Math Chapter 11
Concepts of Division Study Guide
Skill #1 Division Sentence
•
A division sentence always begins with the total number, or largest
number. You are trying to find out how many groups or how many in each
group.
•
Example: 21 ÷ 2 = ____ 21 in all divided into 2 groups = 7 in each group
21 in all with 2 in each group = 7 groups
Skill #2 Modeling Division
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•
Division figures out how many are in each group
Students should be able to model this with a drawing. Draw the groups
first, then give one to each group until you reach your total number
•
Example: 14 ÷ 2 = _____
•
•
Division also figures out how many groups there are
Students should be able to model this with a drawing. Draw the total
number first, then circle the number in each group until all have been
circled
•
Example: 12 ÷ 4 = _____
Skill #4 Division as Repeated Subtraction
• Division is also repeated subtraction, or subtracting the same
number over and over until 0 is reached
• Example: 8 ÷ 2 =4
8-2=6
6-2=4
4-2=2
2-2=0
-2
-2
-2
-2
Skill #5 Model Division Using an Array
• Division can be solved through the use of an array
•
Example: 20 ÷ 5 =4
SOLVING USING ROWS
I will draw a row of 5
first. Then I will
continue to add a
row of 5 until I have
reached 20. When I
am finished, I know
that there are 4
rows of 5. So,
20 ÷ 5 = 4.
SOLVING USING COLUMNS
I will draw a column
of 5 first. Then I will
continue to add a
column of 5 until I
have reached 20.
When I am finished, I
know that there are
4 columns of 5. So,
20 ÷ 5 = 4.
Skill #6 Multiplication and Division Relationship
•
•
•
Multiplication and Division are INVERSE OPERATIONS.
Multiplication can be used to solve division.
Division can also be thought of as a missing factor problem in
multiplication
•
Examples: 30 ÷ 6 = ____
30 ÷ 6 = 5
Think: 6 x ___ = 30
6 x 5 = 30
Skill #7 Fact Families
•
A fact family is a set of related multiplication and division number
sentences
•
Examples:
6, 7, 42
6 x 7 = 42
7 x 6 = 42
42 ÷ 6 = 7
42 ÷ 7 = 6
4, 4, 16
4 x 4 = 16
16 ÷ 4 = 4
Skill #8 Problem Solving: Writing a Number Sentence
•
Students should be able to solve word problems by writing a number
sentence
•
Example:
Sally has 45 stickers. She gave some to 9 different friends. How
many stickers did each friend get?
45 ÷ 9 = 5 stickers