We can write an addition sentence to represent the story. 15 � ? � 20


5 birds joined the first 15 birds.


3 10 � � 25

15

20

?

10

25

?

What is added to 15 tomake 20?Think of a relatedsubtraction sentence.20 � 15 � ?

What is added to 10 tomake 25?25 � 10 � ?


15

LEARN Find an Unknown Change in an Addition Sentence (page 149)

Children learn to translate a problem into an addition sentence with an unknown change.


• Point out that this problem, again, has the same context as the ones in the two preceding Learn features. Ask: What has changed in the problem this time? (The number of birds that fl ew to the tree is not given.)


• Draw children’s attention to the bar model. Ask: What do we have to fi nd this time? (How many more birds fl ew to the tree.) What do we have to do to fi nd the change in the number of birds? (Answers vary. Example: Subtract 15 from 20.)


• Have children notice that the unknown is the number of birds that fl ew to the tree, which is the change in the number of birds.

• Using the bar model, guide children to write the addition sentence with the unknown change on the board.

• Tell children that in this addition sentence, the change is unknown. The change in this case is the number of birds that joined the birds on the tree at fi rst.

• Have children subtract 15 from 20 to fi nd the unknown change, 5.


3 This exercise provides practice in fi nding an unknown change in an addition sentence.




LEARN You can find an unknown result in a subtractionsentence.

There were 22 apples in a basket at a farmers’ market. A farmer sold 15 of the apples. How many apples were left?

We can write a subtraction sentence to represent the stor 22 � 15� ?

22 � 15 � 7 So, the missing number is 7.

7 apples were left.


4 25 � 7 �

15

22

?

7

25

?

ry.

Think of a relatedaddition sentence.15 � ? � 22

7 � ? � 25


18

LEARN Find an Unknown Result in a Subtraction Sentence (page 150)

Children learn to translate a problem into a subtraction sentence with an unknown result.


• As they read the problem, draw the bar model on the board to model the given information in each line of the problem.

• Ask: What do we have to fi nd? (the number of apples left) What do you think this is, an addition or a subtraction story? (subtraction) Why? (take away scenario)

• Ask: What do we have to do to fi nd the number of apples left? (subtract 15 from 22)

• Draw children’s attention to the bar model. Prompt them to see that the unknown is the number of apples left, which can be derived by subtracting 15 from 22.

• Using the bar model, guide children to write the subtraction sentence with the unknown result on the board.

• Tell children that in this subtraction sentence, the result is unknown. The result in this case is the number of apples left.

• Have children subtract 15 from 22 to fi nd the unknown result, 7.


4 This exercise provides practice in fi nding an unknown result in a subtraction sentence.





LEARN You can find an unknown start number in asubtraction sentence.

There were some apples in a basket at a farmers’ market. A farmer sold 15 of the apples. There were 7 apples left. How many apples were there in the basket at first?

We can write a subtraction sentence to represent the story.

? � 15 � 7

15 � 7 � 22. So, the missing number is 22. 22 � 15 � 7

22 apples were in the basket at first.


5 � 6 � 15

15

?

7

6

?

15

Write the subtraction sentenceas an addition sentence.

? � 6 � 1515 � 6 � ?


21

LEARN Find an Unknown Start Number in a Subtraction Sentence (page 151)

Children learn to translate a problem into a subtraction sentence with an unknown start number.


• Point out that this problem has the same context as the one in the preceding Learn. Ask: What has changed in the problem this time? (The number of apples at the beginning is not given; the number of apples remaining is provided.)


• Draw children’s attention to the bar model. Ask: What do we have to fi nd? (How many apples there were at the beginning.) What do we have to do to fi nd the start number? (Answers vary. Example: Add 15 and 7.)


• Prompt them to see that the unknown is the number of apples at fi rst, which is the start number.

• Using the bar model, guide children to write the subtraction sentence with the unknown start number on the board.

• Tell children that in this subtraction sentence, the start number is unknown. The start number in this case is the number of apples at the beginning.

• Have children add 15 and 7 to fi nd the unknown start number, 22.


5 This exercise provides practice in fi nding an unknown start number in a subtraction sentence.




LEARN You can find an unknown change in a subtractionsentence.

There were 22 apples in a basket at a farmers’ market. A farmer sold some of the apples. There were 7 apples left. How many apples were sold?

We can write a subtraction sentence to representthe story.

22 � ? � 7

22 � 7 � 15 So, the missing number is 15. 22 � 15 � 7

15 apples were sold.


6 32 � � 24

?

22

7

?

32

24

Write the subtractionsentence in another way. 22 � 7 � ?

Write the subtraction sentence in anotherway.


8

LEARN Find an Unknown Change in a Subtraction Sentence (page 152)

Children learn to translate a problem into a subtraction sentence with an unknown change.


• Ask: What has changed in the problem this time? (The number of apples sold is not given.)


• Draw children’s attention to the bar model. Ask: What do we have to fi nd this time? (the number of apples sold) What do we have to do to fi nd the change in the number of apples? (Answers vary. Example: Subtract 7 from 22.)

• Prompt them to see that the unknown is the number of apples sold, which is the change in the number of apples.

• Using the bar model, guide children to write the subtraction sentence with the unknown change on the board.

• Tell children that in this subtraction sentence, the change is unknown. The change in this case is the number of apples sold.

• Have children subtract 7 from 22 to fi nd the unknown change, 15.


6 This exercise provides practice in fi nding an unknown change in a subtraction sentence.





HANDS-ON ACTIVITY

Work in pairs.

Find the missing number. Then rewrite the given problem in 2 different ways.Write 1 problem with an unknown start number and the other with anunknown change. Write the addition or subtraction sentences and find theunknown.

1 Carlos has 42 game cards. He buys 15 more.How many game cards does he have altogether?42 � 15 � ?

2 There were 35 crayons in a box. Min took 18 crayons. How many crayonswere left in the box?35 � 18 � ?

essonessonnessonLe 3 ore Addition and Subtraction d Subre Ad nbtraction nd Subddition andore AddMor 153

Unknown start number: Carlos had some game cards. Then he bought 15 more. He now has 57 game cards altogether. How

Unknown change: Carlos had 42 game cards. He bought some more. He now has 57 game cards altogether. How many game

Carlos bought 15 game cards.

Unknown start number: There were some crayons in a box. Min takes 18 crayons. There are 17 crayons left in the box.

Unknown change: There were 35 crayons in a box. Min took some crayons. There are 17 crayons left in the box. How many

Min took 18 crayons from the box.

LET’S PRACTISEWhat are the missing numbers? Use the bar models to help you.

1 There are 15 stickers on a page. Alex puts more stickers on the page.

There are now 28 stickers altogether on the page. How many stickers did Alex put on the page?

2 There were some frogs in a pond. 9 of the frogs leaped away.

There are now 16 frogs left. How many frogs were there in the pond at first?

15

28

?15 � � 28

Alex put stickers on the page.

9

?

16 � 9 � 16

There were frogs in the pond at first.

3 � 15 � 33 4 17 � � 32

5 � 6 � 18 6 28 � � 19

?

33

15

18

?

6

17

32

?

?

28

19

What is the missing number in each number sentence?


1313

2525

18 15

24 9

153–154 CHAPTER 4: LESSON 3

Let’s Practise (page 154)

Exercises 1 and 4 provide practice in fi nding an unknown change in an addition problem.

Exercises 2 and 5 provide practice in fi nding an unknown start number in a subtraction problem.

Exercise 3 provides practice in fi nding an unknown start number in an addition sentence.

Exercise 6 provides practice in fi nding an unknown change in a subtraction sentence.

Hands-On Activity:

Writing Problems in Different Ways(page 153)

This activity provides children with the opportunity to explore writing problems in different ways to better understand the construct of a problem.

• Have children work in pairs.

• Lead children to see that in both the given problems, the unknowns are results of an addition or subtraction story.

• Allow children time to think of how they can rewrite each problem such that the unknown changes.

• Encourage children to draw bar models to help them better interpret the parts of the problem.

• Conclude that given two parts they can fi nd the whole; given the whole and one of the parts, they can fi nd the other part.



CRITICAL THINKING AND PROBLEM SOLVING

Put on Your Thinking Cap! (page 155)

These problem-solving exercises enable children to apply their knowledge of addition and subtraction strategies. Children work individually or in groups to answer the questions and present their solutions to the class.

• 1 and 2 Read and explain the questions, ensuring children understand what they are trying to fi nd (the two starting numbers).

• In 1 if necessary, help children get started by drawing a number bond for 382 with question marks in the two circles underneath to highlight what they are trying to fi nd.

• Encourage children to consider the sequencing of the mental strategies in order to work backwards through each problem. Drawing a fl owchart or diagram may help some children to show the sequencing.

• Discuss the answers with the class after they have had a chance to check their answers by working forward through the questions Jacintha and Ahmad started with.

READING AND WRITING MATH

Math Journal (page 155)

This section allows children to refl ect on and apply their understanding of mental subtraction to a specifi c number sentence.

• Have them look at the subtraction problem 728 – 60.

• Point out that the problem requires them to subtract tens from a 3-digit number.

• Lead them to deduce that they can use the subtract 100 then add the extra tens or ones strategy.

• Have them write the steps in the subtraction of 60 from 728 using the two strategies.


Which strategy would you use to subtract 60 from 728? Why?Explain your steps.

MATH JOURNAL

1 Jacintha adds 2 numbers to get 382. She adds 80 to the first number, then subtracts 3 from the result. Find the 2 numbers that Jacintha was adding.

2 Ahmad subtracts 2 numbers to get 727.He subtracts 100 from the first number, then adds 4 to the result. Find the 2 numbers that Ahmad was subtracting.

PUT ON YOUR THINKING CAP!


Answers will vary. Sample: Subtract 100 and add tens to the result, because you cannot subtract 6 tens from 2 tens.

Curricular Competencies: Understanding and Solving,

Strategies: Work Backwards





• Understanding and Solving• Connecting and Refl ecting

Problem-Solving Strategies

• Work Backwards

Children can try the Put on Your Thinking Cap! Challenging Practice and Problem Solving pages in Online Workbook 3A. These pages (with the answers) are available online.

Differentiation Options Depending on children’s success with the Online Workbook pages, use these materials as needed.Extension: Enrichment 3A, Put on Your Thinking Cap!


Chapter Wrap Up (page 156)

Use the examples to review the various strategies for adding and subtracting. As you work through the examples, encourage children to identify the characteristics of the addition and subtraction problems to select the most suitable strategy for the numbers involved.

Have children review the concepts and skills from Chapter 4 with the Chapter Review/Test in Online Workbook 3A. These pages (with the answers) are available online.

CHAPTER WRAP UP Different strategies can be used to add and subtractnumbers.

KEY IDEA

Adding 3-digit numbers and ones121 � 8 Step 1 1 � 8 � 9 Step 2 120 � 9 � 129

Adding 3-digit numbers and tens121 � 70 Step 1 20 � 70 � 90 Step 2 101 � 90 � 191

269 � 60 Step 1 269 � 100 � 369 Step 2 369 � 40 � 329

Adding 2-digit numbers to2-digit numbers45 � 69 Step 1 5 � 9 � 14 Step 2 40 � 60 � 100 Step 3 100 � 14 � 114

Adding 3-digit numbers and2-digit numbers119 � 76 Step 1 119 � 80 � 199 Step 2 199 � 4 � 195

119 � 99 Step 1 119 � 100 � 219 Step 2 219 � 1 � 218

Subtracting ones from 2-digit numbers63 � 6 Step 1 60 � 6 � 54 Step 2 54 � 3 � 57

Subtracting 2-digit numbers from2-digit numbers82 � 71 Step 1 2 � 1 � 1 Step 2 80 � 70 � 10 Step 3 10 � 1 � 11

Subtracting ones from 3-digit numbers119 � 4 Step 1 9 � 4 � 5 Step 2 110 � 5 � 115

Subtracting tens from 3-digit numbers232 � 20 Step 1 30 � 20 � 10 Step 2 202 � 10 � 212

341 � 70 Step 1 341 � 100 � 241 Step 2 241 � 30 � 271

Subtracting 2-digit numbers from3-digit numbers259 � 38 Step 1 259 � 40 � 219 Step 2 219 � 2 � 221

Addition and Subtraction Strategies

Addition Strategies Subtraction Strategies


156 CHAPTER 4: WRAP UP



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