Math Gr4 Ch5

Chapter 5
Multiplication and Division Facts
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5

Lesson 5-1 Relate Multiplication and Division
Lesson 5-2 Algebra: Multiplication and Division
Properties
Lesson 5-3 Multiply and Divide Facts Through 5
Lesson 5-4 Problem-Solving Skill: Choose an
Operation
Lesson 5-5 Multiply and Divide Facts Through 10
Lesson 5-6 Multiply with 11 and 12
Lesson 5-7 Problem-Solving Investigation: Choose
a Strategy
Lesson 5-8 Multiply Three Numbers
Lesson 5-9 Factors and Multiples
Lesson 5-10 Prime and Composite Numbers

5-1 Relate Multiplication and Division

Five-Minute Check (over Chapter 4)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3

Meaning of Multiplication and Division


• I will understand how multiplication and division
are related.

• fact family


Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.


Standard 4MR2.3 Use a variety of methods, such
as words, numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.


Write a fact family
for the array.

There are 3 rows, 6
columns, and a total
of 18 objects.

3 × 6 = 18 6 × 3 = 18
18 3=6 18 ÷ 6 = 3


Write a fact family for the
array.

A. 3 6 = 15; 6 3 = 15; 15 3 = 6; 15 6=3

B. 3 5 = 15; 5 3 = 15; 15 3 = 5; 15 5=3

C. 4 5 = 15; 5 4 = 15; 15 4 = 5; 15 5=4

D. 3 5 = 20; 5 3 = 20; 20 3 = 5; 20 5=3


Write the fact family for the numbers 5, 7, and 35.

Do the same thing you would if there was an array of
5 rows, 7 columns, and a total of 35 pieces.

5 × 7 = 35 7 × 5 = 35
35 5=7 35 ÷ 7 = 5


Write the fact family for the numbers 3, 7, and 21.

A. 3 8 = 21; 8 3 = 21; 21 3 = 8; 21 8=3

B. 3 7 = 22; 7 3 = 22; 22 3 = 7; 22 7=3

C. 3 7 = 21; 7 3 = 21; 21 3 = 7; 21 7=3

D. 3 7 = 21; 7 3 = 21; 21 3 = 7; 21 7=3


Jorge has 42 pictures he wants to place in an
album. If six pictures fit on each page, how many
pages will he fill?

Find 42 6. You can use a related multiplication fact
to help you divide.


42 6=

42 6=7

Answer: So, Jorge will fill 7 pages.


Lisa has 24 markers. She wants to split them
equally among her and her two friends. How
many markers will each get?

A. 5

B. 6

C. 7

D. 8

5-2 Algebra: Multiplication and Division Properties

Five-Minute Check (over Lesson 5-1)
Key Concepts: Multiplication Properties
Key Concepts: Division Facts
Example 1
Example 2
Example 3


• I will use multiplication and division properties.

• Commutative Property • Identity Property
• Associative Property • Zero Property


Standard 4AF1.0 Students use and interpret
variables, mathematical symbols, and properties
to write and simplify expressions and sentences.


Identify the property shown by 9 × 0 = 0.

A number is multiplied by 0, and the product is 0. This
is the Zero Property of Multiplication.

Answer: Zero Property of Multiplication


Identify the property shown by 2 × 4 = 8 and
4 × 2 = 8.

A. Commutative Property

B. Associative Property

C. Identity Property

D. Zero Property


Complete (5 × 6) × 2 = 5 × ( 6 × ). Identify the
property used.

(5 × 6) × 2 = 5 × ( 6 × )

A 2 completes the number sentence. The way in which
the factors are grouped does not change the product.
This is the Associative Property of Multiplication.

Answer: 2; Associative Property of Multiplication


Complete (7 × 4) × 9 = 7 × ( 4 × ). Identify the
property used.

A. 7; Associative Property of Addition

B. 9; Associative Property of Multiplication

C. 4; Associative Property of Multplication

D. 9; Commutative Property of Multiplication


Rafi went to the park with his brother and his sister.
Together they had three kites. How many kites did
each person have?

3 3 = 1

According to the rule, a non-zero number divided by the
same number is 1.

Answer: So, each person will get 1 kite.


Trevor and 4 of his friends are celebrating his
birthday at his house. His mom made 5 sandwiches
for all of them to eat. How many sandwiches will
each person get?

A. 5

B. 3

C. 1

D. 1

5-3 Multiply and Divide Facts Through 5

Main Idea
Example 1
Example 2


• I will recognize multiplication and division facts
0 through 5.


division of whole numbers and understand


Standard 4MR2.3 Use a variety of
methods, such as
words, numbers, symbols, charts, graphs, tables,
diagrams, and models, to explain mathematical
reasoning.


At the indoor track, eight laps equal one mile. If
Tanya runs 3 miles, how many laps did she run?

You need to find 8 × 3.


One Way: Skip Count

Start at 0. Count by 8s. So, 8 × 3 = 24.


Another Way: Area Model

8 × 3 = 24

Count the squares. There is a total of 24
squares.


A classroom has 4 sets of crayon boxes. There
are 5 crayons in each set. How many crayons
are there total?

A. 10

B. 15

C. 20

D. 25


Ernesto’s family uses two rolls of film each week
of their vacation. If they used a pack of six rolls of
film, how long was their vacation?

You need to find 6 2.

There are different strategies to use when finding
division facts.


One Way: Skip Count

Start at 6. Count back by 2s until you reach 0.
Count the number of times you subtracted.
6÷2=3


Another Way: Related Facts

6 ÷2=

6 ÷2=3

Answer: So, Ernesto’s family vacation was
3 weeks long.


There are 3 calculators in a classroom of 15
students. How many students per calculator
are there?

A. 5

B. 4

C. 3

D. 2

5-4 Problem-Solving Skill: Choose an Operation

Main Idea
Example 1: Problem-Solving Skill


• I will choose an operation to solve a problem.


Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant information,
sequencing and prioritizing information,
and observing patterns.


division of whole numbers and understand the


There are 9 rows on the Twisted Zipper roller
coaster. Each row has 4 seats. What operation do
you need to use to find how many people can
ride the roller coaster at a time?


Understand
What facts do you know?
• There are 9 rows.
• There are 4 seats per row.

What do you need to find?
• The operation you should use to find how many
people can ride the roller coaster at a time.


Plan
You should multiply because there are groups of
the same number in each group. Multiply the
number of rows by the number of seats per row.


Solve
Multiply to find the answer.

9 × 4 = 36

Answer: So, 36 people can ride the roller coaster
at a time.


Check
Look back at the problem. Find 9 × 4 another way to
see if you get the same answer. You can use an array.

9 × 4 = 36. So, the answer is correct.


Main Idea
Example 1
Example 2


• I will recognize multiplication and division facts
through 10.


involving addition, subtraction, multiplication,
and division of whole numbers and understand


Standard 4MR3.2 Note the method of deriving
the solution and demonstrate a conceptual
understanding of the derivation by solving
similar problems.


A mini-bus has 8 rows with 4 seats in each row.
How many people can be seated in the mini-bus?

Find 8 × 4.


One Way: Area Model

There are 32 squares in all. So, 8 × 4 = 32.


Another Way: Related Fact

8×4=

8 × 4 = 32

Answer: So, 32 people can be seated in the
mini-bus.


In a small school theater, there are 9 rows of
seats and 9 seats per row. How many seats are
there in all?

A. 18

B. 81

C. 9

D. 72


Filipa noticed that there are 2 pages of
advertisements for every article she reads
in a magazine. If she saw a total of 16
pages of advertisements, how many
articles did she read?

There are 16 pages of advertisements. Divide
16 by 2 to find how many articles Filipa read.


16 ÷ 2 =

16 ÷ 2 = 8

Answer: So, Filipa read 8 articles.


Check

The area model shows 16 squares in rows of 2. Count
the number of rows.

So, 16 ÷ 2 = 8.


Jordan saw a sign saying that for every lap she
runs around the park, it is equal to 3 miles. If
Jordan ran 12 miles, how many laps did she run?

A. 2

B. 3

C. 4

D. 5

5-6 Multiply with 11 and 12

Example 1
Example 2


• I will recognize multiplication facts for 11 and 12.

• Distributive Property of Multiplication


Standard 4MR3.3 Develop generalizations of
the results obtained and apply them in other
circumstances.


Pang works at a bakery. He received an order for
9 dozen bagels. How many bagels does he need
to fill the order?

There are 12 bagels in one dozen. So, you need to find
9 × 12.


Think of 9 × 12 as (9 × 10) + (9 × 2).


9 × 12 = (9 × 10) + (9 × 2)
= 90 + 18
= 108

Answer: So, 108 bagels are needed to fill a 9
dozen order.


Sarah wants to order 5 dozen cookies for her party.
How many cookies will she have total?

A. 60

B. 55

C. 10

D. 5


A group of 11 friends went to a minor league ball
game. The total ticket cost was $99. How much did
each ticket cost?

Use a related multiplication fact to help you find
$99 ÷ 11.


$99 ÷ 11 =

$99 ÷ 11 = $9

Answer: So, each ticket cost $9.


Candace and 10 of her friends went ice-skating at
the local rink. The total cost for all of them to skate
was $77. How much did it cost per person?

A. $10

B. $11

C. $77

D. $7

5-7 Problem-Solving Investigation: Choose a Strategy

Main Idea
Example 1: Problem-Solving Investigation


• I will choose the best strategy to solve a problem.


Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.


the relationships among the operations.


KASA: I go to ballet lessons every
week. I dance 2 hours during every
lesson. I dance a total of
6 hours each week.

YOUR MISSION: Find how many ballet
lessons Kasa has in 4 weeks.


Understand
What facts do you know?
• Kasa dances 2 hours during each lesson.
• She dances a total of 6 hours each week.

What do you need to find?
• Find how many lessons she has in 4 weeks.


Plan
Divide the number of hours Kasa practices each
week by the number of hours each lesson lasts.
Then multiply by 4, the number of weeks.


Solve
hours per hours per lessons
week lesson per week

6 ÷ 2 = 3

So, Kasa has 3 ballet lessons each week.


Solve
lessons lessons in
per week weeks 4 weeks

3 × 4 = 12

Answer: So, Kasa has 12 ballet lessons in
4 weeks.


Check
Look back at the problem. Check your answer by
dividing the number of lessons in 4 weeks by the
number of weeks. 12 ÷ 4 = 3. Then, multiply the
number of hours per lesson by the number of
lessons each week. 2 × 3 = 6. So, the answer is
correct.

5-8 Multiply Three Numbers

Main Idea
Example 1


• I will multiply 3 factors.


Standard 4AF1.0 Students use and interpret
variables, mathematical symbols, and
properties to write and simplify expressions
and sentences.


Mrs. Chu ordered 4 boxes of fruit bars to sell at the
baseball concession stand. Each box contains 3
bars, and each bar has 2 pieces. How many pieces
did she order?

You need to find 4 3 × 2. There are two ways to group
the numbers.


One Way Another Way

Multiply 4 × 3 first. Multiply 3 × 2 first.

4×3×2 4×3×2
(4 × 3) × 2 4 × (3 × 2)
12 × 2 4×6
24 24

Answer: So, Mrs. Chu ordered 24 pieces.


Mr. Hawkins ordered 3 boxes of cookies for him
and his family. Each box contains 3 packs of
cookies, and each pack contains 2 cookies. How
many total cookies does he have?

A. 9

B. 6

C. 18

D. 8

5-9 Factors and Multiples

Example 1
Example 2


• I will find factors and multiples of whole numbers.

• factor
• multiple


Standard 4NS4.1 Understand that many whole
numbers break down in different ways (e.g. 12
= 4 × 3 = 2 × 6 = 2 × 2 × 3).


Standard 4MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models to
explain mathematical reasoning.


How could Mrs. Salgado arrange the desks if she
had 25 desks?

Think of number pairs that result in a product of 25.
1 × 25 = 25


5 × 5 = 25

The factors of 25 are 1, 5, and 25. The different arrays
show the ways that the desks can be arranged.

Answer: So, the desks can be arranged in 2 ways.


If Mrs. Rameriez has 16 desks in her classroom,
how many ways can she arrange them?

A. 1 16, 2 8, 4 4

B. 1 16

C. 2 8, 4 4

D. 1 16, 2 8


Identify the first five multiples of 9.

On a multiplication table, look across the row for 9, or
down the column for 9. All of the numbers listed in the
row or the column are multiples of 9.


Answer: So, the first five multiples of 9 are
0, 9, 18, 27, and 36.


Identify the first five multiples of 6.

A. 12, 18, 24, 30, 36

B. 0, 6, 12, 18, 24

C. 17, 20, 23, 26, 29

D. 30, 36, 42, 48, 54

5-10 Prime and Composite Numbers

Key Concepts: Prime and Composite Numbers
Example 1
Example 2
Example 3

Prime and Composite Numbers


• I will determine if a number is prime or composite.

• composite number
• prime number


Standard 4NS4.2 Know that numbers such as 2,
3, 4, 7, and 11 do not have any factors except for
1 and themselves and that such numbers are
called prime numbers.


Tell whether 39 is prime, composite, or neither.

Find the factors of 39.

1 39
3 13

Factors of 39: 1, 3, 13, 39.

Answer: Since 39 has more than two factors, it
is a composite number.



A. prime

B. composite

C. neither

D. both




1 23

Factors of 23: 1, 23.

Answer: Since 23 has exactly two distinct
factors, it is a prime number.



A. prime

B. composite

C. neither

D. both




1 18
2 9
3 6

Factors of 18: 1, 2, 3, 6, 9, 18.

Answer: Since 18 has more than two factors, it
is a composite number.



A. prime

B. composite

C. both

D. neither

5

Five-Minute Checks

Meaning of Multiplication and Division

Prime and Composite Numbers

5

Lesson 5-1 (over Chapter 4)
Lesson 5-2 (over Lesson 5-1)

5
(over Chapter 4)

How long did the Hamel family swim?

A. 9 hours

B. 4 hours

C. 3 hours

D. 5 hours

5
(over Chapter 4)

What activity did they spend the most time doing?

A. beach

B. boat

C. hiking

D. shopping

5
(over Lesson 5-1)

Identify the property shown.
5 2=2 5

A. Commutative Property of Addition

B. Identity Property

C. Associative Property of Multiplication

D. Commutative Property of Multiplication

5
(over Lesson 5-1)

8 1=8

A. Zero Property


C. Commutative Property of Multiplication

D. Associative Property of Multiplication

5
(over Lesson 5-1)

(6 2) 3=6 (2 3)

A. Associative Property of Multiplication



D. Zero Property

5
(over Lesson 5-1)

12 0=0

A. Identity Property

B. Zero Property

C. Associative Property of Multiplication

D. Commutative Property of Multiplication

5
(over Lesson 5-1)

7 9=9 7

A. Associative Property of Multiplication

B. Zero Property


D. Identity Property

5
(over Lesson 5-2)

Write the fact family for each set of numbers.
2, 4, 8

A. 2 + 2 = 4, 4 + 4 = 8, 4 – 2 = 2, 8 – 4 = 4

B. 8 + 8 = 16, 16 – 8 = 8

C. 2 4 = 8, 4 2 = 8, 8 4 = 2, 8 2=4

D. 2 2 = 4, 4 4 = 16, 8 8 = 64

5
(over Lesson 5-2)

Write the fact family for each set of numbers.
5, 8, 40

A. 5 8 = 40, 8 5 = 40, 40 8 = 5, 40 5=8

B. 5 + 5 = 10, 8 + 8 = 16, 40 + 40 = 80

C. 5 1 = 5, 8 1 = 8, 40 1 = 40

D. 5 8 = 40, 8 5 = 40

5
(over Lesson 5-2)

Divide. Use a related multiplication fact.
10 5 = __

A. 15

B. 5

C. 2

D. 50

5
(over Lesson 5-2)

Divide. Use a related multiplication fact.
48 6 = __

A. 6

B. 8

C. 42

D. 12

5
(over Lesson 5-3)

Multiply or divide.
4 3

A. 7

B. 1

C. 13

D. 12

5
(over Lesson 5-3)

Multiply or divide.
3 10

A. 9

B. 13

C. 30

D. 7

5
(over Lesson 5-3)

Multiply or divide.
5 5

A. 25

B. 10

C. 0

D. 50

5
(over Lesson 5-3)

Multiply or divide.
12 2

A. 10

B. 14

C. 5

D. 6

5
(over Lesson 5-3)

Multiply or divide.
32 4

A. 28

B. 8

C. 36

D. 6

5
(over Lesson 5-3)

Multiply or divide.
45 5

A. 50

B. 9

C. 40

D. 8

5
(over Lesson 5-4)

Tell which operation you would use to solve the
problem. Then solve. At the picnic, Salvador ate 3
hot dogs. Together, Salvador and Aidan ate 7 hot
dogs. How many hot dogs did Aidan eat?

A. Addition; 10

B. Division; 3.5

C. Subtraction; 4

D. Subtraction; 7

5
(over Lesson 5-5)

Multiply 8 5.

A. 13

B. 45

C. 40

D. 35

5
(over Lesson 5-5)

Multiply 9 6.

A. 45

B. 54

C. 15

D. 64

5
(over Lesson 5-5)

Divide 64 8.

A. 7

B. 56

C. 9

D. 8

5
(over Lesson 5-5)

Multiply 4 6.

A. 24

B. 10

C. 12

D. 18

5
(over Lesson 5-5)

Divide 32 8.

A. 24

B. 6

C. 4

D. 3

5
(over Lesson 5-6)

Find the product of 12 5.

A. 17

B. 7

C. 60

D. 65

5
(over Lesson 5-6)


A. 100

B. 21

C. 111

D. 110

5
(over Lesson 5-6)


A. 110

B. 66

C. 60

D. 160

5
(over Lesson 5-6)


A. 108

B. 120

C. 96

D. 109

5
(over Lesson 5-6)


A. 72

B. 84

C. 96

D. 48

5
(over Lesson 5-6)


A. 110

B. 111

C. 121

D. 101

5
(over Lesson 5-6)


A. 84

B. 108

C. 88

D. 96

5
(over Lesson 5-6)


A. 121

B. 102

C. 132

D. 122

5
(over Lesson 5-7)

Use any strategy to solve. Leticia is on a swim
team that practices 4 days each week. Each
practice is 3 hours long. How many hours per week
does Leticia have swim practice?

A. 20 hours

B. 15 hours

C. 7 hours

D. 12 hours

5
(over Lesson 5-8)

Find the product of 3 4 5.

A. 45

B. 60

C. 35

D. 27

5
(over Lesson 5-8)


A. 36

B. 69

C. 96

D. 56

5
(over Lesson 5-8)


A. 54

B. 45

C. 24

D. 63

5
(over Lesson 5-8)


A. 32

B. 20

C. 48

D. 26

5
(over Lesson 5-8)


A. 46

B. 40

C. 34

D. 64

5
(over Lesson 5-9)

Identify the first 5 multiples of 3.

A. 1, 3, 6, 12, 24

B. 3, 6, 9, 12, 15

C. 1, 6, 9, 12, 15

D. 0, 1, 3, 6, 9

5
(over Lesson 5-9)


A. 1, 2, 3, 4, 6

B. 0, 1, 2, 3, 4

C. 12, 24, 36, 48, 60

D. 1, 12, 24, 48, 96

5
(over Lesson 5-9)


A. 1, 3, 9, 18, 27

B. 9, 18, 27, 36, 45

C. 0, 1, 9, 18, 27

D. 3, 6, 12, 24, 48

5
(over Lesson 5-9)

Find all the factors of 55.

A. 0, 1, 2, 5, 11

B. 1, 5, 11

C. 1, 5, 110

D. 1, 5, 11, 55

5
(over Lesson 5-9)

Find all the factors of 23.

A. 1, 2, 3, 23

B. 1, 23

C. 1, 23, 46

D. 0, 2, 3

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Math Gr4 Ch5

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