1. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes , 31, 43, 55,… , 64, 50, 36,… , 4.1, 4.8, 5.5, … , , , , …

2. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes , 31, 43, 55,….

3. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes , 31, 43, 55,… Each term is found by adding 12 to the previous term. The next three terms are 67, 79, 91

4. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes , 64, 50, 36,….

5. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes.
, 64, 50, 36,….
Each term is found by adding -14 to the previous term.
The next three terms are 22, 8, - 6

6. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes , 4.1, 4.8, 5.5, ….

7. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes.
, 4.1, 4.8, 5.5, ….
Each term is found by adding 0.7 to the previous term.
The next three terms are 6.2, 6.9, 7.6

8. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes , , , , …

9. 5 Minute Check
Describe the sequence then find the next three terms. Complete in your notes.
, , , , …
9 12 , , , ,
Each term is found by adding to the previous term.
The next three terms are , , ,

10. Lesson 7.5.3 Properties of Operations
Tuesday, May 12
Lesson Properties of Operations

11. Properties of Operations
Objective: To identify and use mathematical properties to simplify algebraic expressions.

12. Properties of Operations
A property is a statement that is true for any number.

13. Properties of Operations
Commutative Property (CP) - The order in which two or more numbers are added or multiplied does not change the sum or product. e.g = e.g. 3 · 2 = 2 · 3 a + b = b + a a · b = b · a Notice with CP, the order changes.

14. Properties of Operations
Associative Property (AP) - The way in which three numbers are grouped when they are added or multiplied does not change the sum or product. e.g. 9 + (7+ 5) = (9 + 7) · (2 · 4)= (3 · 2) · 4 a + (b+ c) = (a + b) + c a · (b · c) = (a · b) · c Notice with AP, the order does not change.

15. Properties of Operations
Identity Properties (IP) - The sum of an addend and zero is the addend. The product of a factor and one is the factor. IP of Addition IP of Multiplication e.g = 9 3 · 1 = 3 a + 0 = a a · 1 = a

16. Properties of Operations
Name the property shown in the statement. 2 · (5 · n) = (2 · 5) · n

17. Properties of Operations
Name the property shown in the statement. 2 · (5 · n) = (2 · 5) · n Associative Property (notice how the terms are in the same order)

18. Properties of Operations
Name the property shown in the statement x + y = 42 + y + x

19. Properties of Operations
Name the property shown in the statement x + y = 42 + y + x Commutative Property (notice how the terms are in a different order)

20. Properties of Operations
Name the property shown in the statement. 3x + 0 = 3x

21. Properties of Operations
Name the property shown in the statement. 3x + 0 = 3x Identity Property of Addition

22. Properties of Operations
Name the property shown in the statement. a + (b + 12) = (b + 12) + a

23. Properties of Operations
Name the property shown in the statement. a + (b + 12) = (b + 12) + a Commutative Property

24. Properties of Operations
Name the property shown in the statement. 3m · 0 · 5m = 0

25. Properties of Operations
Name the property shown in the statement. 3m · 0 · 5m = 0 Identity Property of Multiplication

26. Properties of Operations
Name the property shown in the statement (c + 17) = (16 + c) + 17

27. Properties of Operations
Name the property shown in the statement (c + 17) = (16 + c) + 17 Associative Property

28. Properties of Operations
You may wonder if any of the properties apply to subtraction or division. If you can find a counterexample, an example that shows that a conjecture is false, the property does not apply.

29. Properties of Operations
State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative.

30. Properties of Operations
State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative. ? 15 ÷ 3 = 3 ÷ 15 State the conjecture.

31. Properties of Operations
State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative. ? 15 ÷ 3 = 3 ÷ 15 State the conjecture. 5 ≠ 1 5 The conjecture is false, since we found a counterexample. Division is not commutative.

32. Properties of Operations
State whether the following conjecture is true or false. If false, provide a counterexample. The difference of two different whole numbers is always less than both of the numbers.

33. Properties of Operations
State whether the following conjecture is true or false. If false, provide a counterexample. The difference of two different whole numbers is always less than both of the numbers. 8 – 2 = 6 State the conjecture. 6 < 2 The conjecture is false, since we found a counterexample.

34. Properties of Operations
State whether the following conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is associative.

35. Properties of Operations
State whether the following conjecture is true or false. If false, provide a counterexample.
Subtraction of whole numbers is associative. ?
(12 – 5) -3 = 12 – (5 - 3) State the conjecture.
4 ≠ 10
The conjecture is false, since we found a counterexample. Subtraction is not associative.

36. Properties of Operations
Simplify each expression. ( 7 + g ) + 5

37. Properties of Operations
Simplify each expression. ( 7 + g ) + 5 What is the operation?

38. Properties of Operations
Simplify each expression. ( 7 + g ) + 5 We can only add or subtract like terms. Which are the like terms?

39. Properties of Operations
Simplify each expression. ( 7 + g ) + 5 We can only add or subtract like terms. Which are the like terms? 7, 5

40. Properties of Operations
Simplify each expression. ( 7 + g ) g g

41. Properties of Operations
Simplify each expression. (m · 11) · m

42. Properties of Operations
Simplify each expression. (m · 11) · m When multiplying variables and constants, multiply the coefficients, then multiply the variables. What is 1 · 11 · 1?

43. Properties of Operations
Simplify each expression. (m · 11) · m When multiplying variables and constants, multiply the coefficients, then multiply the variables. What is 1 · 11 · 1 = 11

44. Properties of Operations
Simplify each expression. (m · 11) · m When multiplying variables and constants, multiply the coefficients, then multiply the variables. What is m · m ?

45. Properties of Operations
Simplify each expression. (m · 11) · m When multiplying variables and constants, multiply the coefficients, then multiply the variables. What is m · m = m² What is the product?

46. Properties of Operations
Simplify each expression. (m · 11) · m 11m · m 11m²

47. Properties of Operations
Simplify each expression. 4 · (3c · 2)

48. Properties of Operations
Simplify each expression. 4 · (3c · 2) 4 · 6c 24c

49. Properties of Operations
Simplify each expression. 3x · (x · 7)

50. Properties of Operations
Simplify each expression. 3x · (x · 7) 3x · 7x 21x²

51. Properties of Operations
Simplify each expression. 9c + (3c + 8)

52. Properties of Operations
Simplify each expression. 9c + (3c + 8) 9c + 3c c + 8

53. Properties of Operations
Simplify each expression. (5n · 9 ) · 2n

54. Properties of Operations
Simplify each expression. (5n · 9 ) · 2n 45n · 2n 90n²

55. Properties of Operations
Simplify each expression (12 + 8a)

56. Properties of Operations
Simplify each expression (12 + 8a) a a

57. Properties of Operations
Simplify each expression. (2 · 4m) · 5m

58. Properties of Operations
Simplify each expression. (2 · 4m) · 5m 8m · 5m 40m²

59. Properties of Operations
Darien ordered a soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15. Use mental math to find the bill.

60. Properties of Operations
Darien ordered a soda for $2.75, a sandwich for $8.50, and a dessert for $3.85. Sales tax was $1.15. Use mental math to find the bill = = = 16.25

61. Properties of Operations
The times of each leg of a relay race for four runners are shown. Use mental math to find the total time for the relay team.

62. Properties of Operations
The times of each leg of a relay race for four runners are shown. Use mental math to find the total time for the relay team = = = 48

63. Properties of Operations
Agenda Notes No Homework – Homework Practice Due by the end of the period Circle all answers and show all work Chapter 7.5 Quiz Friday, May 15