Algebraic Properties August 31

Warm Up Grab a tracking sheet from the basket on your way in and put your supplies you got over the weekend on your desk so that I can give you your homework stamp. Begin on the warm up questions below on your own sheet of paper. 1.Evaluate the expression if a = 4 and b = -2: 2.Evaluate the expression if x = -3: 2x 2 + 9x + 14

Today’s Objectives Housekeeping: ▫Organize Binders ▫Return tracking sheets SWBAT identify and define the properties of real numbers. SWBAT use the distributive property to simplify expressions (going forward and backward) Quiz return/answer questions. OUR TEST IS THIS THURSDAY, SEPTEMBER 6th

Binder Organization I am passing out a sheet that should go in front of your binders. Throughout the semester, I will have surprise binder checks (USUALLY on test days ) These should be easy 100s to boost your grade. In order to earn a 1oo you must: ▫Have your binder in class ▫Have it organized the way it is outlined on the sheet I am passing out.

Tracking Sheets I will return your tracking sheets from last week. Monday was a freebie day. Each stamp was worth 5 points. I gave you participation and class work for every day last week because you all got all of your work done. This week: same thing goes for class work. In order to earn a participation stamp, you must raise your hand to ask a question or answer a question at some point during class.

Commutative Property What words do you think of when you hear “COMMUTATIVE” Movement! You can ADD and MULTIPLY in any order a + b = __________ (Addition) = _______ a ⋅ b= ____________ (Multiplication) 2 ⋅ 3 = ______

Associative Property What words do you think of when you hear “ASSOCIATIVE” Grouping! You can REGROUP terms. (a + b) + c = __________ (Addition) (4 + 5) + 6 = ______________ (a ⋅ b)c = ____________ (Multiplication) (4 ⋅ 5)6 = ______________

Addition Identity What can be added to ANYTHING that will not change the value? ZERO Identity Property of Addition a + 0 = ____5½ + 0 =____

Multiplication Identities What can be multiplied to ANYTHING that will not change the value? ONE Identity Property of Multiplication k ⋅ 1 = ______ ⋅ 1 = ______

Multiplication Identities What happens when you multiply by 0? Does it happen every time? Zero Property of Multiplication y ⋅ 0 = ________ 48 ⋅ 0 = _________

Symmetric Property What words do you think of when you hear “SYMMETRIC” What does it mean to have symmetry? Same on each side m + n = ______98 ⋅ 6y = _____________

Can you match the example to the property? What Property is shown in each of the following equations?

Think/Pair/Share The following equalities represent the Distributive Property: 4(a + b) = 4a + 4b -5(2x – 8) = -10x + 40 a(b + c) = ab + ac THINK (silently): What is the Distributive Property? PAIR: Discuss your answer with your partners. SHARE: Discuss your answer with the class.

Distributive Property a(b + c) = ab + ac Multiply whatever is outside of the (parenthesis) to every term inside the (parenthesis). Draw arrows!

“I do” Distribute: 2(6x – 1) -(3 + h)

“You do” Distribute: 3(1 + a) -4(x – 2) x(2 + 5)

Distributive Property in reverse We can also use the distributive property “backwards” In other words, we can UNDISTRIBUTE the greatest common factor of each term ▫What is the greatest common factor? ▫Example:

“I do” 15x + 5 4x – x

“You do” 2x x + 5x -x – 7

White boards Let’s use the next few minutes to practice what we’ve gone over today. I will pass out whiteboards, markers, and tissues to everyone. If you choose to color or write anything besides math on your whiteboard, you will complete the rest of the problems on paper.

White Board Practice Distribute: 3(x + 8)

Write an example of the associative property.

White Board Practice Distribute: -6(2x – 1)

White Board Practice Un-distribute: 25 – 5 Hint: __(__ - __)

Write an example of the commutative property.

White Board Practice Un-distribute: 12x – 4

White Board Practice Distribute: a(b + 1)

Which property is illustrated below: = 3

White Board Practice Distribute: -(x – 9)

Which property is illustrated below? = 0

White Board Practice Un-distribute: -x – 2

Which property is illustrated below: 10 = 10 1

Write an example of the symmetric property.

Quizzes If your test grade is higher than your quiz grade, then I will replace your quiz grade with your test grade.

Homework Complete the properties worksheet. Come to tutoring this afternoon if you would like to go over your quiz some more!

Ticket Out 1.What is the Distributive Property? 2.Think back to the quiz on Friday. Which topics do you think you did well on? Which topics do you need to study more for the test on THURSDAY?