1. Name:________________________________________________________________________________Date:_____/_____/__________ Circle the part of the problem that should be performed FIRST: 3. Fill-in-the-chart: 4. Evaluate using the Order of Operations: 5. Evaluate when x = -4 and y = 8 : Quiz Day– for real this time!! Algebraic Expression Coefficient(s)Variable(s)Constant(s) -5 + x - 8y + 1 (-4) 2 ÷ 4 - (-5 + 1)- 2 2 ÷ 2(-3 + 5) 2 (y – x) ÷ 2(x) 2 1. 35 ÷ 7 + 4(-2)2. (8 – 9 + 3 2 ) ÷ 2

3. Today’s Lesson: What: properties Why: To identify and apply the commutative, associative, distributive, identity, inverse, and zero properties. What: properties Why: To identify and apply the commutative, associative, distributive, identity, inverse, and zero properties.

4. Commutative Property: + = + EXAMPLES: a + b = b + a OR 5 + 3 = 3 + 5 a b = b a 5 3 = 3 5 EXAMPLES: a + b = b + a OR 5 + 3 = 3 + 5 a b = b a 5 3 = 3 5 ___________ CHANGES! Your Turn: Apply the Commutative Property by finishing the below examples: 1) 6 + 7 = 2) 4 + 3 + 2 = 3) -5+(x + 2) = 4) 6 8 = 5) 3x y = 6) -2(a +b) = ORDER 7 + 6 3 + 2 + 4 (x + 2) + -5 8 6 3yx (a + b)(-2) Works for both Addition and Multiplication

5. + + + + = ________________ CHANGES! EXAMPLES: a + (b + c) = (a + b) + c OR 3 + (5 + 4) = (3 + 5) + 4 a (b c) = (a b) c 3 (5 4) = (3 5) 4 EXAMPLES: a + (b + c) = (a + b) + c OR 3 + (5 + 4) = (3 + 5) + 4 a (b c) = (a b) c 3 (5 4) = (3 5) 4 1) 4 + (7 + 3) = 2) (3 + y) + 2x = 3) (xy)z = 4) 3(-2 5) = Your Turn: Apply the Associative Property by finishing the below examples: Associative Property: GROUPING (4 + 7) + 3 3 + (y + 2x) x(yz) (3 -2 ) 5 Works for both Addition and Multiplication

6. + + = EXAMPLES: a (b + c) = a(b) + a(c) OR 3(5 + 4) = 3(5) + 3(4) EXAMPLES: a (b + c) = a(b) + a(c) OR 3(5 + 4) = 3(5) + 3(4) Distributive Property: 1) 4 (2 + 3) = 2) 2(x + y) = 3) (-5x + 1) 8 = 4) x(9 + 3) = Your Turn: Apply the Distributive Property by finishing the below examples: 4(2) + 4(3) 2(x) + 2(y) 8(-5x) + 8(1) 9x + 3x

7. Just remember you can secure your identity if you: Add ______ OR Multiply by _____ EXAMPLES: a + 0 = a OR 5 + 0 = 5 a 1 = a OR 5 1 = 5 EXAMPLES: a + 0 = a OR 5 + 0 = 5 a 1 = a OR 5 1 = 5 Nobody wants to lose their identity! Identity Property: ZERO ONE Your Turn: Apply the Identity Property by finishing the below examples: 1) 4 + 0 = _____ 2) x + ____ = x 4) -5x _____ = -5x 4 8 0 1

8. ALL ABOUT THE _________________! ALL ABOUT THE _________________! This is like a zero pair! Inverse Property: 1) -8 + 8 = _____ 2) 2y + _____ = 0 Your Turn: Apply the Inverse Property by finishing the below examples: OPPOSITE 0 -2y 1

9. Zero Property of Multiplication: ANSWER IS ALWAYS _______________! ANSWER IS ALWAYS _______________! If you have 5 empty plates, how much food do you have? Answer: Zero! 5 0 = 0 If you have 5 empty plates, how much food do you have? Answer: Zero! 5 0 = 0 Your Turn : Apply the Zero Property by finishing the below examples: 1) 12 0 = ____ 2) -5x ___ = 0 3) x(0) = _____ ZERO 000

10. END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

11. Commutative Property: + =+ EXAMPLES: a + b = b + a OR 5 + 3 = 3 + 5 a b = b a 5 3 = 3 5 EXAMPLES: a + b = b + a OR 5 + 3 = 3 + 5 a b = b a 5 3 = 3 5 ____________________ CHANGES! Your Turn: Apply the Commutative Property by finishing the below examples: 1.6 + 7 = ________ 2. 4 + 3 + 2 = ________ 3. -5 + (x + 2) = _________ 4.6 8 = _________ 5. 3x y = __________ 6. -2 (a + b) = __________ Associative Property: EXAMPLES: a + (b + c) = (a + b) + c OR 3 + (5 + 4) = (3 + 5) + 4 a (b c) = (a b) c 3 (5 4) = (3 5) 4 EXAMPLES: a + (b + c) = (a + b) + c OR 3 + (5 + 4) = (3 + 5) + 4 a (b c) = (a b) c 3 (5 4) = (3 5) 4 + + + + = _____________________ CHANGES! Works for both Addition and Multiplication Your Turn: Apply the Associative Property by finishing the below examples: 1. 4 + (7 + 3) = __________ 2. (3 + y) + 2x = __________ 3. (xy)z = __________ 4. 3(-2 5) = __________ Math-7 NOTES DATE: ______/_______/_______ What: properties Why: To identify and apply the commutative, associative, distributive, identity, inverse, and zero properties. What: properties Why: To identify and apply the commutative, associative, distributive, identity, inverse, and zero properties. NAME: Works for both Addition and Multiplication

12. Distributive Property: + + = EXAMPLES: a (b + c) = a(b) + a(c) OR 3(5 + 4) = 3(5) + 3(4) EXAMPLES: a (b + c) = a(b) + a(c) OR 3(5 + 4) = 3(5) + 3(4) Your Turn: Apply the Distributive Property by finishing the below examples: 1. 4 (2 + 3) = __________ 2. 2(x + y) = __________ 3.(-5x + 1) 8 = __________ 4. x(9 + 3) = __________ Just remember you can secure your identity if you: Add ___________ OR Multiply by ____________ EXAMPLES: a + 0 = a OR 5 + 0 = 5 a 1 = a OR 5 1 = 5 EXAMPLES: a + 0 = a OR 5 + 0 = 5 a 1 = a OR 5 1 = 5 Identity Property: Nobody wants to lose their identity! Your Turn: Apply the Identity Property by finishing the below examples: 1. 4 + 0 = _____ 2. x + ____ = x 3.8 1 = _____ 4. -5x _____ = -5x

13. Inverse Property: Zero Property of Multiplication: Your Turn: Apply the Zero Property by finishing the below examples: 1. 12 0 = _____ 2. -5x _____ = _____ 3. x(0) = _____ This is like a zero pair! ALL ABOUT THE _____________________________! ALL ABOUT THE _____________________________! ANSWER IS ALWAYS ________________! ANSWER IS ALWAYS ________________! If you have 5 empty plates, how much food do you have? Answer: Zero! 5 0 = 0 If you have 5 empty plates, how much food do you have? Answer: Zero! 5 0 = 0

14. Math-7 homework NAME:_______________________________________________________________________________ DATE: _____/_____/__________ Cut out the property examples at the bottom of this page. Then, paste each example into the appropriate property box.