Date:
P
H A TE
Using Bar Models:
Multiplication and Division
R
C
Name:
9
Worksheet 1 Real-World Problems: Multiplication
Study the bar models. Then complete the sentence.
Example
A
Twice means 2 times.
B
B
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1.
is twice as many as
A
.
P
Q
is three times as many as
2.
.
A
B
3.
is four times as many as
.
is five times as many as
.
P
Q
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Name:
Date:
Draw bar models to show each statement.
Example
A is three times as many as B.
A
4.
C is four times as many as D.
5.
E is twice as many as F.
6.
G is five times as many as H.
164
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B
Chapter 9 Lesson 9.1
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Name:
Date:
Express the bar model as a multiplication sentence.
Example
7
?
⫻
5
⫽
35
12
7.
⫻
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7
⫽
Solve. Use the bar models to help you.
Example
9
1 unit
5 units
9
5 ⴛ 9 ⴝ 45
?
8.
15
1 unit
6 units
?
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Name:
Date:
Solve. Draw bar models to help you.
Example
Jack is weighs twice as much as Chris.
Chris weighs 42 kilograms.
How much does Jack weigh?
Chris
Jack
⫻
84
Jack weighs
9.
42
⫽
kilograms.
Terell packs some books into two boxes.
The first box has 16 books in it.
The second box has three times as many books as the
first box has.
How many books does the second box have?
⫻
⫽
The second box has
10.
books.
Lesley spends $24.
Megan spends five times as much as Lesley.
How much money does Megan spend?
Megan spends $
166
84
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2
.
Chapter 9 Lesson 9.1
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Name:
Date:
Write a word problem using the bar model given.
Then solve the problem.
Example
12 kg
wheat
flour
rice
? kg
Mr. Tee buys 12 kilograms of wheat flour.
He buys 3 times as much rice as wheat flour.
How much rice does he buy?
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3 ⫻ 12 ⫽ 36
Mr. Tee buys 36 kilograms of rice.
11.
$18
Peter
Andrea
$?
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Name:
168
Date:
12.
28
Shirley
Ben
?
Chapter 9 Lesson 9.1
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Worksheet 2 Real-World Problems: Two-step
Problems with Multiplication
Complete.
Example
8
40
32
8
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4
1.
⫻
8
⫽
⫹
32
⫽
40
32
15
⫹
⫻
⫽
⫽
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2.
⫻
3.
⫻
170
MS_Reteach 3A_Ch09_163-188.indd 170
⫽
24
⫽
⫹
⫽
⫹
⫽
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Name:
Date:
18
Chapter 9 Lesson 9.2
11/2/09 2:23:03 PM
Name:
Date:
Solve. Use bar models to help you.
Example
A company employs 78 workers at its factory.
The company opens another factory.
The second factory employs three times as many workers
as the first factory.
a. How many workers does the second factory employ?
78
?
?
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3 ⫻ 78 ⫽ 234
The second factory employs 234 workers.
b. How many workers do both factories employ?
78 ⫹ 234 ⫽ 312
Both factories employ 312 workers.
4.
In February, 32 members join a new club.
During the spring, five times as many members join the club.
How many club members are there at the end of spring?
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Name:
5.
Date:
A store owner buys 24 boxes of apples.
Each box contains 8 apples.
During a sale, he sells 63 of his apples.
a. How many apples does he have at first?
6.
In the auditorium, Brad arranges 35 rows of chairs.
Each row has 7 chairs.
During the performance, 78 chairs are empty.
a. How many chairs does Brad arrange?
b. How many people attend the performance?
172
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b. How many apples does the store owner have left after the sale?
Chapter 9 Lesson 9.2
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Name:
Date:
7.
A farmer keeps 27 chicks and 18 ducklings in each coop.
She has 9 coops. How many chicks and ducklings does
the farmer have altogether?
8.
Sally has 56 stamps.
Sarah has three times as many stamps as Sally.
Their brother, Peter, has 45 stamps less than Sarah.
How many stamps does Peter have?
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Date:
Write a two-step word problem using the bar models.
Ask a friend to solve the problem.
Example
$42
Alice
Belinda
Alice has $42.
Belinda has 4 times as much money as Alice.
a. How much money does Belinda have?
4 ⫻ $42 ⫽ $168
Belinda has $168.
How much money do Alice and Belinda altogether?
$42 ⫹ $168 ⫽ $210
Alice and Belinda have $210 altogether.
9.
72 beads
Paola
Tasha
Min
168 beads
174
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b.
Chapter 9 Lesson 9.2
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Date:
Worksheet 3 Real-World Problems: Division
Complete the division sentence.
Use the bar model to help you.
Example
35
?
⫼
35
⫽
7
72
1.
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5
?
⫼
2.
⫽
42
?
⫼
⫽
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Solve. Use bar models to help you.
Example
54
6
1 unit
units
54
54 6 9
?
3.
84
units
unit
Complete the division sentence.
Use the bar model to help you.
Example
3
3
?
48
4.
⫼
3
5
⫽
5
?
⫼
176
16
45
48
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?
⫽
Chapter 9 Lesson 9.3
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Name:
Date:
Solve. Use bar models to help you.
Example
A shopkeeper puts 32 eggs equally into 4 egg trays.
How many eggs does each tray have?
32
?
32 ⫼ 4 ⫽ 8
Each tray has 8 eggs.
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5.
Lionel has $729.
He divides the money equally among 9 children.
How much money does each child get?
?
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6.
Date:
Shirley collects 72 pineapples.
She puts them equally into 8 boxes.
How many pineapples are in each box?
Solve. Use bar models to help you.
Example
Jerry puts 48 stamps equally into 6 envelopes.
How many stamps are in each envelope?
?
48
48 ⫼ 6 ⫽ 8
Each envelope has 8 stamps.
178
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?
Chapter 9 Lesson 9.3
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Name:
Date:
7.
A hotel chef fries 35 eggs for breakfast in a hotel.
He divides them equally among 7 plates.
How many eggs are on each plate?
8.
A milkman delivers the same amount of milk to 8 households.
He delivers a total of 48 cartons of milk.
How many cartons of milk does each household get?
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Solve. Use bar models to help you.
Example
Lisa has 76 beads. She puts all of the beads into bags.
She puts 4 beads into each bag.
How many bags does Lisa use?
76
beads
4
4
? bags
9.
Janice sells 45 oranges to a buyer.
She puts 5 oranges into each bag.
How many bags does Janice use for all of the oranges?
oranges
5
5
? bags
180
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76 ⫼ 4 ⫽ 19
Lisa uses 19 bags.
Chapter 9 Lesson 9.3
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Name:
Date:
Robert collects 132 bunches of olives.
He puts 6 bunches in each box.
How many boxes does Robert use to pack all of the olives?
10.
bunches
6
6
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? boxes
Solve. Use bar models to help you.
Example
Talia uses 40 toothpicks to make pentagons.
Each pentagon is made with 5 toothpicks.
How many pentagons does Talia make in all?
40 toothpicks
5
5
? pentagons
40 ⫼ 5 ⫽ 8
Talia makes 8 pentagons in all.
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Date:
11.
Margaret has 648 coins.
She arranges them in her coin book so that each page has 8 coins.
How many pages are needed to hold all of Margaret’s coins?
12.
Mr. Nelson has 628 liters of kerosene.
He pours all of the kerosene equally into 4 cans.
How many liters of kerosene does each can have in it?
182
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Name:
Chapter 9 Lesson 9.3
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Date:
Worksheet 4 Real-World Problems: Two-step
Problems with Division
Solve. Use bar models to help you.
Example
Billy has twice as many stamps as Natalia.
They have 96 stamps altogether.
How many stamps does Billy have?
Natalia
96
Billy
?
3
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1 unit
96 ⴜ 3 ⴝ 32
2
Billy has
1.
96
units
units
64
2 ⴛ 32 ⴝ 64
stamps.
Jeron moves three times as many bricks as Matthew.
They move 136 bricks altogether.
How many bricks does Jeron move?
Matthew
Jeron
?
units
1 unit
units
Jeron moves
bricks.
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Date:
Solve. Use bar models to help you.
Example
Jessica spends four times as much money as Kathy.
Both of them spend $275 altogether.
How much money does Jessica spend?
$275
?
2.
184
In a math competition, Gabriel completes three times
as many problems as Harry.
Both of them complete 72 problems.
How many problems does Gabriel complete?
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5 units $275
1 unit
$275 ⫼ 5 ⫽ $55
4 units 4 ⫻ $55 ⫽ $220
Jessica spends $220.
Chapter 9 Lesson 9.4
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Name:
Date:
Solve. Use bar models to help you.
Example
Mrs. Lee buys 3 pairs of shoes and a suitcase for $495.
The suitcase costs $261.
a. How much do the 3 pairs of shoes cost?
$261
suitcase
?
$495
shoes
?
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$495 ⫺ $261 ⫽ $234
3 pairs of shoes cost $234.
b. How much does each pair of shoes cost?
$234 ⫼ 3 ⫽ $78
Each pair of shoes costs $78.
3.
Rosanna buys 8 packages of pencils.
Each package has 24 pencils.
She divides all the pencils equally into 6 boxes.
a. How many pencils does Rosanna buy in all?
b. How many pencils does each box contain?
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4.
Date:
Mr. Chan buys 862 apples and oranges.
He keeps all of the 254 oranges in a box. He packs all of the apples
equally into 4 crates.
a. How many apples does Mr. Chan buy?
5.
Jane has 189 stickers.
Adam has 251 stickers.
They put all of their stickers equally into 5 boxes.
How many stickers does each box have?
6.
Michael has 992 cartons of milk.
He packs the cartons equally into 8 boxes.
He sells each carton for $3.
How much money does Michael earn for each box of milk?
186
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b. How many apples are packed into each crate?
Chapter 9 Lesson 9.4
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Name:
Date:
Write a word problem using the bar models.
Then solve the problem.
Example
6 blocks
84 blocks
84 blocks are arranged in groups of 6 blocks each.
How many groups are there?
84 ⫼ 6 ⫽ 14
There are 14 groups.
7.
10 pages
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Mr. Lim
15 pages
Mr. Smith
Mr. Samy
?
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8.
Date:
Alfred
$125
Kofi
Jeffery
$42
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?
188
Chapter 9 Lesson 9.4
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