Name
8.2
ALGEBRA
?
Number and
Operations—3.4.F, 3.4.K
Algebraic Reasoning—
3.5.B Also 3.4.D, 3.5.D
MATHEMATICAL PROCESSES
3.1.E
Associative Property
of Multiplication
Essential Question
How can you use the Associative Property of
Multiplication to find products?
Connect You have learned the Associative
Property of Addition. When the grouping of the
addends is changed, the sum stays the same.
(2 + 3) + 4 = 2 + (3 + 4)
Math Idea
Always multiply the numbers
inside the parentheses first.
The Associative Property of Multiplication states
that when the grouping of the factors is changed,
the product is the same. It is also called the
Grouping Property of Multiplication.
Unlock
Unlock the
the Problem
Problem
Each car on the roller coaster
has 2 rows of seats. Each row has
2 seats. There are 3 cars in each
train. How many seats are on
each roller coaster train?
• Underline what you need to find.
• Describe the grouping of the seats.
© Houghton Mifflin Harcourt Publishing Company
Use an array.
You can use an array
to show 3 × (2 × 2).
You can change the grouping with
parentheses and the product is the same.
3 × (2 × 2) = ■
(3 × 2) × 2 = ■
3×_=_
_×2=_
So, there are 3 cars with 4 seats in
each car.
There are _ seats on each roller
coaster train.
Math Talk
Mathematical Processes
Explain why the products
3 × (2 × 2) and (3 × 2) × 2
are the same.
Module 8
243
Example
Use the Commutative and Associative Properties.
You can also change the order of the factors.
The product is the same.
(4 × 3) × 2 = ■
4 × (3 × 2) = ■
4 × (3 × 2) = ■
Associative Property
4×_=_
4 × (2 × 3) = ■
Commutative Property
(4 × 2) × 3 = ■
Associative Property
_×3=_
Share
Share and
and Show
Show
1.
Find the product of 5, 2, and 3. Write another way to
group the factors. Is the product the same? Why?
2.
(2 × 1) × 7
3.
3 × (3 × 4)
4.
5 × (2 × 5)
5.
3 × (2 × 6)
Algebra Find the unknown factor.
6.
7 × (2 × _ ) = 56
7.
60 = (2 × _ ) × 6
8.
_ × (2 × 2) = 32
9.
42 = 7 × (2 × _ )
10.
8 × (5 × _ ) = 40
11.
0 = _ × (25 × 1)
244
© Houghton Mifflin Harcourt Publishing Company
Write another way to group the factors. Then find
the product.
Name
Problem
Problem Solving
Solving
© Houghton Mifflin Harcourt Publishing Company
Use the graph for 12–13.
14.
Sense or Nonsense? Each week,
Kelly works 2 days for 4 hours each day and
earns $5 an hour. Len works 5 days for 2 hours
each day and earns $4 an hour. Kelly says
they both earn the same amount. Does this
statement make sense? Explain.
15.
Representations What number sentence
does this array represent? Write another way to
group the factors.
ze
r.
Fr
ee
M
lF
or
ce
Ka
St
ee
da
Multi-Step A Kingda Ka
train has 4 seats per car, but the last car
has only 2 seats. How many seats are
on one Kingda Ka train?
Cars per Train
13.
7
6
5
4
3
2
1
0
ng
Multi-Step Each car on the Steel
Force train has 3 rows with 2 seats
in each row. How many seats are
on the train? Draw a quick picture.
Ki
12.
Roller Coasters
Roller Coaster
Write Math
Show Your Work
Module 8 • Lesson 2
245
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 an array, area model, or a strip diagram to represent
and solve.
16.
17.
18.
Michael plays a fishing game at the school carnival. He
plays 4 times and catches 3 fish each time. For each fish
Michael catches, he wins a set of 3 toy planes. How many
toy planes does Michael win?
A
18
C
36
B
12
D
9
Emma helps at a farm 2 days each week. She works
4 hours each day and earns $8 for each hour. How
much money does Emma earn each week?
A
$64
C
$48
B
$40
D
$32
Multi-Step Mrs. Lee has 25 baskets of books. She wants
to put them on the 2 bookcases in her classroom. Each
bookcase has 4 shelves. Each shelf can hold 3 baskets.
How many baskets will be left over?
A
7
C
10
B
1
D
5
TEXAS Test Prep
246
Mark has 2 rows of 3 car models on each of his 3 shelves.
How many car models does he have?
A
11
B
9
C
8
D
18
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19.
H o mewo rk
and Practice
8.2
Number and Operations—3.4.F, 3.4.K
Algebraic Reasoning—3.5.B Also 3.4.D, 3.5.D
MATHEMATICAL PROCESSES 3.1.E
Name
Associative Property of Multiplication
ALGEBRA
Write another way to group the factors. Then find the product.
1.
(3 × 2) × 5
2.
6 × (2 × 2)
3.
5 × (2 × 4)
4.
(2 × 3) × 6
Problem
Problem Solving
Solving
Use the pictograph for 5–7.
5.
Mario’s sticker books have 4 rows of
3 stickers in each row. How many
stickers are in Mario’s books?
Draw a picture.
Sticker Books
Name
Number of Books
Mario
Tamisha
Pang
© Houghton Mifflin Harcourt Publishing Company
Key: Each
= 1 sticker book
6.
Pang’s sticker books have 3 rows
of 3 stickers. He uses 5 stickers.
How many stickers are still in the sticker books? ______
7.
Tamisha’s sticker books have 3 rows of 3 stickers in
each row. If Mario’s sticker books have 4 rows of 3
stickers in each row, who has more stickers? Explain.
Module 8 • Lesson 2
247
TEXAS Test Prep
Lesson
Lesson Check
Check
10.
12.
248
Malcolm put stamps on 5 pages
of an album. He puts 3 rows of
2 stamps on each page. How many
stamps does Malcolm have in his
album?
A
10
B
30
C
20
D
25
Zeff, Maggie, and Jani each make
2 kites. Each kite has 4 tails. How
many tails are there on all of the
kites?
A
8
B
24
C
12
D
18
Multi-Step Gwen has 30 action
figures. She puts them in 2 boxes.
Each box holds 3 rows of 4 action
figures. How many action figures
will be left over?
A
24
B
6
C
8
D
21
9.
11.
13.
Ana works at the library 3 days each
week. She works for 2 hours each day
and earns $7 each hour. How much
money does Ana earn each week?
A
$42
B
$21
C
$12
D
$35
There are 6 boxes of paints. Each box
has 3 rows of 2 paint cans. Which
shows how many paint cans in all?
A
6 + (3 × 2) = 12
B
(6 × 3) + 2 = 20
C
(6 × 3) × 2 = 18
D
6 × (3 × 2) = 36
Multi-Step Reggie has 65 quilt
patches. He makes 2 quilts with
5 rows of 6 patches in each quilt. How
many quilt patches will be left over?
A
43
B
8
C
5
D
52
© Houghton Mifflin Harcourt Publishing Company
8.