2. Welcome to Interactive Chalkboard Pre-Algebra Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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4. Contents Lesson 1-1Using a Problem-Solving Plan Lesson 1-2Numbers and Expressions Lesson 1-3Variables and Expressions Lesson 1-4Properties Lesson 1-5Variables and Equations Lesson 1-6Ordered Pairs and Relations Lesson 1-7Scatter Plots

5. Lesson 1 Contents Example 1Use the Four-Step Problem-Solving Plan Example 2Use Inductive Reasoning Example 3Choose the Method of Computation

6. Example 1-1a ExploreThe problem gives the cost for the first pizza and the discount for each additional pizza ordered. We need to find the cost per pizza for an order of 8 pizzas. PlanUse the information given to solve the problem. Look for a pattern in the costs. Extend the pattern to find the cost per pizza for an order of 8 pizzas. Pizza The price of a large cheese pizza at Paul’s Pizza Place is $9.25. You receive a $0.50 discount for each additional pizza ordered, up to 10. So, one pizza costs $9.25, two pizzas cost $8.75 each, three pizzas cost $8.25 each, and so on. If you need 8 pizzas for a party, what is the cost per pizza?

7. Example 1-1b SolveFirst, find the pattern. 1 pizza costs $9.25. 2 pizzas cost $9.25 – $0.50 or $8.75 each. 3 pizzas cost $8.75 – $0.50 or $8.25 each. Now, extend the pattern. 4 pizzas cost $8.25 – $0.50 or $7.75 each. 5 pizzas cost $7.75 – $0.50 or $7.25 each. 6 pizzas cost $7.25 – $0.50 or $6.75 each. 7 pizzas cost $6.75 – $0.50 or $6.25 each. 8 pizzas cost $6.25 – $0.50 or $5.75 each.

8. Example 1-1c Answer: The cost per pizza for an order of 8 pizzas would be $5.75. ExamineIt costs $9.25 for one pizza with a discount of $0.50 for each additional pizza ordered. For an order of 8 pizzas, the cost per pizza would be or

9. Example 1-1d Movie Rental The cost of renting movies at Mike’s Marvelous Movie House is advertised as $5 for the first movie and $3.50 for each additional movie. Find the cost of renting 6 movies. Answer: The cost of renting 6 movies is $22.50.

10. 1, 4, 16, 64, 256, ? Example 1-2a Find the next term in 1, 4, 16, 64, 256, …. Answer:Assuming the pattern continues, the next term is

11. Example 1-2b Draw the next figure in the pattern. Answer: The shaded point on the triangle moves in the following pattern: right, top, bottom, left, right, top. Assuming the pattern continues, the shaded point will be located on the bottom in the next figure.

12. Example 1-2c Answer: 23 a.Find the next term in 48, 43, 38, 33, 28, … b.Draw the next figure in the pattern. Answer:

13. Example 1-3a Planets The chart shows the distance of selected planets from the Sun. About how much farther is it from Earth to the Sun than from Mercury to the Sun? Mercury Venus Earth Planet Distance from Sun (millions of miles) 36.00 67.24 92.90 141.71 Mars

14. Example 1-3b ExploreYou know the distance from Earth to the Sun and the distance from Mercury to the Sun. You need to find about how much farther it is from Earth to the Sun than from Mercury to the Sun. PlanThe question uses the word about, so an exact answer is not needed. We can solve the problem using estimation. Estimate each distance and then subtract. Distance from Mercury to the Sun: SolveDistance from Earth to the Sun:

15. Example 1-3c Answer:So, Earth is about 57 million miles further from the Sun than Mercury. Subtract 36 from 93. ExamineSince, the answer makes sense.

16. Example 1-3d School Enrollment East Elementary School has 792 students enrolled. West Elementary School has 518 students enrolled. About how many more students does East Elementary have than West Elementary? Answer:East Elementary has about 270 more students enrolled than West Elementary.

17. End of Lesson 1

18. Lesson 2 Contents Example 1Evaluate Expressions Example 2Translate Phrases into Expressions Example 3Use an Expression to Solve a Problem

19. Example 2-1a Answer: 22 Add 6 and 16. Multiply 8 and 2. Find the value of.

20. Example 2-1b Answer: 9 Multiply 3 and 3. Divide 24 by 8. Find the value of.

21. Example 2-1c Answer: 1 Subtract 49 from 50. means. means 7 times 7. Evaluate. Find the value of.

22. Example 2-1d Answer: 60 Multiply 2 and 4. Add 12 and 8. Multiply 3 and 20. Evaluate. Find the value of.

23. Example 2-1e Answer: 16 Divide 80 by 5. Rewrite as a division expression. Evaluate and. Find the value of.

24. Example 2-1f Answer: 6 Answer: 11 Answer: 13 Answer: 12 Answer: 2 Find the value of each expression. a. b. c. d. e.

25. Example 2-2a Write a numerical expression for the verbal phrase. Phrasethe quotient of eighteen and six Expression Key Wordquotient Answer:

26. Example 2-2b Write a numerical expression for the verbal phrase. Phrasethe sum of nine and five Key Wordsum Expression Answer:

27. Example 2-2c Write a numerical expression for each verbal phrase. a.the product of three and five b.the difference of seventeen and six Answer:

28. Example 2-3d Earnings Madison earns an allowance of $5 per week. She also earns $4 per hour baby-sitting, and usually baby-sits 6 hours each week. Write and evaluate an expression for the total amount of money she earns in one week. Words$5 allowance per weekplus$4 per hour spent baby-sitting 5 Expression

29. Example 2-3e Multiply. Add. Answer: Madison earns $29 in one week.

30. Example 2-3f Shopping The Good Price Grocery Store advertises a special on 2-liter bottles of soft drinks. The first bottle purchased is $1.50 and each bottle after that is $1.20. Write and evaluate an expression for the total cost when 8 bottles are purchased. Answer: The total cost for 8 bottles is $9.90.

31. End of Lesson 2

32. Lesson 3 Contents Example 1Evaluate Expressions Example 2Evaluate Expressions Example 3Translate Verbal Phrases into Expressions Example 4Use an Expression to Solve a Problem

33. Example 3-1a Evaluateif and. Subtract 12 from 27. Add 15 and 6. Answer: 21 Replace x with 27 and y with 12.

34. Example 3-1b Answer: 8 Evaluateif and.

35. Example 3-2a Multiply. Subtract. Answer: 12 Replace y with 4 and x with 3. Evaluate if,, and.

36. Example 3-2b Answer: 1 Subtract 3 from 7. Divide. Rewrite as a division expression. Replace z with 7, x with 3, and y with 4. Evaluate if,, and.

37. Example 3-2c Multiply 4 and 4. Add 3 and 16. Replace z with 7, x with 3, and y with 4. Evaluate if,, and.

38. Example 3-2d Multiply 5 and 7. Add 35 and 19. Subtract 15 from 54. Answer: 39

39. Example 3-2e Evaluate each expression if,, and. Answer: 3 Answer: 6 Answer: 11 a. b. c.

40. Example 3-3a Translate the phrase into an algebraic expression. 35 more than the number of tickets sold Words35 more than the number of tickets sold VariableLet t represent the number of tickets sold. 35 more than the number of tickets sold Expression 35t Answer: The expression is.

41. Example 3-3b Translate the phrase into an algebraic expression. the difference of six times a number and ten Wordsthe difference of six times a number and ten VariableLet n represent the number. the difference of six times a number and ten Answer: The expression is. Expression 6n6n10 Expression

42. Example 3-3c Translate each phrase into an algebraic expression. a.eight less than the number of cookies baked b.the sum of twelve and five times a number Answer:

43. Words$3 for an adult ticket and $1 for a student ticket $3 for an adult ticket and $1 for a student ticket Example 3-4a Theater East Middle School sold tickets for a school play. The price of an adult ticket was $3 and the price of a student ticket was $1. Write an expression that can be used to find the total amount of money collected. Expression 3a3a1s1s VariablesLet a number of adult tickets and s number of student tickets.

44. Example 3-4b Answer: The expression can be used to find the total amount of money collected.

45. Example 3-4c Theater East Middle School sold tickets for a school play. The price of an adult ticket was $3 and the price of a student ticket was $1. Suppose 70 adult tickets and 85 student tickets were sold. How much money was collected? Multiply. Add. Answer: The amount of money collected was $295. Replace a with 70 and s with 85.

46. Example 3-4d Retail The Read It Bookstore is advertising a sale. The price of hardback books is $9.50 and the price of paperback books is $4.50. a. Write an expression that can be used to find the total amount of money spent at the bookstore. b. Suppose Emily buys 5 hardback books and 4 paperback books. Find the total amount she spent at the book sale. Answer: $65.50 Answer:

47. End of Lesson 3

48. Lesson 4 Contents Example 1Identify Properties Example 2Mental Math Example 3Find a Counterexample Example 4Simplify Algebraic Expressions

49. Example 4-1a Name the property shown by the statement. Answer:The order of the numbers changed. This is the Commutative Property of Multiplication.

50. Example 4-1b Name the property shown by the statement. Answer:The grouping of the numbers and variables changed. This is the Associative Property of Addition.

51. Example 4-1c Name the property shown by the statement. Answer:The number was multiplied by one. This is the Multiplicative Identity Property.

52. Example 4-1d a. b. c. Name the property shown by each statement. Answer:Associative Property of Multiplication Answer: Communicative Property of Addition Answer: Multiplicative Property of Zero

53. Find mentally. Group 20 and 5 together because. It is easy to multiply by 100 mentally. Example 4-2a Multiply 18 and 100 mentally. Answer: 1800 Associative Property of Multiplication Multiply 20 and 5 mentally.

54. Example 4-2b Answer: 800 Find mentally.

55. Example 4-3c State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative. Write two division expressions using the Commutative Property, and then check to see whether they are equal. State the conjecture. Divide. We found a counterexample. That is,. So, division is not commutative. Answer: The conjecture is false.

56. Example 4-3d State whether the following conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is commutative. Answer: The conjecture is false.

57. Example 4-4a Simplify Substitution Property of Equality; Answer: 15r Associative Property of Multiplication

58. Example 4-4b Commutative Property of Addition Associative Property of Addition Substitution Property of Equality; Answer: Simplify.

59. Example 4-4c Answer: Simplify each expression. a. b.

60. End of Lesson 4

61. Lesson 5 Contents Example 1Solve an Equation Example 2Solve an Equation Example 3Solve Simple Equations Mentally Example 4Identify Properties of Equality Example 5Translate Sentences Into Equations

62. Value for p44 + p = 53 True or False? Example 5-1a Find the solution of. Is it 11, 9, or 7? Replace p with each value. Answer: Therefore, the solution of is 9. 11 false 7 9 true

63. Find the solution of. Is it 11, 13, or 15? Example 5-1b Answer: 15

64. Example 5-2a Read the Test Item The solution is the value that makes the equation true. Solve the Test Item Test each value. Multiple-Choice Test Item Which value is the solution of ? A 5 B 4 C 3 D 2

65. Example 5-2b Answer Choice A: Substitute 5 for x. Replace x with 5.

66. Example 5-2c Answer Choice B: Substitute 4 for x. Replace x with 4.

67. Example 5-2d Answer Choice C: Substitute 3 for x. Replace x with 3.

68. Example 5-2e Answer Choice D: Substitute 2 for x. Answer: Since 3 makes the equation true, the answer is C. Replace x with 2.

69. Example 5-2f Multiple-Choice Test Item Which value is the solution of ? A 1 B 2 C 3 D 4 Answer: Since 2 makes the equation true, the answer is B.

70. Example 5-3a Answer: The solution is 8. Think: What number times 7 is 56 ? Solve mentally.

71. Example 5-3b Answer: The solution is 55. Think: What number minus 15 is 40 ?

72. Example 5-3c Solve each equation mentally. Answer: 21 Answer: 13 a. b.

73. Name the property of equality shown by the statement. If, then. Example 5-4a Answer:If a = b, then b = a. This is the Symmetric Property of Equality.

74. Name the property of equality shown by the statement. Ifand, then. Example 5-4b Answer:If a = b and b = c, then a = c. This is the Transitive Property of Equality.

75. Example 5-4c Name the property of equality shown by each statement. Answer: Transitive Property of Equality a. If and, then. b. If, then. Answer: Symmetric Property of Equality

76. Example 5-5a The quotient of a number and four is nine. Find the number. WordsThe quotient of a number and four is nine. VariableLet n = the number. Define the variable. The quotient of a number and four is nine. 9 Equation

77. Example 5-5b Answer: The solution is 36. Write the equation. Think: What number divided by 4 is 9 ?

78. Example 5-5c The sum of a number and seven is twelve. Find the number. Answer: 5

79. End of Lesson 5

80. Lesson 6 Contents Example 1Graph Ordered Pairs Example 2Identify Ordered Pairs Example 3Relations as Tables and Graphs Example 4Apply Relations

81. Example 6-1a Graph the ordered pair (3, 4) on a coordinate system. Step 1Start at the origin. Step 2Since the x-coordinate is 3, move 3 units to the right. Step 3Since the y-coordinate is 4, move 4 units up. Draw a dot. (3, 4)

82. Example 6-1b Graph the ordered pair (0, 2) on a coordinate system. Step 1Start at the origin. Step 2Since the x-coordinate is 0, you will not need to move to the right. Step 3Since the y-coordinate is 2, move 2 units up. Place the dot on the axis. (0, 2)

83. Example 6-1c Graph each ordered pair on a coordinate system. a.(2, 5) b.(4, 0) Answer:

84. Example 6-2a Write the ordered pair that names point G. Step 1Start at the origin. Step 2Move right on the x-axis to find the x-coordinate of point G, which is 1. Step 3Move up the y-axis to find the y-coordinate, which is 1. Answer: The ordered pair for point G is (1, 1).

85. Example 6-2b Write the ordered pair that names point H. Step 1Start at the origin. Step 2Move right on the x-axis to find the x-coordinate of point H, which is 4. Step 3Since the y-coordinate is zero, you will not need to move up. Answer: The ordered pair for point H is (4, 0).

86. Example 6-2c Write the ordered pair that names each point. Answer: The ordered pair for point A is (2, 3). Answer: The ordered pair for point B is (0, 6).

87. Example 6-3a Express the relation {(1, 4), (2, 2), (3, 0), (0, 2)} as a table and as a graph. Then determine the domain and range. xy 14 22 30 02 (1, 4) (2, 2) (3, 0) (0, 2)

88. Example 6-3b Express the relation {(1, 4), (2, 2), (3, 0), (0, 2)} as a table and as a graph. Then determine the domain and range. The domain is {1, 2, 3, 0}. The range is {4, 2, 0}.

89. Example 6-3c Express the relation {(4, 1), (3, 2), (0, 1), (2, 3)} as a table and as a graph. Then determine the domain and range. xy 41 32 01 23 The domain is {4, 3, 0, 2}. The range is {1, 2, 3}.

90. Example 6-4a Earnings Austin earns $5 an hour doing yard work. Suppose x represents the number of hours Austin works. xy(x, y) 1 5(1, 5) 210(2, 10) 315(3, 15) 420(4, 20) 525(5, 25) Make a table of ordered pairs in which the x-coordinate represents the hours worked and y represents the amount of money Austin earns for 1, 2, 3, 4, and 5 hours of work.

91. Example 6-4b Earnings Austin earns $5 an hour doing yard work. Suppose x represents the number of hours Austin works. Graph the ordered pairs. xy(x, y) 1 5(1, 5) 210(2, 10) 315(3, 15) 420(4, 20) 525(5, 25)

92. Example 6-4c Earnings Austin earns $5 an hour doing yard work. Suppose x represents the number of hours Austin works. Describe the graph. Answer: The points appear to fall in a line.

93. Example 6-4d Baking Sue is following a recipe for cookies which requires 2 cups of sugar for each batch of cookies made. Suppose x represents the number of batches made. Make a table of ordered pairs in which the x-coordinate represents the number of batches made and y represents the number of cups of sugar needed for 1, 2, 3, 4, and 5 batches made. xy(x, y) 1 2(1, 2) 2 4(2, 4) 3 6(3, 6) 4 8(4, 8) 510(5, 10)

94. Example 6-4e Baking Sue is following a recipe for cookies which requires 2 cups of sugar for each batch of cookies made. Suppose x represents the number of batches made. Graph the ordered pairs. xy(x, y) 1 2(1, 2) 2 4(2, 4) 3 6(3, 6) 4 8(4, 8) 510(5, 10)

95. Example 6-4f Baking Sue is following a recipe for cookies which requires 2 cups of sugar for each batch of cookies made. Suppose x represents the number of batches made. Describe the graph. Answer: The points appear to fall in a line.

96. End of Lesson 6

97. Lesson 7 Contents Example 1Construct a Scatter Plot Example 2Interpret Scatter Plots Example 3Use Scatter Plots to Make Predictions

98. Example 7-1a Retail Sales The table shows the average cost of a loaf of bread from 1920-2000. Make a scatter plot of the data. Year192019301940 Cost (¢) 1298 Year195019601970 Cost (¢) 142024 Year198019902000 Cost (¢) 527299 Let the horizontal axis, or x-axis, represent the year.

99. Example 7-1b Let the vertical axis, or y-axis, represent the cost. Retail Sales The table shows the average cost of a loaf of bread from 1920-2000. Make a scatter plot of the data. Year192019301940 Cost (¢) 1298 Year195019601970 Cost (¢) 142024 Year198019902000 Cost (¢) 527299

100. Example 7-1c Then graph ordered pairs (years, cost). Retail Sales The table shows the average cost of a loaf of bread from 1920-2000. Make a scatter plot of the data. Year192019301940 Cost (¢) 1298 Year195019601970 Cost (¢) 142024 Year198019902000 Cost (¢) 527299

101. Example 7-1d Birth Statistics The table shows the number of babies born at Central Hospital during the past eight months. Make a scatter plot of the data. MonthJan.Feb.Mar.Apr. Number of Babies 1221179 MonthMayJuneJulyAug. Number of Babies 15261811

102. Example 7-2a Determine whether a scatter plot of the data for the following might show a positive, negative, or no relationship. Explain your answer. height of basketball player and number of rebounds As the height increases, the number of rebounds increases. Answer: positive relationship

103. Example 7-2b Determine whether a scatter plot of the data for the following might show a positive, negative, or no relationship. Explain your answer. shoe size and test scores As shoe size increases, test scores fluctuate. Answer: no relationship

104. Determine whether a scatter plot of the data for the following might show a positive, negative, or no relationship. Explain your answer. a. outside temperature and heating bill b. eye color and test score Example 7-2c Answer: As the outside temperature decreases, the heating bill will increase. This is a negative relationship. Answer: Eye color and test score have no relationship.

105. Example 7-3a Temperature The table shows temperatures in degrees Celsius and the corresponding temperatures in degrees Fahrenheit. Make a scatter plot of the data. °F32415059 °C 051015 °F687786 °C 202530 Let the horizontal axis represent degrees Celsius.

106. Example 7-3b Let the vertical axis represent degrees Fahrenheit. Graph the data. °F32415059 °C 051015 °F687786 °C 202530 Temperature The table shows temperatures in degrees Celsius and the corresponding temperatures in degrees Fahrenheit. Make a scatter plot of the data.

107. Example 7-3c Yes, a positive relationship is shown. As °C increase, so do °F. Does the scatter plot show a relationship between °C and °F? Explain.

108. By looking at the pattern on the graph, we can predict that the Fahrenheit temperature corresponding to 35°C would be about 95 degrees. Example 7-3d Predict the Fahrenheit temperature for 35°C.

109. Example 7-3e Study Skills The table shows hours spent studying for a test and the corresponding test score. Hours3251 Score 72759068 Hours426 Score 857092 a.Make a scatter plot of the data.

110. Example 7-3e Study Skills The table shows hours spent studying for a test and the corresponding test score. Hours3251 Score 72759068 Hours426 Score 857092 b.Does the scatter plot show a relationship between hours studied and a student’s test score? Answer:Yes, a positive relationship exists. As hours studied increases, so does the test score.

111. Example 7-3e Study Skills The table shows hours spent studying for a test and the corresponding test score. Hours3251 Score 72759068 Hours426 Score 857092 c.Predict the test score for a student who spends 7 hours studying. Answer: By looking at the pattern in the graph, we can predict that studying 7 hours would correspond to a test score between 95 and 100.

112. End of Lesson 7

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