1. Splash Screen

3. Lesson 1 Menu Five-Minute Check (over Chapter 1) Main Idea and Vocabulary California Standards Example 1: Write Integers for Real-Life Situations Example 2: Write Integers for Real-Life Situations Example 3: Graph Integers Key Concept: Absolute Value Example 4: Evaluate Expressions Example 5: Evaluate Expressions

11. Lesson 1 CA Preparation for Standard 6NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

12. Lesson 1 Ex1 Write an integer for the following situation. a total rainfall of 2 inches below normal Answer: Because it represents below normal, the integer is –2. Write Integers for Real-Life Situations

14. Lesson 1 Ex2 Write an integer for the following situation. a seasonal snowfall of 3 inches above normal Answer: Because it represents above normal, the integer is +3. Write Integers for Real-Life Situations

16. Lesson 1 Ex3 Graph Integers Graph the set of integers  –1, 3, –2  on a number line. Draw a number line. Then draw a dot at the location of each integer.

18. Lesson 1 KC 1

19. Lesson 1 Ex4 Evaluate Expressions Evaluate the expression |–5|. On the number line, the graph of –5 is 5 units from 0. Answer: So, |–5| = 5.

21. Lesson 1 Ex5 Evaluate the expression |–4| – |–3|. |–4| – |–3| = 4 – 3 |–4| = 4, |–3| = 3 = 1 Subtract. Answer: 1 Evaluate Expressions

23. End of Lesson 1

24. Lesson 2 Menu Five-Minute Check (over Lesson 2-1) Main Idea California Standards Key Concept: Compare Integers Example 1: Compare Two Integers Example 2: Standards Example

32. Lesson 2 CA Preparation for Standard 6NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

33. Lesson 2 KC 1 Interactive Lab: Comparing and Ordering Integers

34. Lesson 2 Ex1 Compare Two Integers Replace the ● with < or > to make –9 ● –5 a true sentence. Answer: Since –9 is to the left of –5, –9 < –5.

36. Lesson 2 Ex2 The lowest temperatures in Europe, Greenland, Oceania, and Antarctica are listed in the table. Which list shows the temperatures in order from coolest to warmest? A –67, –87, 14, –129 B 14, –67, –87, –129 C –129, –87, –67, 14 D –67, –87, –129, 14

37. Lesson 2 Ex2 Read the Item To order the integers, graph them on a number line. Answer: C Order the integers from least to greatest by reading from left to right: –129, –87, –67, 14. Solve the Item

39. End of Lesson 2

40. Lesson 3 Menu Five-Minute Check (over Lesson 2-2) Main Idea and Vocabulary California Standards Key Concept: Compare Integers Example 1: Naming Points Using Ordered Pairs Example 2: Graph an Ordered Pair Example 3: Locate an Ordered Pair Example 4: Identify Quadrants

48. Lesson 3 CA Reinforcement of Standard 5AF1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane. Standard 6MR2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

49. Lesson 3 KC 1

50. Lesson 3 Ex1 Naming Points Using Ordered Pairs Write the ordered pair that names point R . Then state the quadrant in which the point is located. Start at the origin. Answer: So, the ordered pair for point R is (–2, 4). Point R is located in Quadrant II. Move left on the x -axis to find the x -coordinate of point R , which is –2. Move to find the y -coordinate, which is 4.

52. Lesson 3 Ex2 Graph an Ordered Pair Graph and label the point M (3, 5). Answer: Draw a coordinate plane. Start at the origin. Move 3 units to the right. Draw a dot and label it M (3, 5). Then move 5 units up.

54. Lesson 3 Ex3 GEOGRAPHY Use the map of Utah shown below. In which quadrant is Vernal located. Vernal is located in the upper right quadrant, Quadrant I. Answer: Quadrant I Locate an Ordered Pair

56. Lesson 3 Ex4 Which of the cities labeled on the map is located in Quadrant IV? Quadrant IV is the bottom-right quadrant. So, Bluff is in quadrant IV. Answer: Bluff Identify Quadrants

58. End of Lesson 3

59. Lesson 4 Menu Five-Minute Check (over Lesson 2-3) Main Idea and Vocabulary California Standards Example 1: Add Integers with the Same Sign Key Concept: Add Integers with the Same Sign Example 2: Add Integers with the Same Sign Key Concept: Additive Inverse Property Example 3: Add Integers with Different Signs Example 4: Add Integers with Different Signs Key Concept: Add Integers with Different Signs Example 5: Add Integers with Different Signs Example 6: Add Integers with Different Signs Example 7: Use the Additive Inverse Property Example 8: Use Integers to Solve a Problem

67. Lesson 4 CA Standard 6NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

68. Lesson 4 Ex1 Add Integers with the Same Sign Find –6 + (–3). Use a number line. Answer: So, –6 + (–3) = –9. From there, move 3 units left to show –3. Move 6 units left to show –6. Start at 0.

70. Lesson 4 KC 1

71. Lesson 4 Ex2 Add Integers with the Same Sign Find –34 + (–21). – 34 + (–21) = –55 Both integers are negative, so the sum is negative. Answer: –55

73. Lesson 4 KC 2

74. Lesson 4 Ex3 Add Integers with Different Signs Find 8 + (–7). Answer: So, 8 + (–7) = 1. Use a number line. Then move 7 units left. Move 8 units right. Start at zero.

76. Lesson 4 Ex4 Find –5 + 4. Answer: So, –5 + 4 = –1. Add Integers with Different Signs Use a number line. Then move 4 units right. Move 5 units left. Start at 0.

78. Lesson 4 KC 3

79. Lesson 4 Ex5 Find 2 + (–7). Answer: –5 Add Integers with Different Signs 2 + (–7) = –5 Subtract absolute values; 2 – 7 = –5. Since –7 has the greater absolute value, the sum is negative.

81. Lesson 4 Ex6 Find –9 + 6. Answer: –3 Add Integers with Different Signs – 9 + 6 = –3 Subtract absolute values; 9 – 6 = 3. Since –9 has the greater absolute value, the sum is negative.

83. Lesson 4 Ex7 Find 11 + (–4) + (–11). Answer: –4 Use the Additive Inverse Property 11 + (–4) + (–11) = 11 + (–11) + (–4) Commutative Property (+) = 0 + (–4) Additive Inverse Property = –4 Identity Property of Addition

85. Lesson 4 Ex8 Use Integers to Solve a Problem OCEANOGRAPHY Oceanographers divide the ocean into three light zones. The deeper the water, the less light shines through. The middle zone is called the Twilight Zone. The lowest part of this zone is 1,000 meters below the surface of the water. The top of this zone lies 800 meters above the lowest zone. What is the depth of the top of the zone? Write an addition sentence to describe this situation. Then find the sum and explain its meaning. Answer: –1,000 + 800; –200 The depth of the top of the middle zone is 200 meters below the surface of the water.

87. End of Lesson 4

88. Lesson 5 Menu Five-Minute Check (over Lesson 2-4) Main Idea California Standards Key Concept: Subtract Integers Example 1: Subtract Positive Integers Example 2: Subtract Positive Integers Example 3: Subtract Negative Integers Example 4: Subtract Negative Integers Example 5: Evaluate an Expression Example 6: Use Integers to Solve a Problem

96. Lesson 5 CA Standard 6NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

97. Lesson 5 KC 1 Interactive Lab: Subtracting Positive and Negative Integers

98. Lesson 5 Ex1 Subtract Positive Integers Find 2 – 15. 2 – 15 = 2 + (–15) To subtract 15, add –15. = –13 Simplify. Answer: –13

100. Lesson 5 Ex2 Subtract Positive Integers Find –13 – 8. Answer: –21 – 13 – 8 = –13 + (–8) To subtract 8, add –8. = –21 Simplify.

102. Lesson 5 Ex3 Subtract Negative Integers Find 12 – (–6). Answer: 18 12 – (–6) = 12 + 6 To subtract –6, add 6. = 18 Simplify.

104. Lesson 5 Ex4 Find –21 – (–8). Answer: –13 Subtract Negative Integers – 21 – (–8) = –21 + 8 To subtract –8, add 8. = –13 Simplify.

106. Lesson 5 Ex5 ALGEBRA Evaluate g – h if g = –2 and h = –7. Answer: 5 Evaluate an Expression g – h = –2 – (–7) Replace g with –2 and h with –7. = –2 + 7 To subtract –7, add 7. = 5 Simplify.

108. Lesson 5 Ex6 Use Integers to Solve a Problem GEOGRAPHY In Mongolia, the temperature can fall to –45ºC in January. The temperature in July may reach 40ºC. What is the difference between these two temperatures? To find the difference in temperatures, subtract the lower temperature from the higher temperature. Answer: The difference between the temperatures is 85 º C. 40 – (–45) = 40 + 45 To subtract –45, add 45. = 85 Simplify.

110. End of Lesson 5

111. Lesson 6 Menu Five-Minute Check (over Lesson 2-5) Main Idea California Standards Key Concept: Multiply Integers with Different Signs Example 1: Multiply Integers with Different Signs Example 2: Multiply Integers with Different Signs Key Concept: Multiply Integers with Same Sign Example 3: Multiply Integers with the Same Sign Example 4: Multiply Integers with the Same Sign Example 5: Multiply Integers with the Same Sign Example 6: Use Integers to Solve a Problem Example 7: Evaluate Expressions

119. Lesson 6 CA Standard 6NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

120. Lesson 6 KC 1

121. Lesson 6 Ex1 Multiply Integers with Different Signs Find 5(–4). Answer: –20 5(–4) = –20 The integers have different signs. This product is negative.

123. Lesson 6 Ex2 Multiply Integers with Different Signs Find –3(9). Answer: –27 – 3(9) = –27 The integers have different signs. This product is negative.

125. Lesson 6 KC 2

126. Lesson 6 Ex3 Multiply Integers with the Same Sign Find –6(–8). Answer: 48 – 6(–8) = 48 The integers have the same sign. This product is positive.

128. Lesson 6 Ex4 Find (–8) 2 . Answer: 64 Multiply Integers with the Same Sign (–8) 2 = (–8)(–8) There are two factors of –8. = 64 The product is positive.

130. Lesson 6 Ex5 Find –2(–5)(–6). Answer: –60 Multiply Integers with the Same Sign – 2(–5)(–6) = [–2(–5)](–6) Associative Property = 10 (–6) –2(–5) = 10 = –60 The product is negative.

132. Lesson 6 Ex6 Use Integers to Solve a Problem MINES A mine elevator descends at a rate of 300 feet per minute. How far below the earth’s surface will the elevator be after 5 minutes? If the elevator descends 300 feet per minute, then after 5 minutes, the elevator will be 300(5) or 1,500 feet below the surface. Thus, the elevator will descend to 1,500 feet below the earth’s surface. Answer: After five minutes, the elevator will be 1,500 feet below the earth’s surface.

134. Lesson 6 Ex7 ALGEBRA Evaluate abc if a = –3, b = 5, and c = –8. Answer: 120 Evaluate Expressions abc = (–3)(5)(–8) Replace a with –3, b with 5, and c with –8. = (–15)(–8) Multiply –3 and 5. = 120 Multiply –15 and –8.

136. End of Lesson 6

137. Lesson 7 Menu Five-Minute Check (over Lesson 2-6) Main Idea California Standards Example 1: Look For a Pattern

143. Lesson 7 CA Standard 6MR1.1 Analyze problems by identifying relationships, . . . , and observing patterns. Standard 6NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

144. Lesson 7 Ex1 Look For a Pattern HAIR Lelani wants to grow an 11-inch ponytail to cut off and donate to a program that makes wigs for children with cancer. She has a 3-inch ponytail now, and her hair grows about one inch every two months. How long will it take for her ponytail to reach 11 inches? Explore You know the length of Lelani’s ponytail now. You know how long Lelani wants her ponytail to grow and you know how fast her hair grows. You need to know how long it will take for her ponytail to reach 11 inches. Plan Look for a pattern. Then extend the pattern to find the solution.

145. Lesson 7 Ex1 Look For a Pattern Solve After the first two months, Lelani’s ponytail will be 3 inches + 1 inch, or 4 inches. Her hair grows according to the pattern below. 3 in. 4 in. 5 in. 6 in. 7 in. 8 in. 9 in. 10 in. 11 in. Answer: 16 months It will take eight sets of two months, or 16 months total, for Lelani’s ponytail to reach 11 inches. Check Lelani’s ponytail grew from 3 inches to 11 inches, a difference of eight inches, in 16 months. Since one inch of growth requires two months and 8 × 2 = 16, the answer is correct. +1 +1 +1 +1 +1 +1 +1 +1

147. End of Lesson 7

148. Lesson 8 Menu Five-Minute Check (over Lesson 2-7) Main Idea California Standards Key Concept: Dividing Integers with Different Signs Example 1: Dividing Integers with Different Signs Example 2: Dividing Integers with Different Signs Key Concept: Divide Integers with the Same Sign Example 3: Dividing Integers with the Same Sign Example 4: Evaluate an Expression Example 5: Real-World Example Concept Summary: Operations with Integers

156. Lesson 8 CA Standard 6NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

157. Lesson 8 KC 1

158. Lesson 8 Ex1 Dividing Integers with Different Signs Find 51 ÷ (–3). Answer: –17 51 ÷ (–3) = –17 The integers have different signs. The quotient is negative.

160. Lesson 8 Ex2 Dividing Integers with Different Signs Answer: –11 The integers have different signs. The quotient is negative. Find

162. Lesson 8 KC 2

163. Lesson 8 Ex3 Dividing Integers with Same Sign Find –12 ÷ (–2). Answer: 6 – 12 ÷ (–2) = 6 The integers have the same sign. The quotient is positive.

165. Lesson 8 Ex4 ALGEBRA Evaluate –18 ÷ x if x = –2. Answer: 9 Dividing Integers with Same Sign – 18 ÷ x = –18 ÷ (–2) Replace x with –2. = 9 Divide. The quotient is positive.

167. Lesson 8 Ex5 Answer: The car’s acceleration is –4 feet per second squared. Subtract 80 from 40. = –4 Divide. PHYSICS You can find an object’s acceleration with the expression , where S f = final speed, S s = starting speed, and t = time. If a car was traveling at 80 feet per second and, after 10 seconds, is traveling at 40 feet per second, what was its acceleration?

169. Lesson 8 CS 1

170. End of Lesson 8

171. CR Menu Image Bank Math Tools Adding Integers Comparing and Ordering Integers Subtracting Positive and Negative Integers

172. IB 1 To use the images that are on the following three slides in your own presentation: 1. Exit this presentation. 2. Open a chapter presentation using a full installation of Microsoft ® PowerPoint ® in editing mode and scroll to the Image Bank slides. 3. Select an image, copy it, and paste it into your presentation.

173. IB 2

174. IB 3

175. IB 4

176. End of Custom Shows This slide is intentionally blank.