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Chapter 6
Division Concepts and Facts
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Division Concepts and Facts
6

Lesson 6-1       Relate Division to Subtraction
Lesson 6-2       Relate Multiplication to Division
Lesson 6-3       Problem-Solving Strategy: Choose
an Operation
Lesson 6-4       Divide by 2
Lesson 6-5       Divide by 5
Lesson 6-6       Problem-Solving Investigation:
Choose a Strategy
Lesson 6-7       Divide by 10
Lesson 6-8       Division Properties
6-1     Relate Division to Subtraction

Five-Minute Check (over Chapter 5)
Main Idea and Vocabulary
California Standards
Example 1: Use Models to Divide
Example 2: Repeated Subtraction

Understand Division
6-1      Relate Division to Subtraction

• I will divide using subtraction.

• division
• divide
6-1     Relate Division to Subtraction

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

Preparation for Standard 3NS2.3 Use
the inverse relationship of multiplication and
division to compute and check results.
6-1   Relate Division to Subtraction

Colm and his brothers have 24 shirts in their closet.
They are sizes small, medium, or large. There is an
equal number of each size. How many shirts of
each size are there?
6-1   Relate Division to Subtraction

Using counters, divide 24 counters equally into
3 groups until all the counters are gone.

8                          8                 8

There are 8 counters in each group. So, 24 ÷ 3 = 8.

Answer: There are 8 shirts of each size.
6-1   Relate Division to Subtraction

Corbin and her sisters have 36 sweaters in their
drawer. They are yellow, pink, green, red, blue, and
purple. There is an equal number of each color.
How many sweaters of each color are there?

A. 7 sweaters

B. 6 sweaters

C. 3 sweaters

D. 8 sweaters
6-1   Relate Division to Subtraction

Coach Green wants to put her 21 softball players
into equal groups of 3. How many equal groups
can she form?

Use repeated subtraction to find 21 ÷ 3.
6-1     Relate Division to Subtraction

One Way: Number Line

Start at 21. Count back by 3s until you reach 0.
How many times did you subtract?
6-1     Relate Division to Subtraction

Another Way: Paper and Pencil

21      18        15        12      9    6    3
–3      –3        –3        –3     –3   –3   –3
18      15        12         9      6    3    0
Subtract groups of 3 until you reach 0. How many
groups did you subtract?

Answer: So, 21 ÷ 3 = 7. Coach Green can form
7 equal groups.
6-1   Relate Division to Subtraction

A classroom game requires teams of 4 students.
In a class of 24 students, how many teams will
there be?

A. 6 teams

B. 7 teams

C. 5 teams

D. 8 teams
6-2     Relate Multiplication to Division

Five-Minute Check (over Lesson 6-1)
Main Idea and Vocabulary
California Standards
Example 1: Relate Multiplication to Division
Example 2: Write a Fact Family

Relate Multiplication to Division
6-2      Relate Multiplication to Division

• I will divide using related multiplication facts.

• dividend                  • quotient
• divisor                   • fact family
6-2     Relate Multiplication to Division

Standard 3NS2.3 Use the inverse
relationship of multiplication and division
to compute and check results.
6-2   Relate Multiplication to Division

Use the array of cherries to write related
multiplication and division sentences.
6-2     Relate Multiplication to Division

One Way: Multiplication

number        number            number
of rows     in each row          in all
2      ×      4         =     8
factor         factor          product
6-2     Relate Multiplication to Division

Another Way: Division

number         number           number in
in all        of rows           each row
8      ÷      2         =      4
dividend        divisor          quotient
6-2   Relate Multiplication to Division

Answer: The related multiplication and division
sentences are 2 × 4 = 8 and 8 ÷ 2 = 4.
6-2   Relate Multiplication to Division

Use the array of stars
to choose related
multiplication and
division facts.

A. 4 ÷ 3 = 1, 3 × 4 = 12

B. 4 × 4 = 16, 3 ÷ 3 = 1

C. 3 × 4 = 12, 12 ÷ 4 = 3

D. 3 × 3 = 9, 9 ÷ 3 = 3
6-2   Relate Multiplication to Division

Use the numbers 5, 6, and 30 to write the related
multiplication and division sentences for this array.

5 × 6 = 30
6 × 5 = 30
30 ÷ 5 = 6
30 ÷ 6 = 5

Notice each fact uses the same three numbers.
6-2   Relate Multiplication to Division

Use the numbers 6, 9, and 54 to choose the related
multiplication and division sentences.

A. 6 × 9 = 54, 9 × 6 = 54, 54 ÷ 9 = 6, 54 ÷ 6 = 9

B. 6 × 6 = 36, 9 × 9 = 81, 54 ÷ 9 = 6, 54 ÷ 6 = 9

C. 54 × 6 = 326, 54 × 9 = 546, 9 ÷ 3 = 3, 6 ÷ 3 = 2

D. 6 × 9 = 54, 6 × 9 = 54, 54 ÷ 9 = 6, 54 ÷ 6 = 9
6-3     Problem-Solving Strategy: Choose an Operation

Five-Minute Check (over Lesson 6-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
6-3      Problem-Solving Strategy: Choose an Operation

• I will choose an operation to use to solve a
problem.
6-3      Problem-Solving Strategy: Choose an Operation

Standard 3MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing
patterns.
6-3      Problem-Solving Strategy: Choose an Operation

Standard 3NS2.3 Use the inverse
relationship of multiplication and division to
compute and check results.
6-3   Problem-Solving Strategy: Choose an Operation

Lakita’s doctor saw patients for 5 hours today.
During this time, the doctor saw 20 patients.
How many patients did the doctor see each
hour if she saw the same number?
6-3   Problem-Solving Strategy: Choose an Operation

Understand
What facts do you know?
• The doctor saw patients for 5 hours.
• She saw 20 patients in all.

What do you need to find?
• The number of patients the doctor saw each hour.
6-3   Problem-Solving Strategy: Choose an Operation

Plan
Think about what is happening. You have a group
of 20 patients. You want to know how many
patients the doctor saw each hour in the 5 hours.
You should use division.
6-3   Problem-Solving Strategy: Choose an Operation

Solve
Divide 20 ÷ 5.

total number         number of        number of
of patients           hours           patients
20          ÷      5         =       4

Answer: So, the doctor saw 4 patients each hour.
6-3   Problem-Solving Strategy: Choose an Operation

Check
You can use multiplication to check division.

Since 5 × 4 = 20, it makes sense that 4 patients would
have been seen each hour.
6-4     Divide by 2

Five-Minute Check (over Lesson 6-3)
Main Idea
California Standards
Example 1: Make Equal Groups
6-4      Divide by 2

• I will divide by 2.
6-4     Divide by 2

Standard 3NS2.3 Use the inverse
relationship of multiplication and division to
compute and check results.
Standard 3MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to explain
mathematical reasoning.
6-4   Divide by 2

Arlo and his brother have 18 water toys in their
pool. If they share the toys equally, how many
will each child get?
To share equally between 2 people means to divide
by 2. You can write a related fact to find 18 ÷ 2 or 2 18.

2×     = 18
6-4   Divide by 2

9
Answer: So, 18 ÷ 2 = 9 or 2 18. Each person will get
9 toys.

Check
The number line shows that 18 divided into groups
of 2 is 9.
6-4   Divide by 2

Tiffany and her cousin have 16 bracelets in the
jewelry box. If they share them equally, how many
will each child get?

A. 9 bracelets

B. 7 bracelets

C. 8 bracelets

D. 6 bracelets
6-5     Divide by 5

Five-Minute Check (over Lesson 6-4)
Main Idea
California Standards
Example 1: Real-World Example
Example 2: Real-World Example
6-5      Divide by 5

• I will learn to divide by 5.
6-5     Divide by 5

Standard 3NS2.3 Use the inverse
relationship of multiplication and division to
compute and check results.

Standard 3MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to explain
mathematical reasoning.
6-5   Divide by 5

Raul stacked 30 boxes on 5 empty shelves in a
storage room. Each shelf had the same number of
boxes on it. How many boxes were on each shelf?

You need to find 30 ÷ 5.
6-5     Divide by 5

One Way: Use Models

There are 30 counters
and 5 counters are in
each group. There are
6 equal groups.
6-5     Divide by 5

Another Way: Repeat Subtraction

30         25       20   15   10       5
–5         –5       –5   –5   –5      –5
25         20       15   10    5       0

Subtract groups of 5 until you reach 0. Count
the number of groups you subtracted.
6-5     Divide by 5

6
Answer: So, 30 ÷ 5 = 6 or 5 30. There are
6 boxes on each shelf.
6-5   Divide by 5

Tim put 32 cans on 4 shelves in a grocery store.
Each shelf has the same number of cans on it.
How many cans are on each shelf?

A. 9 cans

B. 6 cans

C. 8 cans

D. 7 cans
6-5   Divide by 5

Niran has a scrapbook for his baseball cards. He
has 25 cards. If 5 cards will fit on a page, how many
pages can he fill?
Write a related multiplication fact to find 25 ÷ 5.

25 ÷ 5 =

5×     = 25

5 × 5 = 25
5
Answer: So, 25 ÷ 5 = 5 or 5 25. Niran can fill 5 pages.
6-5   Divide by 5

Check

The model show that 25 ÷ 5 = 5.

25 divided into groups of 5 forms 5 groups.
5 groups of 5 = 25
6-5   Divide by 5

Heather has a photo album for her vacation. She
has 63 photos. If 6 photos fit on each page, how
many pages can she fill?

A. 7 pages

B. 8 pages

C. 9 pages

D. 10 pages
6-6     Problem-Solving Investigation: Choose a Strategy

Five-Minute Check (over Lesson 6-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
6-6      Problem-Solving Investigation: Choose a Strategy

• I will choose the best strategy to solve a problem.
6-6     Problem-Solving Investigation: Choose a Strategy

Standard 3MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant information,
sequencing and prioritizing information,
and observing patterns.
6-6     Problem-Solving Investigation: Choose a Strategy

Standard 3NS2.3 Use the inverse
relationship of multiplication and division
to compute and check results.
6-6    Problem-Solving Investigation: Choose a Strategy

KINAH: I want to plant a vegetable
garden. I have 6 tomato plants,
5 pepper plants, and 5 zucchini
plants. I want to put the plants
into 4 equal rows.

YOUR MISSION: Find how many plants
should be planted in each row.
6-6     Problem-Solving Investigation: Choose a Strategy

Understand
What facts do you know?
• Kinah has 6 tomato, 5 pepper, and 5 zucchini
plants.
• She wants to plant them in 4 equal rows.

What do you need to find?
• Find how many plants to put in each row.
6-6     Problem-Solving Investigation: Choose a Strategy

Plan
You need to look at how to arrange items. So, the
draw a picture strategy is a good choice.
6-6     Problem-Solving Investigation: Choose a Strategy

Solve
The picture shows 6 + 5 + 5 or 16 plants. There
are 4 equal groups of 4 plants.

Since 16 ÷ 4 = 4, Kinah needs to plant 4 plants
in each row.
6-6     Problem-Solving Investigation: Choose a Strategy

Check
Look back at the problem. Since 4 × 4 = 16, you
know that the answer is correct.
6-7     Divide by 10

Five-Minute Check (over Lesson 6-6)
Main Idea
California Standards
Example 1: Real-World Example
6-7      Divide by 10

• I will learn to divide by 10.
6-7     Divide by 10

Standard 3NS2.3 Use the inverse
relationship of multiplication and division
to compute and check results.
6-7     Divide by 10

Standard 3MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to
explain mathematical reasoning.
6-7   Divide by 10

Juanita arranged her 80 football cards into stacks
of 10. How many stacks does she have?

You need to find 80 ÷ 10.
6-7     Divide by 10

One Way: Use Repeated Subtraction

80    70    60     50     40     30      20     1
– 10 – 10   – 10   – 10   – 10   – 10    – 10
70    60    50     40     30     20     10 0

Subtract groups of 10 until you reach 0.
Count the number of groups you subtracted.
You subtracted 10 groups eight times.
6-7     Divide by 10

Another Way: Use a Related Fact

Write a related multiplication fact to find 80 ÷ 10.

You know that 10 × 8 = 80.
8
So, 80 ÷ 10 = 8 or 10 80.

Answer: So, Juanita has 8 stacks.
6-7   Divide by 10

George put his 60 bananas into bunches of 10.
How many bunches does he have?

A. 10 bunches

B. 8 bunches

C. 6 bunches

D. 5 bunches
6-8     Division Properties

Five-Minute Check (over Lesson 6-7)
Main Idea
California Standards
Key Concept: Division Properties
6-8      Division Properties

• I will learn to use properties about using 1 and 0
in division.
6-8     Division Properties

Standard 3NS2.6 Understand the special
properties of 0 and 1 in division.
Standard 3NS2.3 Use the inverse
relationship of multiplication and division
to compute and check results.
6-8   Division Properties
Division Concepts and Facts
6

Five-Minute Checks

Math Tool Chest

Image Bank

Understand Division

Relate Multiplication to Division
Division Concepts and Facts
6

To use the images that are on the
following four slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
Division Concepts and Facts
6
Division Concepts and Facts
6
Division Concepts and Facts
6
Division Concepts and Facts
6
Division Concepts and Facts
6

Lesson 6-1      (over Chapter 5)
Lesson 6-2      (over Lesson 6-1)
Lesson 6-3      (over Lesson 6-2)
Lesson 6-4      (over Lesson 6-3)
Lesson 6-5      (over Lesson 6-4)
Lesson 6-6      (over Lesson 6-5)
Lesson 6-7      (over Lesson 6-6)
Lesson 6-8      (over Lesson 6-7)
Division Concepts and Facts
6
(over Chapter 5)

One tricycle has 3 wheels. Two tricycles have
6 wheels. How many wheels will there be on
6 tricycles?

A. 16 wheels

B. 18 wheels

C. 9 wheels

D. 12 wheels
Division Concepts and Facts
6
(over Lesson 6-1)

Divide. Use a number line or paper and pencil.
16 ÷ 8

A. 3

B. 6

C. 2

D. 8
Division Concepts and Facts
6
(over Lesson 6-1)

Divide. Use a number line or paper and pencil.
9÷3

A. 3

B. 6

C. 1

D. 9
Division Concepts and Facts
6
(over Lesson 6-1)

Divide. Use a number line or paper and pencil.
35 ÷ 7

A. 10

B. 5

C. 7

D. 12
Division Concepts and Facts
6
(over Lesson 6-1)

Divide. Use a number line or paper and pencil.
24 ÷ 4

A. 6

B. 7

C. 12

D. 14
Division Concepts and Facts
6
(over Lesson 6-2)

Write the fact family for the following set of
numbers: 3, 8, 24.

A. 8 × 3 = 24, 3 × 8 = 24, 24 ÷ 8 = 3, 24 ÷ 3 = 8

B. 8 × 3 = 24, 8 × 4 = 32, 24 ÷ 3 = 8, 32 ÷ 4 = 8

C. 24 × 3 = 8, 24 × 8 = 3, 8 ÷ 3 = 24, 3 ÷ 8 = 24

D. 8 + 3 = 11, 3 + 8 = 11, 11 – 8 = 3, 11 – 3 = 8
Division Concepts and Facts
6
(over Lesson 6-2)

Write the fact family for the following set of
numbers: 1, 5, 5.

A. 5 × 1 = 5, 1 × 5 = 5, 5 ÷ 5 = 1, 1 ÷ 5 = 5

B. 5 × 1 = 5, 5 × 5 = 25, 5 ÷ 1 = 5, 25 ÷ 5 = 5

C. 1 × 5 = 5, 5 × 1 = 5, 5 ÷ 1 = 5, 5 ÷ 5 = 1

D. 5 × 1 = 1, 1 × 5 = 5, 5 ÷ 1 = 1, 5 ÷ 5 = 5
Division Concepts and Facts
6
(over Lesson 6-3)

Solve. Gracia had 6 daises and 9 roses. How
many flowers did Gracia have in all?

A. 15 flowers

B. 3 flowers

C. 13 flowers

D. 2 flowers
Division Concepts and Facts
6
(over Lesson 6-3)

Solve. Brian had 6 pots each with 2 lilacs. How
many lilacs did Brian have?

A.   10 lilacs

B.   12 lilacs

C.   9 lilacs

D.   4 lilacs
Division Concepts and Facts
6
(over Lesson 6-4)

Divide. Write a related multiplication fact.
18 ÷ 2

A.   9; 2 × 9 = 18

B.   2; 9 × 2 = 18

C.   18; 6 × 3 = 18
Division Concepts and Facts
6
(over Lesson 6-4)

Divide. Write a related multiplication fact.
6÷2

A.   2; 2 × 3 = 6

B.   4; 2 × 4 = 8

C.   3; 2 × 3 = 6
Division Concepts and Facts
6
(over Lesson 6-4)

Divide. Write a related multiplication fact.
12 ÷ 2

A.   6; 2 × 6 = 12

B.   6; 2 × 3 = 6

C.   10; 2 × 10 = 20
Division Concepts and Facts
6
(over Lesson 6-4)

Divide. Write a related multiplication fact.
16 ÷ 2

A.   4; 4 × 4 = 16

B.   8; 2 × 8 = 16

C.   32; 2 × 16 = 32
Division Concepts and Facts
6
(over Lesson 6-4)

Divide. Write a related multiplication fact.
10 ÷ 2

A.   10; 5 × 2 = 10

B.   5; 5 × 3 = 15

C.   5; 2 × 5 = 10
Division Concepts and Facts
6
(over Lesson 6-4)

Divide. Write a related multiplication fact.
8÷2

A.   4; 2 × 4 = 8

B.   6; 2 × 4 = 8

C.   3; 2 × 3 = 6
Division Concepts and Facts
6
(over Lesson 6-4)

Divide. Write a related multiplication fact.
14 ÷ 2

A.   9; 3 × 3 = 13

B.   7; 2 × 7 = 14

C.   12; 4 × 3 = 12
Division Concepts and Facts
6
(over Lesson 6-4)

Divide. Write a related multiplication fact.
4÷2

A.   2; 2 × 2 = 4

B.   8; 2 × 4 = 8

C.   6; 3 × 4 = 12
Division Concepts and Facts
6
(over Lesson 6-5)

Divide. Write a related multiplication fact.
25 ÷ 5

A.   5; 5 × 5 = 25

B.   10; 6 × 6 = 36

C.   15; 3 × 5 = 15
Division Concepts and Facts
6
(over Lesson 6-5)

Divide. Write a related multiplication fact.
50 ÷ 5

A.   25; 5 × 5 = 25

B.   10; 10 × 5 = 50

C.   15; 3 × 5 = 15
Division Concepts and Facts
6
(over Lesson 6-5)

Divide. Write a related multiplication fact.
5÷5

A.   10; 2 × 5 = 10

B.   5; 1 × 1 = 1

C.   1; 1 × 5 = 5
Division Concepts and Facts
6
(over Lesson 6-5)

Divide. Write a related multiplication fact.
35 ÷ 5

A.   7; 5 × 7 = 35

B.   5; 5 × 6 = 30

C.   12; 3 × 4 = 12
Division Concepts and Facts
6
(over Lesson 6-6)

Three men are standing in line. Mr. Smith is
3 inches taller than Mr. Sanchez. Mr. Jones is
2 inches shorter than Mr. Smith. Which man
is shortest?

A. Mr. Smith

B. Mr. Sanchez

C. Mr. Jones
Division Concepts and Facts
6
(over Lesson 6-7)

Divide 70 ÷ 10.

A. 7

B. 10

C. 11

D. 70
Division Concepts and Facts
6
(over Lesson 6-7)

Divide 30 ÷ 10.

A. 10

B. 13

C. 3

D. 11
Division Concepts and Facts
6
(over Lesson 6-7)

Divide 50 ÷ 10.

A. 5

B. 10

C. 15

D. 20
Division Concepts and Facts
6
(over Lesson 6-7)

Divide 20 ÷ 10.

A. 2

B. 10

C. 15

D. 20
Division Concepts and Facts
6
(over Lesson 6-7)

Divide 90 ÷ 10.

A. 9

B. 15

C. 90

D. 100
Division Concepts and Facts
6
(over Lesson 6-7)

Divide 100 ÷ 10.

A. 1

B. 100

C. 0

D. 10
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