Name
6.5
ALGEBRA
?
Number and
Operations—3.4.E, 3.4.K
Algebraic Reasoning—3.5.B
Also 3.4.D
MATHEMATICAL PROCESSES
3.1.C, 3.1.E
Commutative Property
of Multiplication
Essential Question
How can you use the Commutative Property of
Multiplication to find products?
Hands
On
Unlock
Unlock the
the Problem
Problem
Dave works at the Bird Store. He arranges 15 boxes
of birdseed in rows on the shelf. What are two
ways he can arrange the boxes in equal rows?
• Circle the number that
is the product.
Activity Make an array.
Materials ■ square tiles ■ MathBoard
Arrange 15 tiles in 5 equal rows.
Draw a quick picture of your array.
How many tiles are in each row? __
What multiplication sentence does your array show? ___
Suppose Dave arranges the boxes in 3 equal rows.
Draw a quick picture of your array.
How many tiles are in each row? __
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What multiplication sentence does your array show? ___
So, two ways Dave can arrange the 15 boxes are
Math Talk
Mathematical Processes
in _ rows of 3 or in 3 rows of _.
Why do 5 rows of 3 and
3 rows of 5 both equal
the same number?
Module 6
197
Multiplication Property The Commutative Property
of Multiplication states that when you change the
order of the factors, the product stays the same. You can
think of it as the Order Property of Multiplication.
2×_=_
3×_=_
Math Idea
Facts that show the Commutative
Property of Multiplication have the
same factors in a different order.
2 × 3 = 6 and 3 × 2 = 6
So, 2 × _ = 3 × _.
Share
Share and
and Show
Show
1.
Write a multiplication sentence for the array.
Math Talk
Mathematical Processes
Explain what the
factor 2 means in each
multiplication sentence.
__
__
Write a multiplication sentence for the model. Then
use the Commutative Property of Multiplication to
write a related multiplication sentence.
198
4.
_×_=_
_×_=_
_×_=_
_×_=_
_×_=_
_×_=_
© Houghton Mifflin Harcourt Publishing Company
3.
2.
Name
Problem
Problem Solving
Solving
5.
Write Math
How is the Commutative Property of Multiplication
like the Commutative Property of Addition?
Algebra Write the unknown factor.
6.
3×7=_×3
7.
9.
6×_=4×9
10.
4 × 5 = 10 × _
_×8=4×6
8.
3×6=_×9
11.
5×8=8×_
Problem
Problem Solving
Solving
12.
Jenna used pinecones to make 18 peanut
butter bird feeders. She hung the same
number of feeders in each of 6 trees. Draw
an array to show how many feeders she
put in each tree.
She put _ bird feeders in each tree.
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13.
14.
Multi-Step There are 4 rows of
6 bird stickers in Don’s sticker album. There
are 7 rows of 5 bird stickers in Lindsey’s album.
How many bird stickers do they have in all?
Write Math
Write two different word problems about
12 birds to show 2 × 6 and 6 × 2. Solve each problem.
Module 6 • Lesson 5
199
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble for the correct answer choice.
You can use objects or models to solve.
15.
16.
17.
Sebastian has 4 equal rows of action figures. There are
5 action figures in each row. One way to find the number
of action figures is to multiply 4 × 5. What is another way
to find the number of action figures?
A
add 4 + 5
C
multiply 5 × 4
B
add 5 + 5
D
multiply 6 × 5
Use Tools Rachel has 24 stamps. She arranges them in
3 rows with 8 stamps in each row. What is another way
she could arrange the 24 stamps?
A
2 rows of 8 stamps
B
8 rows of 3 stamps
C
8 rows of 4 stamps
D
6 rows of 3 stamps
Multi-Step Mr. Diaz sets out 6 rows of glasses with
3 glasses in each row. Mrs. Diaz sets out 3 rows
of glasses with 6 glasses in each row. How many
glasses do Mr. and Mrs. Diaz set out in all?
A
36
C
18
B
54
D
24
18.
200
Communicate Which is an example of the
Commutative Property of Multiplication?
A
2×6=3×4
C
2×4=4×2
B
4×1=4×1
D
2+3=3×2
© Houghton Mifflin Harcourt Publishing Company
TEXAS Test Prep
H o mewo rk
and Practice
6.5
Number and Operations—3.4.E, 3.4.K
Algebraic Reasoning—3.5.B Also 3.4.D
MATHEMATICAL PROCESSES 3.1.C, 3.1.E
Name
Commutative Property of Multiplication
ALGEBRA
Write a multiplication sentence for each model. Then use the
Commutative Property of Multiplication to write a related
multiplication sentence.
1.
3.
2.
_×_=_
_×_=_
_×_=_
_×_=_
Josh made 14 potholders. He put
an equal number of potholders in
each of 2 boxes. Write two related
multiplication sentences to show
how many potholders Josh made.
4.
Lu Chen has 21 rocks in a collection.
He puts the same number of rocks
in each of 3 boxes. Draw an array
to show how many rocks are in
each box.
6.
Dikembe has 3 packs of 10 baseball
cards. He writes 3 × 10 = 30 to show
the number of cards. Write another
multiplication sentence to show the
number of baseball cards.
_×_=_
_×_=_
Problem
Problem Solving
Solving
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5.
Serena makes 5 belts. Each belt has
4 beads. Serena writes 5 × 4 = 20
to show the number of beads. Write
another multiplication sentence to
show the number of beads.
Module 6 • Lesson 5 201
TEXAS Test Prep
Lesson
Lesson Check
Check
9.
11.
202
There are 7 vases with 5 flowers in
each vase. Gina multiplies 7 × 5 to
find the number of flowers. What is
another way to find the number of
flowers?
8.
A photo album has 8 pages with
6 photos on each page. Cory
multiplies 8 × 6 to find the number
of photos. What is another way to
find the number of photos?
A
add 7 + 5
A
add 6 + 8
B
add 5 + 7
B
multiply 6 × 8
C
multiply 5 × 7
C
add 8 + 6
D
multiply 7 × 7
D
multiply 6 × 6
Demi has 36 toy cars. She puts them
in 4 rows with 9 in each row. What is
another way Demi can arrange the
toy cars to show the Commutative
Property of Multiplication?
10.
Risa makes this model.
A
6 rows of 6
B
3 rows of 12
Which of the following can Risa
write to show the Commutative
Property of Multiplication?
C
9 rows of 4
A
3×2=2×3
D
2 rows of 18
B
2×2=3×3
C
3×2=1×6
D
3×2=1×6
Multi-Step Juan puts 3 rows of
5 stickers in a book. Then he puts
5 rows of 3 stickers on the next page.
How many stickers does Juan put in
the book?
12.
Multi-Step One classroom has
4 rows of 5 chairs. Another
classroom has 5 rows of 4 chairs.
How many chairs are there in both
classrooms?
A
15
A
20
B
16
B
19
C
30
C
25
D
25
D
40
© Houghton Mifflin Harcourt Publishing Company
7.