3.4 to algebra progress correctionkey=d lesson multiply ... · 4.nbt.b.5 multiply a whole number of...

163A Chapter 3Chapter 3

About the MathProfessional Development

About the MathProfessional Development

LESSON AT A GLANCE

Progressto AlgebraLESSON 3.4

Professional Development Videos

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

iTools: Base-Ten Blocks

Progress to AlgebraTeaching for DepthIn this lesson, students learn how to record partial products in vertical form. Sometimes partial products are recorded beginning with the greatest place value because:

• the expanded form of a number is written starting with the greatest place value.

• the Distributive Property, when written with the numbers broken apart (expanded form), starts with the greatest place value.

• the area model that represents the partial products starts with the greatest place value.

In middle and high school, when students multiply binomials, they are often taught a mnemonic FOIL (fi rst, outer, inner, last). If this method is applied to recording partial products, students record the greatest place value fi rst.

Multiply Using Partial Products

Learning ObjectiveUse place value and partial products to multiply 2-digit numbers.

Language ObjectiveStudent pairs explain how to use place value to multiply 2-digit numbers, and then ask a partner to explain the partial products strategy.

MaterialsMathBoard

F C R Focus:Common Core State Standards

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP4 Model with mathematics. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning.

F C R Coherence:Standards Across the GradesBefore3.OA.B.5

Grade 44.NBT.B.5

After5.NBT.B.5

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency...........On Your Own, Practice and HomeworkLevel 3: Applications..................................Think Smarter and Go Deeper

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 143J.

FOCUS COHERENCE RIGOR

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=D

ENGAGE1

Lesson 3.4 163B

Daily RoutinesCommon Core

Daily RoutinesCommon Core

How can you use place value and partial

products to multiply 2-digit numbers?

with the Interactive Student Edition

Essential QuestionHow can you use place value and partial products to multiply 2-digit numbers?

Making ConnectionsInvite students to tell you what they know about multiplying two-digit numbers.

When can you multiply two two-digit numbers in real life? Possible answer: finding the number of students in a school that has at least 10 classrooms

Learning ActivityConnect the story to the problem.

• What are you trying to find in this problem? the total weight of the rocks

• How many bags of rocks does the owner of the diner need for the rock garden? 24 bags

• How much does each bag of rocks weigh? 45 pounds

• What mathematical operation could you use to solve the problem? multiplication

Have students think about how they might use partial products to find the total weight of the rocks.

Literacy and Mathematics• Have one partner act out weighing each bag of rocks. Have the

other partner record the weight of each bag as it is weighed.

• Have students write their own word problems about the bags of rocks.

1 23 4 Fluency BuilderMultiply 2-Digit Numbers by 1-Digit Numbers Write the following examples on the board. Have students practice multiplying 2-digit numbers by 1-digit numbers. Have students check answers with a partner.

24 × 4 = 96

51 × 3 = 153

36 × 7 = 252

87 × 2 = 174

92 × 5 = 460

Problem of the Day 3.4Use rounding to estimate the product 3 × 2,810. 9,000

Vocabulary

Common Core Fluency Standard 4.NBT.B.5

• Interactive Student Edition• Multimedia Glossary e

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DifferentiatedInstruction1

2

3 DifferentiatedDifferentiatedInstruction

EXPLORE2

Name

tens ones

43

325

__

8 0 0

6 0

2 0 0

1 1 5

1, 0 7 5

Record the product.

1. 2. 3.

4. 5. 6.


Multiply 25 3 43. Record the product.

Think: I can use partial products to find 25 3 43.

Step 1 Multiply the tens by the tens. 20 × 4 tens = 80 tens, or 800.

Step 2 Multiply the ones by the tens. 20 × 3 ones = 60 ones, or 60.

Step 3 Multiply the tens by the ones. 5 × 4 tens = 20 tens, or 200.

Step 4 Multiply the ones by the ones. 5 × 3 ones = 15 ones, or 15.

Step 5 Add the partial products. 800 + 60 + 200 + 15 = 1,075.

So, 25 3 43 5 1,075 .

38 3 95

_

85 3 72

_

76 3 23

_

46 3 52

_

59 3 38

_

25 3 62

_

Lesson 3.4Reteach

3,610

2,700720150

1 40

6,120

5,600350160

1 10

2,392 1,748

1,400120210

1 18

2,000300

801 12

2,242

1,500270400

1 721,550

1,200300

401 10

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3-11 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

4_MNLEAN343085_C03R04.indd 11 2/12/14 2:23 PM

Name

35250210

+ 1,500

1,995

Reverse and RecordWhen Nestor records 2-digit by 2-digit multiplication, he always records the partial products in the following order:

(1) Multiply the tens by the tens.(2) Multiply the ones by the tens.(3) Multiply the tens by the ones.(4) Multiply the ones by the ones.

One day he decides to reverse the order. He starts by multiplying the ones by the ones and works backward to multiplying the tens by the tens. He uses this strategy to multiply some numbers. Will Nestor’s strategy give him the correct products?

Use Nestor’s new strategy to find the products below. The first problem has been completed for you.

1. 2. 3.

4. 5. 6.

7. Stretch Your Thinking How can Nestor check that his products are correct?

75  3 27

 _

59  3 95

 _

83  3 19

 _

44  3 63

 _

31  3 22

 _

57  3 35

 _

Lesson 3.4Enrich

45250810

1 4,5005,605

27720

301 8001,577

35490100

1 1,4002,025

12120240

1 2,4002,772

Possible answer: Nestor can multiply again in the original

order of the tens by the tens, the ones by the tens, the tens by

the ones, and the ones by the ones to check the products.

26020

1 600682


EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

3-12

4_MNLEAN343085_C03E04.indd 12 2/12/14 2:22 PM

1

2

3

1

2

3 DifferentiatedInstruction

Progressto Algebra

30

4

50 7

30

4

50 7

30

4

50 7

30

4

50 7

Unlock the ProblemUnlock the Problem

MATHEMATICAL PRACTICES 8MathTalk

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Multiply Using Partial ProductsEssential Question How can you use place value and partial products to multiply 2-digit numbers?

Lesson 3.4

Chapter 3 163

connect You know how to break apart a model to find partial products. How can you use what you know to find and record a product?

Multiply. 34 × 57 Estimate. 30 × 60 = __

SHADE THE MODEL THINK AND RECORD

So, 34 × 57 = 1,938. Since 1,938 is close to the estimate of 1,800, it is reasonable.

57 × 34

__

57 ×34

__

1,500

57 ×34

__

1,500

210

__

57 ×34

__

1,500

210

200

+

← Multiply the tens by the tens.

30 × 5 tens = 150 tens

← Multiply the ones by the tens. 30 × 7 ones = 210 ones

← Multiply the tens by the ones. 4 × 5 tens = 20 tens

← Multiply the ones by the ones. 4 × 7 ones = 28 ones← Add the partial products.

STEP 1

STEP 2

STEP 3

STEP 4

Use Repeated Reasoning You can write 10 × 4 ones = 40 ones as 10 × 4 = 40. What is another way to write 10 × 3 tens = 30 tens?

Number and Operations in Base Ten—4.NBT.B.5

MATHEMATICAL PRACTICESMP1, MP2, MP4, MP8

1,800

10 × 30 = 300

1,500

210

200

28

1,938

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4_MNLESE342200_C03L04.indd 163 07/10/14 7:52 PM

Problem Type: Area • Unknown Product

163 Chapter 3

Enrich 3.4Reteach 3.4

LESSON 3.4

Unlock the Problem MATHEMATICAL PRACTICES

MP6 Attend to precision. The model in this lesson connects to the symbolic form of the Distributive Property.34 × 57 = (30 + 4) × (50 + 7) = (30 × 50) + (30 × 7) + (4 × 50) + (4 × 7)Since students work from left to right on the model, they fi rst multiply and record the product of tens times tens in the vertical form. Ask students to describe each step in the model and the corresponding recording.

• How did you use place value to help you multiply two 2-digit numbers? Possible answer: I fi rst multiplied the tens in 57 by the tens in 34.Then I multiplied the ones in 57 by the tens in 34.Then I multiplied the tens in 57 by the ones in 34. Then I multiplied the ones in 57 by the ones in 34.

• How did partial products help you to multiply two 2-digit numbers? Possible answer: it was easy to multiply the factors in place-value parts. Then I could add the smaller products together.

• How could you estimate to check for reasonableness? Possible answer: 30 × 60 = 1,800; 1,800 is close to 1,938.

MathTalk Use Math Talk to focus on

students’ understanding of renaming numbers.

• How do you write 3 tens and 30 tens in standard form? Possible answer: Write each number followed by a zero in the ones place.

ELL Strategy: Model Concepts

Write on the board 14 × 36.

• Describe and model the steps you take as you solve the problem.

• Have students apply the same process to another problem. Students can use your language and steps as a model.

36× 14 300 10 times 3 tens 60 10 times 6 ones 120 4 times 3 tens+ 24 4 times 6 ones 504 Add the partial products.

4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

DO NOT EDIT--Changes must be made through "File info"CorrectionKey=D

120 16

600

4

20 80

30 4


Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and Show MATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD

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164

The apples from each tree in an orchard can fill 23 bushel baskets. If 1 row of the orchard has 48 trees, how many baskets of apples can be filled?

Multiply. 48 × 23 Estimate. 50 × 20 = ______

So, 1,104 baskets can be filled.

1. Find 24 × 34.

Example

3 4

× 2 4

__

THINK RECORD

STEP 1

Multiply the tens by the tens.

STEP 2

Multiply the onesby the tens.

STEP 3

Multiply the tensby the ones.

STEP 4

Multiply the ones bythe ones. Then addthe partial products.

23 × 48

__

← 40 × ______ tens = ______ tens

23 × 48

__

800

← 40 × ______ ones = ______ ones

23 × 48

_

800

120

← 8 × ______ tens = ______ tens

23 × 48

_

800

120

160

+

__ ← 8 × ______ ones = ______ ones

Evaluate Reasonableness How do you know your answer is reasonable?

Possible answer: since 1,104 is close to the estimate of 1,000, it is reasonable.

1,000

6 0 0

8 0 1 2 0

2 80

3 120

2 16

3 24

800

120

160

1,104

24

+ 1 6

__

8 1 6

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4_MNLESE342200_C03L04.indd 164 22/02/14 11:50 AM

COMMON ERRORS COMMON ERRORS

EXPLAIN3

Advanced LearnersAdvanced Learners

Problem Type: Equal Groups • Unknown Product

Lesson 3.4 164

ExampleA bushel is a U.S. customary unit of dry volume. A bushel of apples weighs about 42 to 48 pounds.Explain to students that estimating before computing an exact answer tells them what a reasonable answer might be.

• How can you use rounding to the greatest place value to estimate the product? Round 48 to 50 and 23 to 20. 50 × 20 = 1,000

• In Step 1, explain why 80 tens is the same as 800. Possible answer: 80 tens means 80 groups of 10. If you added 10 eighty times you would get 800.

• How do you line up the partial products when you record them? I line up the ones places.

DEEPER

MP8 Look for and express regularity in repeated reasoning. After students determine that the product 48 × 23 = 1,104, give them an opportunity to represent 1,104 in different ways. Ask volunteers to write their ways on the board. Possible answers: 1,000 + 100 + 4; 11 hundreds + 4 ones; 23 × 2 × 24; 552 × 2; 1,105 − 1 Students should generalize that there are many ways to represent any number.

Error Students may not align the partial products on the ones place.

Example

Springboard to Learning Give students ruled paper turned sideways or grid paper to help them align the partial products correctly.

Share and Show MATHBOARDMATHBOARDMBOARDMMMMBOARDBOARDBOARDBOARDMATHATHABOARDMMMMAAAATHATHATHTHTHATHATHATHAATHAAAATHAAATHATHTHTHATHATHAAATHATHATHAAATHABOARDBOARDBOARDBOARD

The fi rst problem connects to the learning model.

1 2 × 1 2 ____

100 20 20 + 4 ______

540

Kinesthetic / VisualIndividual

Materials 2 number cubes, 1-Centimeter Grid Paper (see eTeacher Resources)

• Challenge students to fi nd products by using either a break-apart place-value model or no model with place value to fi nd partial products. Give students grid paper to record their work.

• Have students toss two number cubes to make a 2-digit number, and record. Have them toss the number cubes again to make another 2-digit number, and record.

• Challenge students to fi nd the product using the method they choose. Have them compare methods and solutions.

HandsOn


Quick Check

If

Rt I RR1

2

3

Quick Check

If

Rt I 1

2

3

Then

On Your OwnOn Your Own


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Chapter 3 • Lesson 4 165

2. 12

× 12

__

3. 31

× 24

__

4. 25

× 43

__

5. 37

× 26

__

Record the product.

Record the product.

MATHEMATICALPRACTICE 2 Reason Abstractly Algebra Find the unknown digits. Complete the problem.

6. 54

× 15

__

7. 87

× 16

__

8. 62

× 56

__

9. 49

× 63

__

10. 38 × 47

14. 53 × 68

11. 46 × 27

15. 76 × 84

12. 72 × 53

16. 92 × 48

13. 98 × 69

17. 37 × 79

Practice: Copy and Solve Record the product.

18. 6

× 4

__

1,4 0 0

1 2 0

2 8 0

+ 2 4

___

19. 2

× 7

__

7,2 0 0

1 8 0

5 6 0

+ 1 4

___

20. 6

× 5

__

1,5 0 0

3 0 0

9 0

+ 1 8

___

21. 3

× 8

__

6 0 0

8 0

2 4 0

+ 3 2

__

Model Mathematics How would you model and record 74 × 25?

144 744 1,075 962

1,786 1,242 3,816 6,762

7

810 1,392 3,472 3,087

3,604 6,384 4,416 2,923

2

1, 8 2 4

89

7, 9 5 4

33

1, 9 0 8

4

2

9 5 2

See Additional Answers, TE p. 165.


4_MNLESE342200_C03L04.indd 165 3/20/14 1:50 AM

PROBLEM TYPE SITUATIONS

165 Chapter 3

On Your Own If students complete the checked exercises correctly, they may continue.MP2 Reason abstractly and quantitatively. Exercises 18–21 require that students use logical reasoning to use the partial products to determine the unknown digits in the factors.

Additional answers:

Math Talk, p. 165

Possible explanation: fi rst draw a rectangle to represent 74 × 25. Then break apart the factors into 70 + 4 and 20 + 5 and draw the smaller rectangles to represent the four partial products. Write the problem in vertical form:

25 × 74 _____

Then multiply the tens by the tens (70 × 2 tens) and record the partial product, 1,400 under the problem. Next, multiply the tens by the ones (70 × 5 ones) and record the partial product, 350 under the problem. Then, multiply the ones by the tens (4 × 2 tens) and record the partial product 80 under the problem. Next, multiply the ones by the ones (4 × 5 ones) and record the partial product 20 under the problem. Finally, add the partial products: 1,400 + 350 + 80 + 20 = 1,850.`

a student misses the checked exercises

Differentiate Instruction with • Reteach 3.4

• Personal Math Trainer 4.NBT.B.5

• RtI Tier 1 Activity (online)

Use the checked exercises for Quick Check.

MathTalk Use Math Talk to focus students'

understanding of lesson concepts.

• How do you model 74 × 25? Possible answer: draw an area model of 74 × 25 and break it apart into 4 parts by tens and ones.

• What is the next step in fi nding the product of 74 × 25? Possible answer: fi nd the area of each part of the model. These are partial products.

• What is the fi nal step? Possible answer: add all the partial products.

Addition and Subtraction

Put Together/Take Apart • Total Unknown Exercise: 13

Multiplication and Division

Equal Groups • Unknown Product Exercises: 12, 13, 14, 15


Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

ELABORATE4

Games

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

Citrus Fruit Weight per Box (in pounds)

Pounds of Citrus Fruit per Box

Key: Each = 10 pounds. Key: Each = 10 pounds.

Orange

Tangelo

Tangerine

Grapefruit

Key: Each = 10 pounds.

Tangerine

WRITE Math • Show Your Work

MATHEMATICAL PRACTICES MODEL • REASON • MAKE SENSE

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166

Use the picture graph for 22–24.

22. MATHEMATICALPRACTICE 4 Use Graphs A fruit-packing

warehouse is shipping 15 boxes of grapefruit to a store in Santa Rosa, California. What is the total weight of the shipment?

23. DEEPER How much less do 13 boxes

of tangelos weigh than 18 boxes of tangerines?

24. What is the weight of 12 boxes of oranges?

25. SMARTER Each person in the United States eats about 65 fresh apples each year. Based on this estimate, how many apples do 3 families of 4 eat each year?

26. DEEPER The product 26 × 93 is greater than 25 × 93. How much greater? Explain how you know without multiplying.

27. SMARTER Margot wants to use partial products to find 22 × 17.

Write the numbers in the boxes to show 22 × 17.

( × ) + ( × ) + ( × ) + ( × )

Problem Solving • ApplicationsProblem Solving • Applications

1,275 pounds

540 pounds

780 apples

1,080 pounds

The difference is 93. Possible explanation:

26 × 93 is one more group of 93 than

25 × 93.

20 10 20 7 2 10 2 7


4_MNLESE342200_C03L04.indd 166 3/11/14 7:07 PM

Lesson 3.4 166

Students take turns using number cards to make and solve 2-digit by 1-digit multiplication problems.

Students read about how Julia uses multiplication to decide how to arrange the stamps in a collection.

Students complete orange Activity Card 5 by using multiplication to find numbers that match given products.

GamesMultiplication Marathon

LiteraturePutting the World on a Page

ActivitiesFirst One Out

Essential QuestionUsing the Language Objective:Reflect Have student partners take turns explaining to answer the Essential Question.How can you use place value and partial products to multiply 2-digit numbers? Possible answer: I can break apart the numbers into tens and ones and multiply to find partial products, and then add the partial products.

Math Journal WRITE Math

Explain why it works to break apart a number by place values to multiply.

MATHEMATICAL PRACTICES

MP4 Model with mathematics. Discuss the picture graph. Students need to find the total weight in one box of each kind of fruit used in Exercises 22–24 before finding the weight of a number of boxes.

SMARTER

Problem 25 requires students to multiply twice to solve this multistep problem. Because multiplication is associative, it does not matter in which order students multiply. Many will multiply 3 × 4 first to find the total people. Others may multiply 4 × 65 first to find the total apples one family eats.

Exercise 27 assesses students’ ability to find the product of two 2-digit numbers using partial products. Students who incorrectly fill in the boxes may have difficulty using the Distributive Property to represent partial products. They may be able to multiply using partial products but not be able to write how to find the partial products in this form.

Math on the Spot Video TutorUse this video to help students model and solve this type of Think Smarter problem.


Meeting Individual Needs

Problem Solving • ThinkingProblem Solving • Applications

Problem SolvingProblem Solving

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Chapter 3 167

Record the product.

1. 23 × 79

__

2. 56 × 32

__

3. 87 × 64

__

4. 33 × 25

__

8. Evelyn drinks 8 glasses of water a day, which is 56 glasses of water a week. How many glasses of water does she drink in a year? (1 year = 52 weeks)

9. Joe wants to use the Hiking Club’s funds to purchase new walking sticks for each of its 19 members. The sticks cost $26 each. The club has $480. Is this enough money to buy each member a new walking stick? If not, how much more money is needed?

5. 94 × 12

__

6. 51 × 77

__

7. 69 × 49

__

1,400

210

180

+ 27

1,817

10. WRITE Math Explain why it works to break apart a

number by place values to multiply.

COMMON CORE STANDARD—4.NBT.B.5 Use place value understanding and properties of operations to perform multi-digit arithmetic.

Practice and HomeworkLesson 3.4

1,792 5,568 825

1,128 3,927 3,381

2,912 glasses No; $14 more is needed.

Check students’ work.


4_MNLESE342200_C03P04.indd 167 2/26/14 3:10 PM

167 Chapter 3

Practice and HomeworkUse the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers.

DO NOT EDIT--Changes must be made through “File info” CorrectionKey=A

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Spiral Review (4.OA.A.1, 4.OA.A.3, 4.NBT.B.5)

168

Lesson Check (4.NBT.B.5)

1. A carnival snack booth made $76 selling popcorn in one day. It made 22 times as much selling cotton candy. How much money did the snack booth make selling cotton candy?

2. List the partial products of 42 × 28.

3. Last year, the city library collected 117 used books for its shelves. This year, it collected 3 times as many books. How many books did it collect this year?

4. Washington Elementary has 232 students. Washington High has 6 times as many students. How many students does Washington High have?

5. List the partial products of 35 × 7. 6. Shelby has ten $5 bills and thirteen $10 bills. How much money does Shelby have in all?

$1,672

351 books

210, 35

800, 40, 320, 16

1,392 students

$180


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Monitoring Common Core Success

Maintaining Focus on the Major WorkThe major work in Grade 4 includes using the four operations with whole numbers to solve problems, as well as using place-value understanding and properties of operations to perform multi-digit arithmetic (4.NBT.B). Chapter 3 expands students’ ability to multiply whole numbers to include multiplying 2-digit numbers by multi-digit numbers. The topics covered often connect to the major work. For example, in Lesson 3.1, students apply place value understanding to round the numbers in a multiplication problem to produce an estimate for the product. In Lessons 3.1–3.4, students learn about the patterns when multiplying with multiples of 10. Students also expand their knowledge of the partial products method of multiplication, which requires addition of whole numbers as well as multiplication.

Connecting Content Across Domains and ClustersIn Lessons 3.1–3.4, a connection is made between Clusters 4.NBT.A and 4.OA.A. Lessons 3.2–3.4 (4.NBT.B) contain several Think Smarter and Go Deeper problems that require students to solve multi-step word problems (4.OA.A). For example, in Lesson 3.4,

problem 25 on page 166 requires the student to first multiply 3 by 4, and then multiply the result by 65 to find the answer.

Building FluencyIn Lessons 3.1–3.4, students enhance their understanding

of 4.NBT.B.4, which requires students to be fluent with addition and subtraction of multi-digit whole numbers. In Lessons 3.3 and 3.4, students use partial products to multiply, first with models and then without. In the partial products process, students are required to add several smaller products of varying numbers of digits to find the overall product.

Build fluency with HMH Mega Math’s fun and engaging activities. Use HMH Mega Math: The Number Games; Up, Up, and Array; Level C and The Number Game; Up, Up, and Array; Level I to strengthen students’ mastery of adding and subtracting within 1,000,000.

1 23 4

Lesson 3.4 168

Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.

DO NOT EDIT--Changes must be made through “File info” CorrectionKey=C

3.4 to algebra progress correctionkey=d lesson multiply ... · 4.nbt.b.5 multiply a whole number of...

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