1. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 1. 2.5 ³= 2. ( ) ⁴ = 3. 0.06² = 4. 3 ⁵ =

2. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 1. 2.5 ³=

3. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 1. 2.5 ³ = 2.5 6.25 x 2.5 x2.5 12 5 3125 500 12500 6.25 15.625

4. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 2. ( ) ⁴ =

5. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 2. ( ) ⁴ = · · · =

6. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 3. 0.06² =

7. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 3. 0.06² =.0036.06 x.06 036 0000.0036

8. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 4. 3 ⁵ =

9. 5 Minute Check Complete on the back of your homework. If you do not have homework, complete on a blank sheet of paper. What is the value? 4. 3 ⁵ = 3 · 3 · 3 · 3 · 3 = 243

10. Friday, Oct 31 Lesson 6.6.2/6.6.3 Numerical Expressions & Algebra: Variables and Expressions

11. Numerical Expressions Objective: To find the value of expressions using the order of operations.

12. Numerical Expressions A numerical expression is a combination of numbers and operations. For example, 3 x 2 + 4 x 4

13. Numerical Expressions The order of operations dictates which operation is to be done first. What does PEMDAS mean? (Please Excuse My Dear Aunt Sally)

14. Numerical Expressions P - Parentheses E - Exponents M - Multiply D - Divide A - Add S - Subtract

15. Numerical Expressions Find the value of 10 - 2 + 8 What do we do first?

16. Numerical Expressions Find the value of 10 - 2 + 8 Step 1 – perform all operations inside parenthesis and rewrite the expression. Since we do not have parenthesis, we go to the next step.

17. Numerical Expressions Find the value of 10 - 2 + 8 Step 2 – Solve all exponents and rewrite the expression. Since we do not have exponents, we go to the next step.

18. Numerical Expressions Find the value of 10 - 2 + 8 Step 3 – Perform all multiplication and division from left to right and rewrite the expression. Since we do not have multiplication or division, we go to the next step.

19. Numerical Expressions Find the value of 10 - 2 + 8 Step 4 – Perform all addition and subtraction from left to right and rewrite the expression. Which operation do we do first?

20. Numerical Expressions Find the value of 10 - 2 + 8 8 + 8 16

21. Numerical Expressions Find the value of 4 + 3 · 5 Do this on your own.

22. Numerical Expressions Find the value of 4 + 3 · 5 4 + 15 Step 3 19 Step 4 All of this inside the triangle must be shown to get full credit on assignment.

23. Numerical Expressions Find the value of 16 ÷ 2 · 4 Do this on your own.

24. Numerical Expressions Find the value of 16 ÷ 2 · 4 8 · 4 Step 3 32 Step 3

25. Numerical Expressions Find the value of 20 ÷ 4 + 17 · (9 – 6) Do this on your own.

26. Numerical Expressions Find the value of 20 ÷ 4 + 17 · (9 – 6) 20 ÷ 4 + 17 · 3 Step 1 5 + 51 Step 3 56 Step 4 All of this inside the triangle must be shown to get full credit on assignment.

27. Numerical Expressions Find the value of 5 + (8² - 2) · 2 Do this on your own.

28. Numerical Expressions Find the value of 5 + (8² - 2) · 2 5 + 62 · 2 Step 1 5 + 124 Step 3 129 Step 4 All of this inside the triangle must be shown to get full credit on assignment.

29. Numerical Expressions Write an expression for total cost of 5 lotions, 2 candles, and 4 lip balms. Find the total cost. Do this on your own.

30. Numerical Expressions Write an expression for total cost of 5 lotions, 2 candles, and 4 lip balms. Find the total cost. 5 · $5 + 2 · $7 + 4 · $2 = $25 + $14 + $8 = $47

31. Numerical Expressions Tickets to a play cost $10 for members and $24 for non-members. Write an expression to find the total cost of 4 non-member tickets and 2 member tickets. Find the total cost. Do this on your own.

32. Numerical Expressions Tickets to a play cost $10 for members and $24 for non-members. Write an expression to find the total cost of 4 non-member tickets and 2 member tickets. Find the total cost. 2 · $10 + 4 · $24 = $20 + $96 = $116

33. Numerical Expressions Luis is finding 9 – 2 + 2. Find his mistake and correct it.

34. Numerical Expressions Luis is finding 9 – 2 + 2. Find his mistake and correct it. He did not add/ subtract from left to right. 9 – 2 + 2 = 9

35. Numerical Expressions Use the expression 34 – 12 ÷ 2 + 7. Place parenthesis in the expression so the value of the expression is 18.

36. Numerical Expressions Use the expression 34 – 12 ÷ 2 + 7. Place parenthesis in the expression so the value of the expression is 18. (34 – 12) ÷ 2 + 7 = 18

37. Numerical Expressions How are grouping symbols helpful in simplifying expressions?

38. Numerical Expressions How are grouping symbols helpful in simplifying expressions?

39. Algebra: Variables and Expressions Algebra is a language of symbols including variables.

40. Algebra: Variables and Expressions Algebra is a language of symbols including variables. A variable is a symbol, usually a letter, that represents a number.

41. Algebra: Variables and Expressions Algebra is a language of symbols including variables. A variable is a symbol, usually a letter, that represents a number. Algebraic expressions contain at least one variable and at least one operation. e.g. n + 2

42. Algebra: Variables and Expressions

43. Evaluate 16 + b, if b = 25 To solve an algebraic expression, rewrite the expression without the variables and use the order of operations to simplify.

44. Algebra: Variables and Expressions Evaluate 16 + b, if b = 25 16 + 25 Expression without variables 41 Step 4

45. Algebra: Variables and Expressions Evaluate x - y, if x = 64 and y = 27 First?

46. Algebra: Variables and Expressions Evaluate x - y, if x = 64 and y = 27 64 – 27 Expression without variables

47. Algebra: Variables and Expressions Evaluate x - y, if x = 64 and y = 27 64 – 27 Expression without variables 37 Step 4 All of this inside the triangle must be shown to get full credit on assignment.

48. Algebra: Variables and Expressions Evaluate x · y, if x = 6 and y = 7 Do this on your own.

49. Algebra: Variables and Expressions Evaluate x · y, if x = 6 and y = 7 6 · 7 42

50. Algebra: Variables and Expressions 1 Evaluate 6x, if x = 2 Do this on your own. Remember, if there is no operation written it is assumed to be multiplication.

51. Algebra: Variables and Expressions 1 Evaluate 6x, if x = 2 1 6 · 2 6 2 3

52. Algebra: Variables and Expressions Evaluate 6t + 4, if t = 3 Do this on your own.

53. Algebra: Variables and Expressions Evaluate 6t + 4, if t = 3 6 · 3 + 4 Expression without variables 18 + 4 Step 3 22 Step 4 All of this inside the triangle must be shown to get full credit on assignment.

54. Algebra: Variables and Expressions Evaluate 6c², if c = 3 Do this on your own.

55. Algebra: Variables and Expressions Evaluate 6c², if c = 3 6 · 3² 6 · 9 54

56. Algebra: Variables and Expressions 1 Evaluate 4x², if x= 8 Do this on your own.

57. Algebra: Variables and Expressions 1 Evaluate 4x², if x= 8 1 4 · ( 8 )² 4 1 1 · 64 4 64 1 16

58. Algebra: Variables and Expressions 1 Evaluate 10a + 7, if a = 5 Do this on your own.

59. Algebra: Variables and Expressions 1 Evaluate 10a + 7, if a = 5 1 10 · 5 + 7 10 5 + 7 2 + 7 9

60. Algebra: Variables and Expressions 1 Evaluate 9e², if e= 3 Do this on your own.

61. Algebra: Variables and Expressions 1 Evaluate 9e², if e= 3 1 9 · ( 3 )² 9 1 1 · 9 9 1

62. Algebra: Variables and Expressions The amount of money that remains from a 20 dollar bill after Malina buys 4 party favors for p dollars each is 20 – 4p. Find the amount remaining if each favor is $3 each. Do this on your own.

63. Algebra: Variables and Expressions The amount of money that remains from a 20 dollar bill after Malina buys 4 party favors for p dollars each is 20 – 4p. Find the amount remaining if each favor is $3 each. $20 – 4p, if p = $3 $20 – 4 · $3 $20 - $12 $8

64. Algebra: Variables and Expressions The volume of a cube can be represented by s³, where s is the length of a side. If the length of a side of a cube is ½ meter, what is the volume? Do this on your own.

65. Algebra: Variables and Expressions The volume of a cube can be represented by s³, where s is the length of a side. If the length of a side of a cube is ½ meter, what is the volume? 1 ( 2 )³ 1 1 2 2 2 = 8 m³

66. Algebra: Variables and Expressions The volume of a cube can be represented by Nate and Lauren each have a calculator. Lauren starts at 100 and repeatedly subtracts 7. Nate starts at 0 and repeatedly adds 3. If they perform each operation at the same time, will they ever land on the same number?

67. Algebra: Variables and Expressions The volume of a cube can be represented by Nate and Lauren each have a calculator. Lauren starts at 100 and repeatedly subtracts 7. Nate starts at 0 and repeatedly adds 3. If they perform each operation at the same time, will they ever land on the same number? Yes, 30

68. Have fun and be careful tonight!

69. Algebra: Variables and Expressions Agenda Notes Homework – Homework Practice 6.6.2/6.6.3 Due at the end of class Mid-Chapter 6.6 Quiz -Tuesday, Nov 4

70. Algebra: Variables and Expressions 5. 9 + 7 x (15 + 3) ÷ 3²

71. Algebra: Variables and Expressions 5. 9 + 7 x (15 + 3) ÷ 3² 9 + 7 x 18 ÷ 3²

72. Algebra: Variables and Expressions 5. 9 + 7 x (15 + 3) ÷ 3² 9 + 7 x 18 ÷ 3² 9 + 7 x 18 ÷ 9

73. Algebra: Variables and Expressions 5. 9 + 7 x (15 + 3) ÷ 3² 9 + 7 x 18 ÷ 3² 9 + 7 x 18 ÷ 9 9 + 126 ÷ 9

74. Algebra: Variables and Expressions 5. 9 + 7 x (15 + 3) ÷ 3² 9 + 7 x 18 ÷ 3² 9 + 7 x 18 ÷ 9 9 + 126 ÷ 9 9 + 14

75. Algebra: Variables and Expressions 5. 9 + 7 x (15 + 3) ÷ 3² 9 + 7 x 18 ÷ 3² 9 + 7 x 18 ÷ 9 9 + 126 ÷ 9 9 + 14 25

76. Algebra: Variables and Expressions 21. ac ÷ (2b)

77. Algebra: Variables and Expressions 21. ac ÷ (2b) 1 9· 3 ÷ (2 · 3)

78. Algebra: Variables and Expressions 21. ac ÷ (2b) 1 9· 3 ÷ (2 · 3) 1 9· 3 ÷ 6

79. Algebra: Variables and Expressions 21. ac ÷ (2b) 1 9· 3 ÷ (2 · 3) 1 9· 3 ÷ 6 3 ÷ 6

80. Algebra: Variables and Expressions 21. ac ÷ (2b) 1 9· 3 ÷ (2 · 3) 1 9· 3 ÷ 6 3 ÷ 6 1 2