Unlock the ProblemUnlock the Problem

Mathematical ProcessesMath Talk

Essential Question?How can you use the Distributive Property to find products?

Name Number and Operations—3.4.E, 3.4.K Algebraic Reasoning—

3.5.B Also 3.4.D, 3.5.DMATHEMATICAL PROCESSES3.1.C, 3.1.D, 3.1.E

• Describe the groups in this problem.

• Circle the numbers you will use to solve the problem.

Mark bought 6 new fish for his

aquarium. He paid $7 for each fish.

How much did he spend in all?

Find 6 × $7.

You can use the Distributive

Property to solve the problem.

The Distributive Property states that

multiplying a sum by a number is the

same as multiplying each addend by the

number and then adding the products.

Activity Materials ■ square tiles

6 × 7 = ■ 6 × 5 6 × 2

Make an array with tiles to show 6 rows of 7.

Break apart the array to make two smaller arrays for facts you know.

6 × 7 = ■ 6 × 7 = 6 × (5 + 2) 6 × 7 = (6 × 5) + (6 × 2)

6 × 7 = _ + _

6 × 7 = _

Think: 7 = 5 + 2 Multiply each addend by 6.

Add the products.

So, Mark spent $ _ for his new fish.

HandsOn

Remembersum—the answer to an addition problem

addends—the numbers being added

What other ways could you break apart the 6 × 7

array?

Distributive Property7.4ALGEBRA

Module 7 229

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Problem SolvingProblem Solving

Mathematical ProcessesMath Talk

4. Shade tiles to make an array that shows

a fact with 7, 8, or 9 as a factor. Write the

fact. Explain how you found the product.

1. Draw a line to show how you could break apart

this 6 × 8 array into two smaller arrays for

facts you know.

• What numbers do you multiply? _ and _

_ and _

• What numbers do you add? _ + _

6 × 8 = 6 × (_ + _)

6 × 8 = (_ × _) + (_ × _)

6 × 8 = _ + _

6 × 8 = _

Write one way to break apart the array.

Then find the product.

2. 3.

Why do you have to add to find the total

product when you use the Distributive Property?

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Problem SolvingProblem Solving

Name

5. Sense or Nonsense? Robin says, “I can

find 8 × 7 by multiplying 3 × 7 and doubling it.“ Does

her statement make sense? Justify your answer.

6. Multi-Step Brandon needs 8 boxes of

spinners for his fishing club. The cost of each box

is $9. How much will Brandon pay?

8 × $9 = ■

Look at how Brandon solved the problem. Find and describe his error.

Use the array to help solve the problem and correct Brandon’s error.

8 × 9 = (4 × 9) + (5 × 9)

8 × 9 = 36 + 45

8 × 9 = 81

8 × 9 = (4 + 4) × 9

8 × 9 = (_ × _) + (_ × _)

8 × 9 = _ + _

8 × 9 = _

So, Brandon will pay $ _ for the spinners.Module 7 • Lesson 4 231

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Daily Assessment TaskDaily Assessment Task

Mathematical ProcessesM

TEXAS Test Prep10. Representation Which number sentence below is an

example of the Distributive Property?

A 6 × 8 = 40 + 8

B (8 × 2) × 3 = 8 × (2 × 3)

C 6 × 8 = 8 × 6

D 6 × 8 = (6 × 2) + (6 × 6)

Fill in the bubble for the correct answer choice.

You may use models or strategies to solve.

7. Use Diagrams Maurice planted 8 rows of popcorn

plants. There are 6 plants in each row. The array

shows Maurice’s garden. How many popcorn plants

does Maurice have?

A 36 C 48

B 42 D 64

8. At a grocery store, the cans of nuts are arranged in

9 rows. There are 6 cans in each row. Which shows

one way to find the total number of cans of nuts?

A (5 + 4) × 6

B (3 + 3) × 6

C (5 + 5) × 6

D (5 + 3) × 6

9. Multi-Step Jillian bought 6 books for $7 each. She paid

with $50. How much change should Jillian receive?

A $37 C $43

B $18 D $8

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Problem SolvingProblem Solving

Homeworkand Practice

Name

Write one way to break apart the array. Then find

the product.

1.

2.

3. Shade tiles to make an array that

shows a fact with 5, 6, or 7 as a factor.

Explain how you found the product.

Distributive Property7.4

Number and Operations—3.4.E, 3.4.KAlgebraic Reasoning—3.5.B Also 3.4.D, 3.5.DMATHEMATICAL PROCESSES 3.1.C, 3.1.D, 3.1.E

4. Shawn makes a tile design by using 7 rows of 8 tiles.

Explain how Shawn can break apart his design to find

how many tiles he used.

ALGEBRA

Module 7 • Lesson 4 233

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TEXAS Test PrepLesson CheckLesson Check

5. There are 8 tables in the art class.

Five students sit at each table. How

many students are in the art class?

A 13

B 40

C 45

D 85

6. Seven large trucks are in a parking

lot. Each truck has 6 wheels. How

many wheels are there in all?

A 67

B 40

C 42

D 13

7. Jonas buys 6 packages of corn. Each

package has 8 ears of corn. Which

way can Jonas use to show how

many ears of corn he buys?

A (4 + 2) × 8

B (3 + 2) × 8

C (6 + 6) × 8

D (4 + 4) × 6

8. A store sells bags of 9 apples.

Mr. Hyon buys 5 bags of apples to

make pies. Which way can Mr. Hyon

use to show how many apples

he buys?

A (4 × 9) + (5 × 9)

B (3 × 5) + (6 × 5)

C (4 × 5) + (5 × 9)

D (3 × 5) + (9 × 5)

9. Multi-Step Minka buys 8 CDs

for $6 each. She pays with three

$20 bills. How much change should

Minka receive?

A $48

B $12

C $34

D $68

10. Multi-Step Kent buys 5 bags of

potatoes that cost $7 each. He gives

the clerk $40. How much change

should Kent receive?

A $35

B $12

C $5

D $52

Fill in the bubble completely to show your answer.

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Name

Module 7 AssessmentVocabulary

Commutative Property

of Multiplication

Distributive Property

multiple

VocabularyVocabulary

Choose the best term from the box to complete

the sentence.

1. A ___ of 4 is any product that has 4 as

one of its factors. (p. 217)

2. This is an example of the ___ Property.

3 × 8 = (3 × 6) + (3 × 2)

This property states that multiplying a sum by a

number is the same as multiplying each addend

by the number and then adding the products. (p. 229)

Concepts and SkillsConcepts and Skills

Write one way to break apart the array.

Then find the product. q TEKS 3.4.E, 3.4.K

3. 4.

Find the product. q TEKS 3.4.E, 3.4.K

5. 3 × 1 = _ 6. 5 × 6 = _ 7. 4 × 7 = _ 8. 2 × 10 = _

9. 2

× 1

_

10. 6

× 6

_

11. 6

× 7

_

12. 6

× 3

_

13. 3

× 8

_

Module 7 235

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TEXAS Test PrepFill in the bubble for the correct answer choice. You may use models to solve.

14. Lorisaw6lightningbugs.Theyeachhad6legs.Howmanylegsdidthelightningbugshaveinall? q TEKS 3.4.E, 3.4.K

A 36

B 6

C 12

D 24

15. Zachgavehisdog1dogbiscuiteachday,for5days.Thenhegavehisdog2dogbiscuitsadayforthenext5 days.HowmanybiscuitsdidZachgivetohisdog?q TEKS 3.4.E, 3.4.K

A 5 C 15

B 30 D 7

16. Annettebought4boxesofpencils.Ifthereare8pencilsineachbox,howmanypencilsdidshebuy? q TEKS 3.4.E, 3.4.K

A 32

B 12

C 16

D 24

17. Shellycanpaint4picturesinaday.Howmanypicturescanshepaintin7days? q TEKS 3.4.E, 3.4.K

Recordyouranswerandfillinthebubblesonthegrid.Besuretousethecorrectplacevalue.

.0 0 0

1 1 1

2 2 2

3 3 3

4 4 4

5 5 5

6 6 6

7 7 7

8 8 8

9 9 9

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