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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