Commutative and Associative Properties

Commutative and Associative Properties

Poll

How is your week going so far?

• Great!

• Good

• Okay

• MEH

• I'm staying hidden from the world today.

Class Expectations

• Camera is turned on (PBIS points are being given to students with their camera on the entire time with them being in the frame)

• Raise a hand, respond in chat, and engage

• Find a quiet place to study.

Multiple Choice

150 + 75 = 75 + 150

• Associative Property of Addition

• Commutative Property of Addition

Commutative Property Video

https://www.youtube.com/watch?v=14SHWWld1z4

Open the Freyer Model Assignment

Open Ended

How would you define the commutative property?

Vocabulary

• Commutative Property of Multiplication: The product of a group of numbers is the same regardless of the order in which the numbers are arranged.

•  Commutative Property of Addition: The sum of a group of numbers is the same regardless of the order in which the numbers are arranged

Examples

•  $a\ +\ b\ =\ b\ +\ a$  

•  $a\times b\ =\ b\times\ a$  

Characteristics

the same addends or factors reversed

Open Ended

Write your own example of the commutative property of addition.

 $\left(a\ +\ b\right)\ +\ c\ =\ a\ +\ \left(b\ +\ c\right)$  

Open Ended

Write your own example of the commutative property of multiplication.

 $a\times b\ =\ b\times\ a$  

NonExamples

•  $a\ -\ b\ \ne\ b\ -\ a$  

•  $a\ \div\ b\ \ne\ b\ \div\ a$  

Multiple Choice

(30 + 20) + 60 = 30 + (20 + 60)

• Associative Property of Addition

• Commutative Property of Addition

Open Ended

How would you define the associative property?

Associative Property

https://www.youtube.com/watch?v=P2QnXOCl6sY

Vocabulary

• Associative Property of Addition: The sum of a set of numbers is the same no matter how the numbers are grouped.

• Associative Property of Multiplication: The product of a set of numbers is the same no matter how the numbers are grouped.

Examples

•  $\left(a\ +\ b\right)\ +\ c\ =\ a\ +\ \left(b\ +\ c\right)$  

•  $\left(a\ \times\ b\right)\ \times\ c\ =\ a\ \times\ \left(b\ \times\ c\right)$  
  

Characteristics

Order is the same, but the grouping changes.

Open Ended

Write your own example of the associative property of addition.

 $\left(a\ +\ b\right)\ +\ c\ =\ a\ +\ \left(b\ +\ c\right)$  

Open Ended

Write your own example of the associative property of multiplication.

 $\left(a\ \times\ b\right)\ \times\ c\ =\ a\ \times\ \left(b\ \times\ c\right)$  

NonExamples

•  $\left(a\ \div\ b\right)\ \div\ c\ \ne\ a\ \div\ \left(b\ \div\ c\right)$  

•  $\left(a\ -\ b\right)\ -\ c\ \ne\ a\ -\ \left(b\ -\ c\right)$  

Closing Questions

Open Ended

Create an equivalent expression for the following:

Commutative Property

2+3+5=

Open Ended

Create an equivalent expression to

Associative Property

5 + (2 + 3) =

Open Ended

Explain why the commutative property and associative property do not work for subtraction or division.