1. Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Warm Up Evaluate each algebraic expression for the given value of the variables. 1. 7x + 4 for x = 6 2. 8y – 22 for y = 9 3. 12x + for x = 7 and y = 4 4. y + 3z for y = 5 and z = 6 46 50 86 8y8y 23

3. Problem of the Day A farmer sent his two children out to count the number of ducks and cows in the field. Jean counted 50 heads. Charles counted 154 legs. How many of each kind were counted? 23 ducks and 27 cows

4. Learn to translate words into numbers, variables, and operations.

5. Although they are closely related, a Great Dane weighs about 40 times as much as a Chihuahua. An expression for the weight of the Great Dane could be 40c, where c is the weight of the Chihuahua. When solving real-world problems, you will need to translate words, or verbal expressions, into algebraic expressions.

6. Turn composition notebook sideways and divide page into 4 sections: ADD Subtract Multiply Divide

7. OperationVerbal Expressions Algebraic Expressions add 3 to a number a number plus 3 the sum of a number and 3 3 more than a number a number increased by 3 subtract 12 from a number a number minus 12 the difference of a number and 12 12 less than a number a number decreased by 12 take away 12 from a number a number less than 12 n + 3 x – 12

8. OperationVerbal Expressions Algebraic Expressions 2 times a number 2 multiplied by a number the product of 2 and a number 6 divided into a number a number divided by 6 the quotient of a number and 6 2m or 2 m ÷ a6a6 ÷ 6 or a

9. Additional Example 1: Translating Verbal Expressions into Algebraic Expressions Write each phrase as an algebraic expression. A. the quotient of a number and 4 quotient means “divide” B. w increased by 5 increased by means “add” w + 5 n4n4

10. Write each phrase as an algebraic expression. Additional Example 1: Translating Verbal Expressions into Algebraic Expressions C. the difference of 3 times a number and 7 the difference of 3 times a number and 7 D. the quotient of 4 and a number, increased by 10 3 x – 7 the quotient of 4 and a number, increased by 10 4n4n + 10

11. Check It Out: Example 1 A. a number decreased by 10 decreased means “subtract” B. r plus 20 plus means “add” r + 20 n – 10 Write each phrase as an algebraic expression.

12. Check It Out: Example 1 Write each phrase as an algebraic expression. C. the product of a number and 5 D. 4 times the difference of y and 8 y – 8 n 5 the product of a number and 5 5n5n 4 times the difference of y and 8 4(y – 8) 4

13. When solving real-world problems, you may need to determine the action to know which operation to use. ActionOperation Put parts together Put equal parts together Find how much more Separate into equal parts Add Multiply Subtract Divide

14. Mr. Campbell drives at 55 mi/h. Write an algebraic expression for how far he can drive in h hours. Additional Example 2A: Translating Real-World Problems into Algebraic Expressions You need to put equal parts together. This involves multiplication. 55mi/h · h hours = 55h miles

15. On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly. Additional Example 2B: Translating Real-World Problems into Algebraic Expressions The total points include 2 points for each short-answer question. Multiply to put equal parts together. In addition to the points for short-answer questions, the total points included 50 points on the essay. Add to put the parts together: 50 + 2q 2q2q

16. Check It Out: Example 2A Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours. You need to put equal parts together. This involves multiplication. 8 units/h · h hours = 8h

17. Check It Out: Example 2B At her job Julie Ann is paid $8 per hour. In addition, she is paid $2 for each unit she produces. Write an expression for her total hourly income if she produces u units per hour. Her total wage includes $2 for each unit produced. Multiply to put equal parts together. In addition the pay per unit, her total income includes $8 per hour. Add to put the parts together: 2u + 8. 2u2u

18. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. Lesson Quiz Write each phrase as an algebraic expression. 1. 18 less than a number 2. the quotient of a number and 21 3. 8 times the sum of x and 15 4. 7 less than the product of a number and 5 x 21 x – 18 8(x + 15) 5n – 7 5. The county fair charges an admission of $6 and then charges $2 for each ride. Write an algebraic expression to represent the total cost after r rides at the fair. 6 + 2r

20. 1. Which of the following is an algebraic expression that represents the phrase ‘15 less than a number’? A. x – 15 B. x + 15 C. 15 – x D. 15x Lesson Quiz for Student Response Systems

21. 2. Which of the following is an algebraic expression that represents the phrase ‘the product of a number and 36’? A. 36xC. B. D. x + 36 Lesson Quiz for Student Response Systems x 36 x

22. 3. Which of the following is an algebraic expression that represents the phrase ‘5 times the sum of y and 17’? A. 5(y + 17) B. y + 17 C. 5y + 17 D. 5(y – 17) Lesson Quiz for Student Response Systems

23. 4. Which of the following is an algebraic expression that represents the phrase ‘9 less than the product of a number and 7’? A. 7x + 9 B. 7x – 9 C. 9x + 7 D. 9x – 7 Lesson Quiz for Student Response Systems

24. 5. A painter charges $675 for labor and $30 per gallon of paint. Identify an algebraic expression that represents the total cost of painting, if the painter used x gallons of paint. A. 30 + 675x B. 675x C. 675 + 30x D. 30x Lesson Quiz for Student Response Systems

25. Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

26. Warm Up Evaluate each expression for y = 3. 1. 3y + y 2. 7y 3. 10y – 4y 4. 9y 5. y + 5y + 6y 12 21 18 27 36

27. Problem of the Day Emilia saved nickels, dimes, and quarters in a jar. She had as many quarters as dimes, but twice as many nickels as dimes. If the jar had 844 coins, how much money had she saved? $94.95

28. Learn to simplify algebraic expressions.

29. Vocabulary term coefficient

30. In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by + and –. 7x + 5 – 3y 2 + y + x3x3 term In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y. Coefficient Variable term

31. Like terms are terms with the same variables raised to the same exponents. The coefficients do not have to be the same. Constants, like 5,, and 3.2, are also like terms. 1212 Like Terms Unlike Terms 3x and 2x 5x 2 and 2x The exponents are different. 3.2 and n Only one term contains a variable 6a and 6b The variables are different w and w7w7 5 and 1.8

32. Identify like terms in the list. Additional Example 1: Identifying Like Terms 3t 5w 2 7t 9v 4w 2 8v Look for like variables with like powers. 3t 5w 2 7t 9v 4w 2 8v Like terms: 3t and 7t 5w 2 and 4w 2 9v and 8v Use different shapes or colors to indicate sets of like terms. Helpful Hint

33. Check It Out: Example 1 Identify like terms in the list. 2x 4y 3 8x 5z 5y 3 8z Look for like variables with like powers. Like terms: 2x and 8x 4y 3 and 5y 3 5z and 8z 2x 4y 3 8x 5z 5y 3 8z

34. x Combining like terms is like grouping similar objects. += x x x xx x xx xxxx x xxxx 4x4x+5x5x =9x9x To combine like terms that have variables, add or subtract the coefficients.

35. Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. Additional Example 2: Simplifying Algebraic Expressions A. 6t – 4t 6t – 4t 2t2t 6t and 4t are like terms. Subtract the coefficients. B. 45x – 37y + 87 In this expression, there are no like terms to combine.

36. Additional Example 2: Simplifying Algebraic Expressions C. 3a 2 + 5b + 11b 2 – 4b + 2a 2 – 6 3a 2 + 5b + 11b 2 – 4b + 2a 2 – 6 5a 2 + b + 11b 2 – 6 Identify like terms. Add or subtract the coefficients. (3a 2 + 2a 2 ) + (5b – 4b) + 11b 2 – 6 Group like terms. Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

37. Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 5y + 3y 8y8y 5y and 3y are like terms. Add the coefficients.

38. Check It Out: Example 2 C. 4x 2 + 4y + 3x 2 – 4y + 2x 2 + 5 9x 2 + 5 Identify like terms. Add or subtract the coefficients. 4x 2 + 4y + 3x 2 – 4y + 2x 2 + 5 Group like terms. (4x 2 + 3x 2 + 2x 2 )+ (4y – 4y) + 5 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.

39. Write an expression for the perimeter of the triangle. Then simplify the expression. Additional Example 3: Geometry Application x 2x + 33x + 2 2x + 3 + 3x + 2 + x (x + 3x + 2x) + (2 + 3) 6x + 5 Write an expression using the side lengths. Identify and group like terms. Add the coefficients.

40. Check It Out: Example 3 x 2x + 1 x + 2x + 1 + 2x + 1 5x + 2 Write an expression using the side lengths. Identify and group like terms. Add the coefficients. Write an expression for the perimeter of the triangle. Then simplify the expression. (x + 2x + 2x) + (1 + 1)

41. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

42. Lesson Quiz: Part I Identify like terms in the list. 1. 3n 2 5n 2n 3 8n 2. a 5 2a 2 a 3 3a 4a 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 3. 4a + 3b + 2a 4. x 2 + 2y + 8x 2 2a 2, 4a 2 5n, 8n 6a + 3b 9x 2 + 2y

43. Lesson Quiz: Part II 5. Write an expression for the perimeter of the given figure. 6x + 8y 2x + 3y x + y

44. 1. Identify the like terms in the list. 6a, 5a 2, 2a, 6a 3, 7a A. 6a and 2a B. 6a, 5a 2, and 6a 3 C. 6a, 2a, and 7a D. 5a 2 and 6a 3 Lesson Quiz for Student Response Systems

45. 2. Identify the like terms in the list. 16y 6, 2y 5, 4y 2, 10y, 16y 2 A. 16y 6 and 16y 2 B. 4y 2 and 16y 2 C. 16y 6 and 2y 2 D. 2y 5 and 10y Lesson Quiz for Student Response Systems

46. Identify an expression for the perimeter of the given figure. A. (4x + 5y)(x + 2y) C. 10x + 14y B. D. 5x + 7y 4x + 5y x + 2y

48. How do you write equivalent expressions using the Distributive Property?

49. In this lesson you will learn how to write equivalent expressions by using the Distributive Property.

50. How do you expand linear expressions that involve multiplication, addition, and subtraction? For example, how do you expand 3(4 + 2x)?

51. Let’s Review Vocabulary: Linear expression Rational coefficient Combine like terms 2v + 3 + 7v - 1 = 9v + 2

52. Let’s Review Core Lesson If we want to write an equivalent expression for multiplying 3 times 6, we can use the Distributive Property. 3(2 + 4)= (3 x 2)+ (3 x 4)

53. Let’s Review Core Lesson Distributive Property Steps: S1: Identify the term outside the ( ). S2: Multiply the outside term by the 1 st inside term. S3: Bring down the correct operation. S4: Multiply the outside term by the 2 nd inside term. S5: Continue multiplying the outside term by any other inside terms. S6: Combine like terms to simplify.

54. Let’s Review A Common Mistake Forgetting to distribute to the second t erm (number). For example, 3(2 + 4) ≠ (3 2) + 4

55. Let’s Review Core Lesson Expand 3(2x + 4) xx 1111 2x + 4 xx 1111 xx 1111 x 1 2x + 4 3 3(2x + 4) = 3(2x) + 3(4)= 6x + 12

56. Let’s Review Core Lesson 4(x + 2) = x + 2 4 x + 2 4x 8 4(x + 2) = 4x + 8

57. Let’s Review Core Lesson 11(3a - 2) Expand and combine like terms: 33a-22 3a - 2 11

58. Let’s Review Guided Practice Simplify: 9(5k - 8)

59. Let’s Review Extension Activities Use a diagram to show why 4(3y + 2) = 12y + 8.

60. Let’s Review Extension Activities Simplify: 5(7y + 1) + 2(9y - 10) + 3(18 - 4y)

61. Let’s Review Quick Quiz 1. Simplify: 7(3x-4) + 2(5 + 6x) 2. Simplify: 11(4 - 8w) + 6(-9w - 5)

63. How do you simplify when there is a negative term? -3(2x -5)

64. In this lesson you will learn how to simplify an expression by distributing a negative term.

65. Let’s Review Core Lesson -4(x + 2) = x + 2 -4 x + 2 -4x -8 -4(x + 2) = -4x - 8

66. Let’s Review Core Lesson -3(2x -5) (-3)(2x) + (-3)(-5) -6x + 15

67. Let’s Review Core Lesson Original ExpressionSimplified Expression -4(x + 2)-4x – 8 -3(2x – 5)-6x + 15 When distributing a negative term, all signs of the terms inside of the parentheses change.

68. In this lesson you have learned how to simplify an expression by distributing a negative term.

69. Let’s Review Guided Practice -3(2x + 4)

70. Let’s Review Extension Activities A student simplified the following expression but made a mistake in the process. Identify the mistake and then explain why it was incorrect. -4(x + y) = -4x + 4y

71. Let’s Review Quick Quiz -3(4x + 7) -5(-x – 8)

73. Let’s Review 1.2(2x – 3) + 3(x + y) + 4(-4x – y) 2.½(6x – 12) 3.Solve (-23)(4) 4.Solve 2/3 + (-5/8) -7x – 6 - y 3x – 6 -96 1/24

74. How do you reverse the distributive property? -4x + 12 = ?(? +?)

75. In this lesson you will learn to reverse the distributive property by factoring an expression.

76. Let’s Review The distributive property tells us that 5(x + 2) = 5x + 10 X + 2 5 5x 10

77. Let’s Review Core Lesson 4x + 12 4x 12 _____ _____ _______

78. Let’s Review Core Lesson 6x + 24 Correct: 6x + 24 = 6(x + 4) What is wrong with this one? 6x + 24 = 3(2x + 8)

79. In this lesson you have learned how to rewrite an expression by factoring the expression.

80. Let’s Review 6x - 9y + 18z

81. Let’s Review 8a + 12b + 16c

82. Let’s Review Guided Practice -3x + 15

83. Let’s Review Guided Practice 15m -30n + 75p

84. Let’s Review Quick Quiz -3x +18 5x - 20

86. Learn to solve one-step equations with integers.

87. Inverse Property of Addition WordsNumbersAlgebra The sum of a number and its opposite, or additive inverse, is 0. 3 + (–3) = 0a + (–a ) = 0

88. Solve each question. Check each answer. Additional Example 1A: Solving Addition and Subtraction Equations –6 + x = –7

89. Additional Example 1B: Solving Addition and Subtraction Equations Solve each equation. Check each answer. p + 5 = –3

90. Additional Example 1C: Solving Addition and Subtraction Equations Solve each equation. Check each answer. y – 9 = –40

91. Check It Out: Example 1A Solve each equation. Check each answer. –3 + x = –9

92. Check It Out: Example 1B Solve each equation. Check each answer. q + 2 = –6

93. Check It Out: Example 1C Solve each equation. Check each answer. y – 7 = –34

94. Solve each equation. Check each answer. Additional Example 2A: Solving Multiplication and Division Equations b –5 = 6

95. Additional Example 2B: Solving Multiplication and Division Equations Solve each equation. Check each answer. –400 = 8y

96. Check It Out: Example 2A Solve each equation. Check each answer. c4c4 = –24

97. Check It Out: Example 2B Solve each equation. Check each answer. –200 = 4x

98. In 2003, a manufacturer made a profit of $300 million. This amount was $100 million more than the profit in 2002. What was the profit in 2002? Additional Example 3: Business Application Let p represent the profit in 2002 (in millions of dollars). This year’s profit 300 is = 300 = 100 + p –100 200 = p The profit was $200 million in 2002. 100 million 100 More than + Last year’s profit p

99. Check It Out: Example 3 Let x represent the money they made last year. This year’s profit 243 is = 243 = 125 + x –125 118 = x The class earned $118 last year. 125 million 125 More than + Last year’s profit x This year the class bake sale made a profit of $243. This was an increase of $125 over last year. How much did they make last year?

100. Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

101. Lesson Quiz Solve each equation. Check your answer. 1. –8y = –800 2. x – 22 = –18 3. – = 7 4. w + 72 = –21 5. Last year a phone company had a loss of $25 million. This year the loss is $14 million more last year. What is this years loss? 4 100 –49 –93 y7y7 $39 million

102. 1. Solve the equation. y + 65= –20 A. y = 45 B. y = 85 C. y = –45 D. y = –85 Lesson Quiz for Student Response Systems

103. 2. Solve the equation. x – 25= –15 A. x = 10 B. x = 20 C. x = 35 D. x = 45 Lesson Quiz for Student Response Systems

104. 3. Solve the equation. –10y = –1000 A. y = –200 B. y = –100 C. y = 100 D. y = 200 Lesson Quiz for Student Response Systems

105. 4. Solve the equation. – — = 6 A. a = 54 B. a = 15 C. a = –15 D. a = –54 Lesson Quiz for Student Response Systems a9a9

106. 5. In an online test, Dick scored –34 points. This was 20 points less than his previous score. What was his previous score? A. 54 points B. 14 points C. –14 points D. –54 points Lesson Quiz for Student Response Systems