1. 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
Welcome to Interactive Chalkboard

2. Splash Screen

3. Lesson 2-1 Integers and Absolute Value Lesson 2-2 Adding Integers
Lesson 2-3 Subtracting Integers
Lesson 2-4 Multiplying Integers
Lesson 2-5 Dividing Integers
Lesson 2-6 The Distributive Property
Contents

4. Example 1 Write Integers for Real-World Situations
Example 2 Compare Two Integers
Example 3 Order Integers
Example 4 Expressions with Absolute Value
Example 5 Algebraic Expressions with Absolute Value
Lesson 1 Contents

5. Write an integer for each situation. a. 32 feet under ground
b. 8 weeks after birth
c. a loss of 6 pounds
Answer: The integer is –32.
Answer: The integer is +8.
Answer: The integer is –6.
Example 1-1a

6. Write an integer for each situation. a. a loss of 12 yards
b. 15 feet above sea level
c. the temperature decreased 4 degrees
Answer: The integer is –12.
Answer: The integer is +15.
Answer: The integer is –4.
Example 1-1b

7. Use the integers graphed on the number line below.
Write two inequalities involving 7 and –4.
Answer: Since 7 is to the right of –4, write .
Since –4 is to the left of 7, write .
Example 1-2a

8. Use the integers graphed on the number line below.
Replace the  with <, >, or = in –2  3 to make a true sentence.
Answer: –2 is less since it lies to the left of 3. So write –2 < 3.
Example 1-2b

9. Use the integers graphed on the number line below.
a. Write two inequalities involving –4 and 1.
b. Replace the  with <, >, or = in 6  –7 to make a true sentence.
Answer:
Answer:
Example 1-2c

10. Graph each integer on a number line.
Weather The high temperatures for the first seven days of January were –8°, 10°, 2°, –3°, –11°, 0°, and 1°. Order the temperatures from least to greatest.
Graph each integer on a number line.
Write the numbers as they appear from left to right.
Answer: The temperatures –11°, –8°, –3°, 0°, 1°, 2°, 10° are in order from least to greatest.
Example 1-3a

11. Football The yards gained during the first six plays of the football game were 5, –3, 12, –9, 6, and –1. Order the yards from least to greatest.
Answer: The yards –9, –3, –1, 5, 6, and 12 are in order from least to greatest.
Example 1-3b

12. The graph of 5 is 5 units from 0.
Evaluate .
The graph of 5 is 5 units from 0.
Answer: 5
Example 1-4a

13. The absolute value of –8 is 8.
Evaluate .
The absolute value of –8 is 8.
The absolute value of –1 is 1.
Simplify.
Answer: 9
Example 1-4b

14. The absolute value of 6 is 6.
Evaluate .
The absolute value of 6 is 6.
The absolute value of –4 is 4.
Simplify.
Answer: 2
Example 1-4c

15. Evaluate each expression. a. b. c. Answer: 9
Example 1-4d

16. The absolute value of –2 is 2.
Algebra Evaluate if .
Replace x with –2.
The absolute value of –2 is 2.
Simplify.
Answer: –6
Example 1-5a

17. Algebra Evaluate if .
Answer: –4
Example 1-5b

18. End of Lesson 1

19. Example 1 Add Integers on a Number Line
Example 2 Add Integers with the Same Sign
Example 3 Add Integers on a Number Line
Example 4 Add Integers with Different Signs
Example 5 Use Integers to Solve a Problem
Example 6 Add Three or More Integers
Lesson 2 Contents

20. Move three units to the right.
Find . 3 4
Start at zero.
Move three units to the right.
From there, move four more units to the right.
Answer:
Example 2-1a

21. Find .
Answer: –7
Example 2-1b

22. Add and . Both numbers are negative, so the sum is negative.
Find .
Add and . Both numbers are negative, so the sum is negative.
Answer: –9
Example 2-2a

23. Find .
Answer: –11
Example 2-2b

24. From there, move 11 units to the left.
Find .
–11 7
Start at zero.
Move 7 units to the right.
From there, move 11 units to the left.
Answer:
Example 2-3a

25. From there, move 9 units to the right.
Find . 9 –2
Start at zero.
Move 2 units to the left.
From there, move 9 units to the right.
Answer:
Example 2-3b

26. Find each sum. a. b.
Answer: 3
Answer: –3
Example 2-3c

27. To find –9 + 10, subtract from . The sum is positive because
Answer: 1
Example 2-4a

28. To find 8 + (–15), subtract from The sum is negative because
Answer: –7
Example 2-4b

29. Find each sum. a. b.
Answer: –3
Answer: 5
Example 2-4c

30. Weather On February 1, the temperature at dawn was –22°F
Weather On February 1, the temperature at dawn was –22°F. By noon it had risen 19 degrees. What was the temperature at noon?
Words The temperature at dawn was –22°F. It had risen 19 degrees by noon. What was the temperature at noon?
Variable Let x the temperature at noon.
Temperature at dawn
plus
increase by noon
equals
temperature at noon. 19
–22
Equation x
Example 2-5a

31. To find the sum, subtract
Solve the equation.
To find the sum, subtract
The sum is negative because
Answer: The temperature at noon was –3°F.
Example 2-5b

32. Answer: Dave completed his hike at 3 feet below sea level.
Hiking Dave started his hike at 32 feet below sea level. During the hike he gained an altitude of 29 feet. At what altitude did Dave complete his hike?
Answer: Dave completed his hike at 3 feet below sea level.
Example 2-5c

33. Additive Inverse Property
Find .
Commutative Property
Additive Inverse Property
Identity Property of Addition
Answer: –4
Example 2-6a

34. Find . Commutative Property Associative Property or –4 Simplify.
Answer: –4
Example 2-6b

35. Find each sum. a. b.
Answer: –9
Answer: 10
Example 2-6c

36. End of Lesson 2

37. Example 1 Subtract a Positive Integer
Example 2 Subtract a Negative Integer
Example 3 Subtract Integers to Solve a Problem
Example 4 Evaluate Algebraic Expressions
Lesson 3 Contents

38. Find .
To subtract 14, add –14.
Simplify.
Answer: –5
Example 3-1a

39. Find .
To subtract 8, add –8.
Simplify.
Answer: –18
Example 3-1b

40. Find each difference. a. b.
Answer: –2
Answer: –22
Example 3-1c

41. Find .
To subtract –4, add 4.
Simplify.
Answer: 19
Example 3-2a

42. Find .
To subtract –7, add 7.
Simplify.
Answer: –3
Example 3-2b

43. Find each difference. a. b.
Answer: 10
Answer: –7
Example 3-2c

44. Weather The table shows the record high and low temperatures recorded in selected states. What is the range for Wyoming?
State
Lowest Temp °F
Highest Temp °F
Utah
–69
117
Vermont
–50
105
Virginia
–30
110
Washington
–48
118
West Virginia
–37
112
Wisconsin
–54
114
Wyoming
–66
Example 3-3a

45. Answer: The range for Wyoming is 180°.
Explore You know the highest and lowest temperatures. You need to find the range for Wyoming’s temperatures.
Plan To find the range, or difference, subtract the lowest temperature from the highest temperature.
Solve
To subtract –66, add 66.
Add 114 and 66.
Answer: The range for Wyoming is 180°.
Example 3-3a

46. Examine. Think of a thermometer
Examine Think of a thermometer. The difference between 114° above zero and 66° below zero must be or 180°. The answer appears to be reasonable.
Example 3-3b

47. Answer: The range for Washington is 166°. –69 117 –50 105 –30 110 –48
Weather The table shows the record high and low temperatures recorded in selected states. What is the range for Washington?
Answer: The range for Washington is 166°.
State
Lowest Temp °F
Highest Temp °F
Utah
–69
117
Vermont
–50
105
Virginia
–30
110
Washington
–48
118
West Virginia
–37
112
Wisconsin
–54
114
Wyoming
–66
Example 3-3c

48. Write the expression. Replace m with 4.
Evaluate if .
Write the expression. Replace m with 4.
To subtract –2, add 2.
Add 4 and 2.
Answer: 6
Example 3-4a

49. Write the expression. Replace x with –14 and y with –2.
Evaluate if and .
Write the expression. Replace x with –14 and y with –2.
To subtract –2, add 2.
Add –14 and 2.
Answer: –12
Example 3-4b

50. Write the expression. Replace p with –11, q with 6, and r with –12.
Evaluate if , , and .
Write the expression. Replace p with –11, q with 6, and r with –12.
Order of operations
Add –5 and 12.
Answer: 7
Example 3-4c

51. a. Evaluate if . Answer: 2 b. Evaluate if and . Answer: –6
c. Evaluate if , , and .
Answer: 2
Answer: –6
Answer: 0
Example 3-4d

52. End of Lesson 3

53. Example 1 Multiply Integers with Different Signs
Example 2 Multiply Integers with the Same Sign
Example 3 Multiply More Than Two Integers
Example 4 Use Integers to Solve a Problem
Example 5 Simplify and Evaluate Algebraic Expressions
Lesson 4 Contents

54. The factors have different signs. The product is negative.
Find .
The factors have different signs. The product is negative.
Answer: –96
Example 4-1a

55. The factors have different signs. The product is negative.
Find .
The factors have different signs. The product is negative.
Answer: –99
Example 4-1b

56. Find each product. a. b.
Answer: –48
Answer: –12
Example 4-1c

57. The two factors have the same sign. The product is positive.
Find .
The two factors have the same sign. The product is positive.
Answer: 64
Example 4-2a

58. Find .
Answer: 24
Example 4-2b

59. Find .
Associative Property
Answer: 154
Example 4-3a

60. Find .
Answer: –120
Example 4-3b

61. Multiple-Choice Test Item A student missed only 4 problems on a test, each worth 20 points. What is the total number of points missed?
A – B – C D –80
Read the Test Item The word missed means losing points, so the loss per problem is –20. Multiply 4 times –20 to find the total number of points lost.
Example 4-4a

62. The product is negative.
Solve the Test Item
The product is negative.
Answer: The answer is D.
Example 4-4b

63. Football A football team loses 3 yards on each of 3 consecutive plays
Football A football team loses 3 yards on each of 3 consecutive plays. Find the total loss.
Answer: –9
Example 4-4c

64. Associative Property of Multiplication
Simplify .
Associative Property of Multiplication
Simplify.
Answer: –42k
Example 4-5a

65. Commutative Property of Multiplication
Simplify .
Commutative Property of Multiplication
Answer: –40ab
Example 4-5b

66. Replace x with –4 and y with 9.
Evaluate if and .
Replace x with –4 and y with 9.
Associative Property of Multiplication
The product of –3 and –4 is positive.
The product of 12 and 9 is positive.
Answer: 108
Example 4-5c

67. a. Simplify . Answer: –12c b. Simplify . Answer: –35mn
c. Evaluate if and .
Answer: –12c
Answer: –35mn
Answer: –162
Example 4-5d

68. End of Lesson 4

69. Example 1 Divide Integers with the Same Sign
Example 2 Divide Integers with Different Signs
Example 3 Evaluate Algebraic Expressions
Example 4 Find the Mean
Lesson 5 Contents

70. Find .
The dividend and the divisor have the same sign. The quotient is positive.
Answer: 7
Example 5-1a

71. The dividend and the divisor have the same sign.
Find .
The dividend and the divisor have the same sign.
The quotient is positive.
Answer: 12
Example 5-1b

72. Find each quotient. a. b.
Answer: 5
Answer: 16
Example 5-1c

73. The signs are different. The quotient is negative.
Find .
The signs are different. The quotient is negative.
Answer: –18
Example 5-2a

74. The signs are different. The quotient is negative.
Find .
The signs are different. The quotient is negative.
Simplify.
Answer: –7
Example 5-2b

75. Find each quotient. a. b.
Answer: –9
Answer: –9
Example 5-2c

76. Replace x with –4 and y with –8.
Evaluate if and .
Replace x with –4 and y with –8.
The quotient of –24 and –8 is positive.
Answer: 3
Example 5-3a

77. Evaluate if and .
Answer: –12
Example 5-3b

78. Find the sum of the quiz scores. Divide by the number of scores.
Sam had quiz scores of 89, 98, 96, 97, and 95. Find the average (mean) of his quiz scores.
Find the sum of the quiz scores. Divide by the number of scores.
Simplify.
Answer: The average of Sam’s quiz scores is 95.
Example 5-4a

79. Find the average (mean) of 10, –12, 9, 15, –4, 0, –1, and 7.
Find the sum of the set of integers. Divide by the number in the set.
Simplify.
Answer: 3
Example 5-4b

80. b. Find the average (mean) of 8, –6, –12, 11, –4, and –21. Answer: 89
a. Kyle had test scores of 89, 82, 85, 93, and 96. Find the average (mean) of his test scores.
b. Find the average (mean) of 8, –6, –12, 11, –4, and –21.
Answer: 89
Answer: –4
Example 5-4c

81. End of Lesson 5

82. Splash Screen

83. Lesson 3-1 The Distributive Property
Contents

84. Example 1 Use the Distributive Property
Example 2 Use the Distributive Property to Solve a Problem
Example 3 Simplify Algebraic Expressions
Example 4 Simplify Expressions with Subtraction
Lesson 1 Contents

85. Use the Distributive Property to write as an equivalent expression
Use the Distributive Property to write as an equivalent expression. Then evaluate the expression.
Multiply.
Add.
Answer: 52
Example 1-1a

86. Use the Distributive Property to write as an equivalent expression
Use the Distributive Property to write as an equivalent expression. Then evaluate the expression.
Multiply.
Add.
Answer: 30
Example 1-1b

87. Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. a. b.
Answer:
Answer:
Example 1-1c

88. Method 1 Find the cost for 1 person, then multiply by 4.
Recreation North Country Rivers of York, Maine, offers one-day white-water rafting trips on the Kennebec River. The trip costs $69 per person, and wet suits are $15 each.
Write two equivalent expressions to find the total cost of one trip for a family of four if each person uses a wet suit.
Method 1 Find the cost for 1 person, then multiply by 4.
cost for 1 person
Example 1-2a

89. Method 2 Find the cost of 4 trips and 4 wet suits. Then add.
cost of 4 wet suits
cost of 4 trips
Example 1-2a

90. Evaluate either expression to find the total cost.
Distributive Property
Multiply.
Add.
Answer: The total cost is $336.
Check You can check your results by evaluating 4($84).
Example 1-2b

91. Movies The cost of a movie ticket is $7 and the cost of a box of popcorn is $2.
a. Write two equivalent expressions to find the total cost for a family of five to go to the movies if each member of the family gets a box of popcorn.
b. Find the total cost.
Answer:
Answer: $45
Example 1-2c

92. Use the Distributive Property to write as an equivalent algebraic expression.
Simplify.
Answer:
Example 1-3a

93. Use the Distributive Property to write as an equivalent algebraic expression.
Simplify.
Answer:
Example 1-3b

94. Use the Distributive Property to write each expression as an equivalent algebraic expression.
Answer:
Answer:
Example 1-3c

95. Distributive Property
Use the Distributive Property to write as an equivalent algebraic expression.
Rewrite as
Distributive Property
Simplify.
Definition of subtraction
Answer:
Example 1-4a

96. Distributive Property
Use the Distributive Property to write as an equivalent algebraic expression.
Rewrite as
Distributive Property
Simplify.
Answer:
Example 1-4b

97. Use the Distributive Property to write each expression as an equivalent algebraic expression.
Answer:
Answer:
Example 1-4c

98. End of Lesson 1

99. End of Custom Shows WARNING! Do Not Remove
This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.
End of Custom Show

100. End of Slide Show

101. Five-Minute Check (over Lesson 1–2) CCSS Then/Now New Vocabulary
Key Concept: Properties of Equality
Key Concept: Addition Properties
Key Concept: Multiplication Properties
Example 1: Evaluate Using Properties
Key Concept: Commutative Property
Key Concept: Associative Property
Example 2: Real-World Example: Apply Properties of Numbers
Example 3: Use Multiplication Properties
Lesson Menu

102. Evaluate the expression 20 – 6 • 3.
B. 38
C. 11
D. 2
5-Minute Check 1

103. Evaluate the expression 2(15 + 3) – 11 • 2.
B. 25
C. 14
D. 2
5-Minute Check 2

104. A. 17
B. 18
C. 20
D. 21
5-Minute Check 3

105. A. 170
B. 165
C. 160
D. 125
5-Minute Check 4

106. The area of a parallelogram is the product of its base and height
The area of a parallelogram is the product of its base and height. What is the area of the parallelogram when n = 3?
A. 16 units2
B. 32 units2
C. 62 units2
D. 80 units2
5-Minute Check 5

107. Simplify 40 ÷ • 2(13 – 7).
A. 48
B. 68
C. 72
D. 156
5-Minute Check 6

108. Mathematical Practices 2 Reason abstractly and quantitatively.
Content Standards
A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
Mathematical Practices
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
Common Core State Standards © Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
CCSS

109. You used the order of operations to simplify expressions.
Recognize the properties of equality and identity.
Recognize the Commutative and Associative Properties.
Then/Now

110. equivalent expressions
additive identity
multiplicative identity
multiplicative inverse
reciprocal
Vocabulary

111. KC 1

112. KC 2

113. KC 3

114. Name the property used in each step.
Evaluate Using Properties
Name the property used in each step.
Substitution: 12 – 8 = 4
Substitution: 15 ÷ 5 = 3
Substitution: 3 – 2 = 1
Example 1

115. Multiplicative Identity: 3(1) = 3
Evaluate Using Properties
Multiplicative Identity: 3(1) = 3
Multiplicative Inverse: (4) = 1
= 4 Substitution: = 4
Answer: 4
Example 1

116. A. 4
B. 5
C. 1
D. 0
Example 1

117. KC 4

118. KC 5

119. Apply Properties of Numbers
HORSEBACK RIDING Migina made a list of trail lengths to find the total miles she rode. Find the total miles Migina rode her horse.
Bent Tree
Knob Hill
Meadowrun
Pinehurst
Example 2

120. = (4.25 + 7.75) + (6.50 + 9.00) Associative (+)
Apply Properties of Numbers
= Commutative (+)
= ( ) + ( ) Associative (+)
= Substitution
= Substitution
Answer: Migina rode 27.5 miles on the trails.
Example 2

121. TRANSPORTATION Darlene rode the city train from the Winchester Street Station to the airport. How far did she travel on the train?
A. 4.5 mi
B. 5.5 mi
C. 6.0 mi
D. 6.2 mi
Example 2

122. 2 ● 8 ● 5 ● 7 = 2 ● 5 ● 8 ● 7 Commutative (×)
Use Multiplication Properties
Evaluate 2 ● 8 ● 5 ● 7 using properties of numbers. Name the property used in each step.
You can rearrange and group the factors to make mental calculations easier.
2 ● 8 ● 5 ● 7 = 2 ● 5 ● 8 ● 7 Commutative (×)
= (2 ● 5) ● (8 ● 7) Associative (×)
= 10 ● 56 Substitution
= 560 Substitution
Answer: 560
Example 3

123. Evaluate 3 ● 5 ● 3 ● 4.
A. 45
B. 36
C. 15
D. 180
Example 3

124. evaluate
order of operations
Vocabulary

125. 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 Use 2 as a factor 6 times. = 64 Multiply.
Evaluate Expressions
Evaluate 26.
26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 Use 2 as a factor times.
= 64 Multiply.
Answer: 64
Example 1

126. Evaluate 44.
A. 64
B. 128
C. 192
D. 256
Example 1

127. KC

128. 48 ÷ 23 ● 3 + 5 = 48 ÷ 8 ● 3 + 5 Evaluate powers.
Use Order of Operations
Evaluate 48 ÷ 23 ●
48 ÷ 23 ● = 48 ÷ 8 ● Evaluate powers.
= 6 ● Divide 48 by 8.
= Multiply 6 and 3.
= 23 Add 18 and 5.
Answer: 23
Example 2

129. Evaluate [(92 – 9) ÷ 12]5.
A. 6
B. 15
C. 30
D. 45
Example 2

130. (8 – 3) ● 3(3 + 2) = 5 ● 3(5) Evaluate inside parentheses.
Expressions with Grouping Symbols
A. Evaluate (8 – 3) ● 3(3 + 2).
(8 – 3) ● 3(3 + 2) = 5 ● 3(5) Evaluate inside parentheses.
= 5 ● 15 Multiply 3 by 5.
= 75 Multiply 5 by 15.
Answer: 75
Example 3

131. 4[12 ÷ (6 – 2)]2 = 4(12 ÷ 4)2 Evaluate innermost expression first.
Expressions with Grouping Symbols
B. Evaluate 4[12 ÷ (6 – 2)]2.
4[12 ÷ (6 – 2)]2 = 4(12 ÷ 4)2 Evaluate innermost expression first.
= 4(3)2 Evaluate expression in grouping symbol.
= 4(9) Evaluate power.
= 36 Multiply.
Answer: 36
Example 3

132. Evaluate the power in the numerator.
Expressions with Grouping Symbols C.
Evaluate the power in the numerator.
Multiply 6 and 2 in the numerator.
Subtract 32 and 12 in the numerator.
Example 3

133. Evaluate the power in the denominator.
Expressions with Grouping Symbols
Evaluate the power in the denominator.
Multiply 5 and 3 in the denominator.
Subtract from left to right in the denominator.
Answer: 2
Example 3

134. A. Evaluate the expression 2(4 + 7) ● (9 – 5).
B. 66
C. 88
D. 68
Example 3

135. B. Evaluate the expression 3[5 – 2 ● 2]2.
C. 108
D. 3
Example 3

136. C.
A. 1 B.
C. 4 D.
Example 3

137. Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2.
Evaluate an Algebraic Expression
Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2.
2(x2 – y) +z2 = 2(42 – 3) + 22 Replace x with 4, y with 3 and z with 2.
= 2(16 – 3) + 22 Evaluate 42.
= 2(13) + 22 Subtract 3 from 16.
= 2(13) + 4 Evaluate 22.
= Multiply 2 and 13.
= 30 Add.
Answer: 30
Example 4

138. Evaluate x3 – y2 + z, if x = 3, y = 2, and z = 5.
B. 28
C. 36
D. 10
Example 4

139. Write and Evaluate an Expression
ARCHITECTURE Each side of the Great Pyramid at Giza, Egypt, is a triangle. The base of each triangle once measured 230 meters. The height of each triangle once measured 187 meters. The area of a triangle is one-half the product of the base b and its height h.
Example 5

140. Write and Evaluate an Expression
A. Write an expression that represents the area of one side of the Great Pyramid.
Example 5

141. B. Find the area of one side of the Great Pyramid.
Write and Evaluate an Expression
B. Find the area of one side of the Great Pyramid.
Replace b with 230 and h with 187.
Multiply 230 by 187.
Multiply by 43,010.
Answer: The area of one side of the Great Pyramid is 21,505 m2.
Example 5

142. Find the area of a triangle with a base of 123 feet and a height of 62 feet.
A ft2
B ft2
C. 15,252 ft2
D. 32 ft2
Example 5