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

2. 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

3. Assignment Review
Text p. 14 #14 – 39

4. 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?

5. 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…

6. Objective
Students will identify algebraic properties

7. 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.

8. 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…

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

10. 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…

11. 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

12. 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…

13. 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…

14. Example
5(3 + 2)
= 25
Proof: 5(3+2) = 5(5) = 25

15. 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

16. 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!

17. 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…

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

19. 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

20. 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…

21. 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…