1. Mathematical Properties
Commutative and Associative

2. S.W.B.A.T
Apply the commutative and associative properties to classroom examples

3. Commutative Property
The word “commutative” comes from “commute” or “move around”
The Commutative Property refers to moving stuff around

4. Examples Addition a + b = b + a 2 + 3 = 3 + 2 Multiplication ab = ba
2 x 3 = 3 x 2

5. Examples 4 x 3 x X 4 x X x 3 3 x X x 4 X x 3 x 4 X x 4 x 3
Use the commutative property to restate:
3 x 4 x X
They do NOT want you to simplify, they want you to move things around
The answer is any of the following
4 x 3 x X
4 x X x 3
3 x X x 4
X x 3 x 4
X x 4 x 3

6. Associative Property
The word “associative” comes from “associate” or “group”
The Associative Property is the rule that refers to grouping

7. Examples Addition a + (b + c ) = ( a + b ) + c
2 + ( ) = ( ) + 4
Multiplication
a ( bc ) = ( ab ) c
2 ( 3 x 4 ) = ( 2 x 3 ) 4

8. Examples Rearrange, using associative property: 2 (3x)
They want you to regroup NOT simplify
You need to show that it is regrouped to
( 2 x 3 ) x
Then you can say that it equals 6x