1.  1. What is the Title of Lesson 1-3?  2. What are the names of the 3 properties associated with Multiplication?  3. What is the difference between the commutative and the associative property? 4. What number is called the additive identity?  5. What number is called the multiplicative identity?

2. By the end of class, students will be able to:  Recognize the properties of equality and identity  Recognize the commutative and associative properties. with 90% or above mastery.

3.  Additive Identity – Any number plus 0 = the number. 0 is called the additive identity. a + 0 = a Example: 2 + 0 = 2  Additive Inverse - Any number and its opposite are additive inverses. Their sum = 0. a + (-a) = 0 Example: 100 + (-100) = 100 - 100 = 0

4.  Multiplicative Identity – The product of a number and 1 is the number. a  1 = 1  a Example:14  1 = 1  14  Multiplicative Inverse - A number times its reciprocal is 1. a  b = 1 b aa, b  0 Example:4  5 = 1 5 4

5.  Multiplicative Property of 0 – The product of any number and 0 is 0. a  0 = 0 Example:9  0 = 0

6.  Commutative Property - The order in which you add or multiply doesn’t change their sum or product. a + b = b +a a(b) = b(a)  Example: 4 + 8 = 8 + 4 7(11) = 11(7)

7.  Associative Property – Grouping numbers does not change the sum or product. (a + b) + c = a + (b + c) Example:(3 + 5) + 7 = 3 + (5 + 7)

8.  Do 37, 39, 43, 45, 47, 57, 58

9. Properties of Equality  Reflexive Property–Any quantity is equal to itself a = a Example: 4 + 7 = 4 + 7 5 = 5  Symmetric Property – If one quantity equals a second, then the second quantity equals the first. If a = b, then b = a. Example: If 8 = 2 + 6, then 2 + 6 = 8.

10.  Substitution Property – A quantity may be substituted for its equal in any expression. If a = b, then a can be replaced for its equal in any expressions. Example: If n = 11, then 4n = 4(11)

11.  Transitive Property – If one quantity equals a second quantity and the second quantity equals the third quantity, then the first quantity equals the third quantity. If a = b and b = c, then a = c Example: If 6 + 9 = 3 + 12 and 3 + 12 = 15, 6 + 9 = 15

12. 14. 6  1 + 5(12 ÷ 4 – 3) 6 6  1 + 5(3 – 3) Substitution 6 6  1 + 5(0) Additive Inverse 6 1  + 5(0) Multiplicative Inverse 1 + 0Multiplicative Property of 0 1Additive Identity

13.  16. Hotel Rates: Important Facts Mon-Fri $72, Tax $5.40 Sat, Sun $63, Tax $5.10 2(72) + 2(5.10) + 2(63) + 2(5.40) 144 + 10.20 + 126 + 10.80 (144 + 126) + (10.20 + 10.80) 270 + 21 = 291 The total cost of the room including tax $291.

14.  29. Scuba Driving Expression 1: 2($10.95) + 3($7.50) + 2($5.00) + 5(418.99) = $21.90 + $22.50 + $10 + $94.95 $149.35 The total sales are $149.35. Expression 2: 2($10.95 + $5) + 3($7.50) + 5($18.99) 2($15.95) + $22.50 + $94.95 $31.90 + $22.50 + $94.95 $149.35

15.  Objectives: By the end of class, students will be able to:  Use the distributive property to evaluate and simplify expressions. with 90% or above mastery.

16.  3 readers are needed The Distributive Property a(b + c) = ab + ac a(b – c) = ab – ac Example: 4(9 – 7) = 4(9) – 4(7) = 36 – 28 = 8

17.  Example: Julio walks 5 days a week. He walks at a fast rate for 7 minutes and cools down for 2 minutes. Use the distributive property to write and evaluate an expression that determines the total number of minutes Julio walks.  5(7 + 2)  5(7) + 5(2)  35 + 10 = 45

18. 11. Time Management: Important Facts In a week, she uses 5 red, 3 yellow and 4 green dots. How many activities does Margo do in 4 weeks? 4(5 + 3 + 4) 4(5) + 4(3) + 4(4) = 20 + 12 + 16 = 48

19.  You can also use the distributive property to multiply numbers easier, 7(49) = 7(50 – 1) 7(50) – 7(1) 350 – 7 = 343 Do p. 29 #3

20.  14(51) = 14(50 + 1) 14(50) + 14(1) 700 + 14 714