Find out how to evaluate and rewrite expressions using the different properties of integers.

1. Properties of
Operations
with Integers
Find out how to evaluate and rewrite
expressions using the different
properties of integers.
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2. Lesson
Outline
• Addition
• Multiplication
• Addition
• Multiplication
Commutative Property Associative Property
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3. Springboard
Question
bacon,
tomato,
lettuce
lettuce
and tomato sandwich
and bacon sandwich?
Does a
taste the same as a
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4. • differentiate commutative
from associative property
• apply commutative and
associative properties in
integer operations
By the end of the lesson,
you'll be able to:
Learning
Outcomes
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5. It applies to
but not to
addition
subtraction
multiplication
division
It states that rearranging the
numbers does not affect the sum
or product of numbers.
Commutative
Property
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6. 2 4 6
What is the sum if you add them
starting from the left most digit?
What is the sum if you add them
starting from the right most digit?
9 5
a + b = b + a
Commutative
Property of Addition
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7. Commutative
Property of
Multiplication
Rotating the grids below doesn't
affect their areas.
2 × 7 is the same as saying 7 × 2
5 × 8 is the same as saying 8 × 5
a × b = b × a
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8. −3 + 9 = 9 +
Try These!
16 × 15 × 13 = 15 × × 16
−4 + (−10) = + (−4)
Addition Multiplication
15 + 19 = 19 +
Use the commutative property
to find the missing numbers.
21 × (−250) = (-250) ×
24 × 50 = 50 ×
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9. −3 + 9 = 9 + 16 × 15 × 13 = 15 × × 16
−4 + (−10) = + (−4) 21 × (−250) = (-250) ×
24 × 50 = 50 ×
21
24
Addition Multiplication
15 + 19 = 19 +
(−3) 13
−10
15
ANSWER KEY
Use the commutative property
to find the missing numbers.
Try These!
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10. It states that changing the
grouping of the numbers using
parentheses does not affect the
sum and product of numbers.
Associative
Property
It applies to
but not to
addition
subtraction
multiplication
division
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11. a + (b + c) = (a + b) + c
Add up all red
fruits first, then
add the bananas.
(A) (B)
Add bananas and
strawberries together,
then add the apples.
Did the total
number of fruits
change?
Associative
Property of Addition
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12. a × (b × c) = (a × b) × c
Associative
Property of
Multiplication 5 2 4
What are the different ways you
can rearrange these numbers to
get the same product?
Example:
5 × (2 × 4)

13. −5 × (2 × 7) = (−5 × 2) × 7
−8 × (7 × 4)= (−8 × 7) × 4
Use the associative property to
determine whether the equations below
are true or false. Drag each equation
to the corresponding column.
Try This!
True
False
90 ÷ 6 ÷ (−3) = 90 ÷ (6 ÷ (−3))
(−2 + 4) + 6 = (−2) + [4 + 6]

14. −5 × (2 × 7) = (−5 × 2) × 7
−8 × (7 × 4)= (−8 × 7) × 4
90 ÷ 6 ÷ (−3) = 90 ÷ (6 ÷ (−3))
(−2 + 4) + 6 = (−2) + [4 + 6]
ANSWER KEY
Use the associative property to
determine whether the equations below
are true or false. Drag each equation
to the corresponding column.
Try This!
True False

15. 27 + 4 + 9
and
9 + 27 + 4
related to
rearranging
the numbers
related to
grouping of
the numbers
3 × (6 × 8)
and
6 × (3 × 8)
99 + (1 + 100)
and
1 + (100 + 99)
3 × 9 × 2
and
9 × 2 × 3
Lesson Check
Group the sticky notes correctly under the two headings:
Commutative Associative

16. 27 + 4 + 9
and
9 + 27 + 4
related to
rearranging
the numbers
related to
grouping of
the numbers
3 × (6 × 8)
and
6 × (3 × 8)
99 + (1 + 100)
and
1 + (100 + 99)
3 × 9 × 2
and
9 × 2 × 3
Lesson Check
Group the sticky notes correctly under the two headings:
Commutative Associative
ANSWER KEY

17. Assignment
Read about the distributive property.
How does it differ from the
commutative and associative
properties? Does it apply to all
operations: addition, subtraction,
multiplication, and division?
Share what you learned with the
class tomorrow.