1. Properties of Math SWBAT identify the properties of operations.

2. Warm Up: Ms. Dalton has 120 students. On a recent assignment, 75% of students got a passing grade. How many students got a failing grade? Ms. Dalton has 120 students. On a recent assignment, 75% of students got a passing grade. How many students got a failing grade? In a recent study, 4 out of 5 people preferred Coke to Pepsi. What percent of people preferred Coke? In a recent study, 4 out of 5 people preferred Coke to Pepsi. What percent of people preferred Coke?

3. Commutative Property of Addition 13 + 8 = 8 + 1313 + 8 = 8 + 13 Changing the order of the numbers does not change the sum. Algebraically: a + b = b + aAlgebraically: a + b = b + a

4. Commutative Property of Multiplication 12 · 5 = 5 · 1212 · 5 = 5 · 12 Changing the order of the numbers does not change the product. Algebraically: a · b = b · aAlgebraically: a · b = b · a

5. Identity Property of Multiplication 9 · 1 = 99 · 1 = 9 Multiplying a number by 1 leaves it unchanged. Algebraically: a · 1 = aAlgebraically: a · 1 = a

6. Identity Property of Addition 4 + 0 = 44 + 0 = 4 Adding a number by 0 leaves it unchanged. Algebraically: a + 0 = aAlgebraically: a + 0 = a

7. Associative Property of Multiplication 2(5 · 3) = (2 · 5)32(5 · 3) = (2 · 5)3 When multiplying more than 2 numbers, the way we group them does not change the product. Algebraically: a(bc) = (ab)cAlgebraically: a(bc) = (ab)c

8. Associative Property of Addition (4 + 2) + 8 = 4 + (2+8)(4 + 2) + 8 = 4 + (2+8) When adding more than 2 numbers, the way we group them does not change the sum. Algebraically: (a + b) + c = a + (b + c)Algebraically: (a + b) + c = a + (b + c)

9. Zero Property of Multiplication 15 · 0 = 015 · 0 = 0 Multiplying a number by 0 is always 0.Multiplying a number by 0 is always 0. Algebraically: a · 0 = 0Algebraically: a · 0 = 0

10. High School Vs College B-ball A standard size high school basketball court is 84 ft long and 50 ft wide in the shape of a rectangle. To find the area of the court you canTo find the area of the court you can use the formula of A = l · wuse the formula of A = l · w A= 84 ft · 50 ftA= 84 ft · 50 ft A= 4200 ft 2 84 ft 50 ft

11. High School vs College B-ball Did you know that a college basketball court is usually 10 ft longer than a high school basketball court? 84 ft 84 ft 10 ft 50 ft Can you think of a method to find the area of the college basketball court?

12. High School vs College B-ball We could do 84 · 50 + 10 · 50We could do 84 · 50 + 10 · 50 4200 + 500 4200 + 500 4700 ft 2 Or we could do 50(84 + 10)Or we could do 50(84 + 10)50(94) 4700 ft 2 Why parenthesis?

13. The Distributive Property The Distributive Property is a property in mathematics which helps to multiply a single term and two or more terms inside parenthesis. Ex: 2(3 + 5) = 2 · 3 + 2 · 5Ex: 2(3 + 5) = 2 · 3 + 2 · 5 8(3 + x) =8(3 + x) = a(3 + 5) =a(3 + 5) =

14. The Distributive Property The distributive property states that the product of a number and a sum is equal to the sum of the individual products of addends and the number. Ex: 2(x + 5) = 2 · x + 2 · 5Ex: 2(x + 5) = 2 · x + 2 · 5

15. Practice Use the distributive property to re-write each expression.Use the distributive property to re-write each expression. a)10( a + 7) =a)10( a + 7) = b)x( 3 + 10) =b)x( 3 + 10) = c)2(x + 10) =c)2(x + 10) = d)7(x + 3) =d)7(x + 3) = e)a(10 + 9) =e)a(10 + 9) = f)3x(x + 10) =f)3x(x + 10) =

16. Making it Stick Associative property of Addition  Associate with a GROUP of friendsAssociate with a GROUP of friends

17. Making it Stick Identity Property of Addition  Yourself!

18. Making it Stick Commutative Property of Multiplication  Swap or ExchangeSwap or Exchange

19. Practice Makes Perfect Complete the following worksheets independently.

20. Exit Ticket 1.Evaluate the expression below and list the properties that you used. 12 + (8 + 46) + 8012 + (8 + 46) + 80 2. Which property of multiplication is shown? 3 · 1 = 3 a. Commutativea. Commutative b. Associativeb. Associative c. Identityc. Identity