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**Properties of Addition**

To identify addition properties

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**MENTAL MATH Tell me which is greater. 1. 2 + 1 or 2 + 2 ______________**

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**Three Properties of Addition**

Addition properties are like special tools. They make it easier to work with numbers.

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**The Commutative Property**

Background The word commutative comes from the verb “to commute.” Definition on dictionary.com Commuting means changing, replacing, or exchanging People who travel back and forth to work are called commuters. Traffic Reports given during rush hours are also called commuter reports.

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**Here are two families of commuters.**

Commuter B Commuter A Commuter A & Commuter B changed lanes. Remember… commute means to change. Commuter A Commuter B

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**Here is another example…**

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**Commutative Property You can add in any order. 5 + 2 = 7 * 2 + 5 = 7**

5 + 2 = * = 7 = * = 16

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**The Associative Property**

Background The word associative comes from the verb “to associate.” Definition on dictionary.com Associate means connected, joined, or related People who work together are called associates. They are joined together by business, and they do talk to one another.

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**Let’s look at another hypothetical situation**

Three people work together. Associate B needs to call Associates A and C to share some news. Does it matter who he calls first?

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**Here are three associates.**

B B calls A first He calls C last A C If he called C first, then called A, would it have made a difference? NO!

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**(The Role of Parentheses)**

In math, we use parentheses to show groups. In the order of operations, the numbers and operations in parentheses are done first. So….

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**You can change the grouping. **

Associative Property You can change the grouping. REMEMBER: Add the numbers in parentheses first. * (6 + 3) + 5 = * 6 + (3 + 5) = 14 * (8 + 2) + 4 = * 8 + (2 + 4) = 14

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**The Identity Property of Addition**

I am me! You cannot change My identity!

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**Zero is the only number you can add to something and doesn’t change.**

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**Identity Property of Addition**

+ 0 = A + 0 = A

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**Let’s practice ! Look at the problem.**

Identify which property it represents.

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(9 + 8) + 7 = 9 + (8 + 7) It is the only addition property that has parentheses.

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= 12 It is the only addition property that has two addends and one of them is a zero.

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9 + 7 = 7 + 9 It is the only addition property that has numbers that change places.

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4 + 6 = 6 + 4 Numbers change places.

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3 + 0 = 3 See the zero?

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(4 + 3) + 2 = 4 + (3 + 2) It has parentheses!

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a + 0 = a Zero!

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a + b = b + a Moving numbers!

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(a + b) + c = a + (b + c) Parentheses! B A C

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Addition using three addends. An associative property is when you group numbers in anyway and the answer stays the same.

Addition using three addends. An associative property is when you group numbers in anyway and the answer stays the same.

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