The document defines key properties used in mathematics such as the commutative property, associative property, identity property of zero, and identity property of one. It provides definitions and examples for each property. The essential question asks how using properties can help represent mathematical relationships. Examples are given to show how the commutative property allows numbers to be added or multiplied in any order, and how the associative property allows grouping of numbers when adding or multiplying.

1. Name ______________________________ Date ___________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 4 Properties
TB 1-5 / OC 3-5
Essential Question: How can using properties help you to represent mathematical relationships?
Vocabulary Definition Example
Commutative
Property
Associative
Property
Identity Property of
Zero
Identity Property of
One
Property of Zero

2. 7x0=0
32 x 1 = 32
45+s = 45 32 x a = 32
Commutative Property

3. Name ______________________________ Date ___________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 4 Properties
TB 1-5 / OC 3-5
Essential Question: How can using properties help you to represent mathematical relationships?
Vocabulary Definition Example
Commutative 18 + 9 = 9 + 18
You can add or
Property multiply numbers in
15 x 2 = 2 x 15
(Ordering) any order
When you are only
Associative adding or only (17+2)+9=17+(2+9)
Property multiplying, you can
(Grouping) group any of the (12x2)x4=12x(2x4)
numbers together.
The sum of any
Identity Property of
number and zero is
Zero 9+0=9
equal to the number
(addition)
(addition)
The product of any
Identity Property of
number and one is
One 5x1=5
equal to the number.
(multiplication)
(multiplication)
The product of any
Property of Zero
number and zero is 7x0=0
(multiplication)
zero.

4. 7x0=0
property of zero
32 x 1 = 32
identity property of one
45 + s = 45 32 x a = 32
Identity Property of Zero Identity Property of One
Commutative Property
12 + 8 9 x (6 x 4)