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**Lesson 1-8 Properties of Real Numbers**

This slide show will be used as an introduction to the properties of equalities taught in pre-algebra and algebra classes. It can also be used as a resource to review the properties in an advanced math class (e.g. algebra II, pre-calculus). However, I used a variation of this slide show previously this year. It was made for a co-taught algebra A course. Primarily, the class has at risk or special education freshman students, as well as a handful of sophomores who have previously failed the course. Students have a difficult time in math classes when it comes to learning about and applying the properties of equality even thought they have used these properties for years in previous math classes. The power point allows me to show examples and also add student examples. Also, incorporating the use of video clips provides another explanation and medium of the use of the properties. I plan on giving (in fact already have given) the students a hand out of the PowerPoint along with a place for notes. Students will be asked to add specific notes to each slide (See individual slides for examples.) NOTE: The sound will help to quiet the class!! Ha! Benchmarks: Michigan Curriculum Framework Standard IV.1 Concepts and Properties of Numbers Students experience counting and measuring activities to develop intuitive sense about numbers, develop understanding about properties of numbers, understand the need for and existence of different sets of numbers, and investigate properties of special numbers

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**Commutative Properties**

Commutative Property of Addition Example: Commutative Property-click to see video Commutative Property of Multiplication Example: Compare/contrast the commutative properties of equality. Talk about whether or not you can use it for division and/or subtraction. Show examples in other operations. In Algebra II we can discuss how the commutative property of equality does not apply to Matrix Multiplication Have students write their own example of each on their paper. I will also have the students write a synonym for commutative. We usually talk about commuting, or moving around to get the students to understand the word.

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**Associative Properties**

Associative Property of Addition Example: Associative Property of Multiplication Example: Associative Property-click to see video Same idea with this slide. We discuss how the word associative means to group. Students are to write this on their papers along with any other meanings or synonyms that we come up with. The short video identifies the

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**Distributive Property**

Example: Distributive Property-click to see video Students have learned about the distributive property in the previous lesson. I have shown them a couple methods of how to use the distributive property including an area model. Now, I am showing them the property on the video and written algebraically. Mrs. Lamb’s math class

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**Identity Properties Identity Property of Addition**

Example: Identity Property of Multiplication Example: In the next two slides we discuss the similarities between the Identity Property and the Inverse Properties. I also begin to hint at these properties will be coming up in the next chapter of solving equations. We will usually start this slide on the next day to students some time to work with the previous properties and give more practice with the distributive property (one that students often trip over).

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**Inverse Properties Inverse Property of Addition**

For every a, there is an additive inverse –a such that a + (-a) = 0 Example: (-5) = 0 Inverse Property of Multiplication For every a ( ), there is a multiplicative inverse such that Example: See previous slide.

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**Properties of Real Numbers**

Example – Identifying Properties Name the property that each equation illustrates. Explain. = 7 + 9 2. 3. t + 0 = t 4. –2(q + 3)= -2q - 6 We will go through these examples together before the students are assigned similar practice problems. After students are able to identify properties then we will be able to use deductive reasoning in justifying steps in simplifying expressions.

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**Properties of Real Numbers**

Answers: Commutative Property of Addition, because the order of the addends changes. Associative Property of Multiplication, because the grouping of the factors changes. Identity Property of Addition, because the sum of a number and zero is the number. Distributive Property, because you are finding the area. Here we will also discuss other reasons that the students wrote.

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**Identify which property that justifies each of the following.**

4 (8 2) = (4 8) 2

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**Identify which property that justifies each of the following.**

4 (8 2) = (4 8) 2 Associative Property of Multiplication

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**Identify which property that justifies each of the following.**

6 + 8 = 8 + 6

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**Identify which property that justifies each of the following.**

6 + 8 = 8 + 6 Commutative Property of Addition

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**Identify which property that justifies each of the following.**

= 12

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**Identify which property that justifies each of the following.**

= 12 Additive Identity Property

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**Identify which property that justifies each of the following.**

5(2 + 9) = (5 2) + (5 9)

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**Identify which property that justifies each of the following.**

5(2 + 9) = (5 2) + (5 9) Distributive Property

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**Identify which property that justifies each of the following.**

5 + (2 + 8) = (5 + 2) + 8

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**Identify which property that justifies each of the following.**

5 + (2 + 8) = (5 + 2) + 8 Associative Property of Addition

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**Identify which property that justifies each of the following.**

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**Identify which property that justifies each of the following.**

Multiplicative Inverse Property

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**Identify which property that justifies each of the following.**

5 24 = 24 5

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**Identify which property that justifies each of the following.**

5 24 = 24 5 Commutative Property of Multiplication

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**Identify which property that justifies each of the following.**

= 0

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**Identify which property that justifies each of the following.**

= 0 Additive Inverse Property

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**Identify which property that justifies each of the following.**

-34 1 = -34

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**Identify which property that justifies each of the following.**

-34 1 = -34 Multiplicative Identity Property

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**Click Below to See Video**

hill.com/sites/ /student_view0/chapter1/lesson8/pers onal_tutor.html 9.html 1.html

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**Click Below to Test Your Skills**

hill.com/sites/ /student_view0/chapter1/le sson8/self-check_quizzes.html berPropertiesConcentration/NumberPropertiesConc entration.html hill.com/sites/ /student_view0/chapter12/l esson1/self-check_quizzes.html

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