Lesson 8: Generate Equivalent Expressions6.AT.7

I can…

I can use the commutative, associative, and identity properties to rewrite expressions.

Key words

• Properties of Operations — Rules that let you change the order or grouping.
• Commutative Property — Changing the order does not change the answer.
• Associative Property — Changing the grouping does not change the answer.
• Identity Property — Add 0 or multiply by 1. The number stays.
• Property — A rule that is always true in math.
• Distributive Property — Multiply by each part inside the ( ).
• Equivalent expressions — Math phrases that look different but give the same value.
• Expand — Multiply so the ( ) are gone.
• Factor an expression — Pull out a number that is in every part.

Steps

1. I have 3 guitarists, 5 drummers, and 2 keyboard players.
2. I can add them as 3 + 5 + 2, which gives 10.
3. The Commutative Property says order does not matter: 5 + 3 + 2 also gives 10.
4. The Associative Property says grouping does not matter: (3 + 5) + 2 = 3 + (5 + 2), both equal 10.

Try it

At the store you put 4 apples, 6 pears, and 3 bananas in a bag. You count them two ways: (4 + 6) + 3 = 4 + (6 + 3). Which property is shown?

Check your answer

Associative Property

The grouping (parentheses) changed but the numbers stayed in the same order, so this is the Associative Property of Addition. Both ways give 13 pieces of fruit.

Sentence starter

I know ___ because ___.

Goal: I can explain my reasoning using the words commutative property, associative property, and identity property.