Ch 1.2.2 – Variables, Expressions, & Properties MJ3 Ch 1.2.2 – Variables, Expressions, & Properties

Bellwork Please take out yesterday’s assignment and leave it on your desk for me to check. Evaluate 3 + 9 – 2 x (8  2) Evaluate if q = 5, r = 6, and s = 3 3r + 2s – 4 6q 3r - 3

Assignment Review Text p. 14 #14 – 39

Quick review Yesterday we discussed: The Order of Operations What is it? What does it tell us to do? Evaluating Algebraic Expressions What is the process Exponents What the exponent tell the base to do? What is that called Evaluating Equations What does it mean if the statement is false? What does it mean if the statement is true?

Before we begin… Please take out your notebook and get ready to work… Yesterday we discussed variables and expressions… Today we will look at the four basic algebraic properties…

Objective Students will identify algebraic properties

Properties The four basic algebraic properties that you are required to know are: Commutative Property Associative Property Distributive Property Identity Property These are not the only algebraic properties. However, at the 8th grade level you are required to be able to recognize and know how to work each of these properties.

Commutative Property The commutative property states: The order in which you add or multiply two numbers does not change the sum or product Here is what it looks like…

Example Addition: a + b = b + a 3 + 5 = 5 + 3 Multiplication:

Associative Property The associative property states: The way three numbers are grouped when added or multiplied does not change the sum or product Here is what it looks like…

Example Addition: a + (b +c) = (a + b) + c 2 + (3 + 8) = (2 + 3) + 8 Multiplication: a ∙ (b ∙ c) = (a ∙ b) ∙ c 3 ∙ (4 ∙ 5) = (3 ∙ 4) ∙ 5

Distributive Property The distributive property states… To add a sum by a number multiply each addend of the sum by the number outside the parenthesis. In other words…Multiply the number outside of the parenthesis by each number inside the parenthesis… Here is what it looks like…

Distributive Property Addition a(b + c) = ab + ac 4(6 + 2) = 4(6) + 4(2) Subtraction: a(b – c) = ab – ac 3(7 – 5) = 3(7) – 3(5) Here is how it works…

Example 5(3 + 2) 15 + 10 = 25 Proof: 5(3+2) = 5(5) = 25

Distributive Property There are 2 ways that you can see the distributive property With the multiplier on the left of the parenthesis With the multiplier on the right of the parenthesis Example 5(2 + 3) OR (2 + 3)5 In either event you multiply what’s on the outside of the parenthesis with EACH term inside the parenthesis

Comments The distributive property is a key algebraic concept…make no mistake about it…you are REQUIRED to be able to recognize and work with the distributive property if you are to pass Algebra 1, which is the first high school math class you will take!

Identity Property The identity property states: The sum of an addend and zero (0) is the number The product of a factor and one is the factor It is expected that you already know this property…you may not know the name…but you should know how it works… Here is what it looks like…

Example Addition: 8 + 0 = 8 Multiplication: 9 ∙ 1 = 9

Your Turn In the notes section of your notebook create an expression the exemplifies each of the following properties Identity property of addition Distributive property of subtraction Associative property of multiplication Commutative property of addition

Summary In the notes section of your notebook summarize the key concepts covered in today’s lesson. Hint: The key concept was the four algebraic properties…

Assignment Text p. 15 # 43 – 48 Reminder Please resist the temptation to write the answer only! I want you to…write each equation first then name the property. The reason for that is the association of writing the problem then naming the property will help you recognize and be able to work each of these properties…