1. 2-1Sets 2-2 The Number System Properties of Real Numbers
Proof Geometry

2. Sets A set is a collection of objects
Each object is called an element of the set
Example

3. Sets: Subset
Subset: If one set contains every element of another set, then we say the second set is a subset of the first.

4. Sets: Union and Intersection
Union: All the elements that belong to one or both sets
Intersection: Set of elements common to both sets

5. The Line Postulate
How many different lines can be drawn between two points?
For every two different points, there is exactly ONE line that contains both points

6. Commutative Properties
Commutative Property of Addition
Example:
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.

7. 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

8. 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.

9. Identity Properties Identity Property of Multiplication
Identity Property of Addition
Example: Zero is the additive identity
Identity Property of Multiplication
Example: One is the multiplicative identity
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).

10. Inverse Properties Inverse Property of Multiplication (Reciprocal)
Example:
Inverse Property of Addition (Opposite)
a + (-a) = 0
Example:
5 + (-5) = 0
See previous slide.

11. Properties of Zero Multiplication property of zero
Addition property of zero

12. Properties of Equality
Substitution Property
If a = b, then either a or b may be substituted for the other in any equation
Example If x = 2 and x + y = 5, then 2 + y = 5
Reflexive Property

13. Properties of Equality
Symmetric Property
If a = b, then b = a
Example If x + 2 = 4 then 4 = x + 2
Transitive Property
If a = b and b = c, then a = c
Example If x = 15 and 15 = then x = 8 + 7

14. Trichotomy Property
For every x an y, one and only one of the following conditions holds:
x<y, x=y, x>y