1. Repeating Decimals
Repeating decimals are decimals that contain a infinite number of digits.
Examples:
0.333… …

2. Non Repeating Decimals
Non repeating decimals are decimals that either end or carry on forever in a random way.
Examples: …
2.7

3. 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

4. Commutative Properties
Commutative Property of Addition
Example:
Commutative Property
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.

5. Associative Properties
Associative Property of Addition
Example:
Associative Property of Multiplication
Example:
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

6. Distributive Property
Example:
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. de Nobrega’s math class

7. 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).

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

9. Order of Operations Parenthesis/Grouping Symbols Exponents
Multiplication and Division – left to right
Addition and/or Subtraction – left to right

10. Grouping Symbols
Grouping symbols include parenthesis, braces, brackets, numerators and denominators of fractions and underneath a radical or inside absolute value symbols.

11. Examples – Using Order of Operations
Evaluate the following:
22(12 + 8) 5
2. 52 ÷ (2 + 11)
3. 7 • ÷ 5

12. Properties of Real Numbers
Example – Identifying Properties
Name the property that each equation illustrates. Explain.
9 + 7 = 7 + 9
t + 0 = t
–(q + 3)= -q - 3
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.

13. 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.