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

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

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

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

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

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.

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

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.

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).

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

Properties of Zero Multiplication property of zero Addition property of zero

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

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 = 8 + 7 then x = 8 + 7

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