6th. Grade-2 integers

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6th. Grade-2 integers

  1. 1. Splash Screen
  2. 2. Chapter Menu <ul><li>Lesson 2-1 Integers and Absolute Value </li></ul><ul><li>Lesson 2-2 Comparing and Ordering Integers </li></ul><ul><li>Lesson 2-3 The Coordinate Plane </li></ul><ul><li>Lesson 2-4 Adding Integers </li></ul><ul><li>Lesson 2-5 Subtracting Integers </li></ul><ul><li>Lesson 2-6 Multiplying Integers </li></ul><ul><li>Lesson 2-7 Problem-Solving Investigation: Look for a Pattern </li></ul><ul><li>Lesson 2-8 Dividing Integers </li></ul>
  3. 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
  4. 4. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 1-1 A. 36 B. 144 C. 1,278 D. 1,728 Evaluate 12 3 . (over Chapter 1)
  5. 5. 5Min 1-2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. 27.6 B. 30.6 C. 33.6 D. 36.6 If a = 4 and b = 3.2, ab + a ( b + 2) = ? (over Chapter 1)
  6. 6. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 1-3 A. 12 B. 8 C. 6 D. 4 Solve 8 x = 64 mentally. (over Chapter 1)
  7. 7. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 1-4 A. Associative Property of Addition B. Commutative Property of Addition C. Distributive Property of Addition D. Identity Property of Addition Name the property shown by 7 + ( x + 43) = (7 + x ) + 43. (over Chapter 1)
  8. 8. 5Min 1-5 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Refer to the figure. Which option displays the complete function table for y = 2 x + 1? (over Chapter 1) A. B. C. D.
  9. 9. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 1-6 A. 3 × 50 + 15.50 × 45 B. 3 × 45 + 15.50 × 50 C. 3 + 50 + 15.50 × 45 D. 3 × 15.50 + 45 × 50 To cater a party, a restaurant charges $50 per hour for the room plus $15.50 per person. Which expression represents the total cost of a 3-hour party for 45 people? (over Chapter 1)
  10. 10. Lesson 1 MI/Vocab <ul><li>integer </li></ul><ul><li>negative integer </li></ul><ul><li>positive integer </li></ul><ul><li>graph </li></ul><ul><li>absolute value </li></ul><ul><li>Read and write integers, and find the absolute value of a number. </li></ul>
  11. 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. 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
  13. 13. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 1 CYP1 A. –4 B. 4 C. 36 D. none of the above Write an integer for the following situation. an average monthly temperature of 4 degrees below normal
  14. 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
  15. 15. Lesson 1 CYP2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –5 B. 5 C. 27 D. none of the above Write an integer for the following situation. a total snowfall of 5 inches above normal
  16. 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.
  17. 17. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 1 CYP3 Graph the set of integers  –2, 1, –4  on a number line. A. B. C. D.
  18. 18. Lesson 1 KC 1
  19. 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.
  20. 20. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 1 CYP4 A. –9 B. 0 C. 9 D. 81 Evaluate the expression |–9|.
  21. 21. Lesson 1 Ex5 Evaluate the expression |–4| – |–3|. |–4| – |–3| = 4 – 3 |–4| = 4, |–3| = 3 = 1 Subtract. Answer: 1 Evaluate Expressions
  22. 22. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 1 CYP5 A. –3 B. 3 C. 13 D. 40 Evaluate the expression |8| – |–5|.
  23. 23. End of Lesson 1
  24. 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
  25. 25. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 2-1 A. –56 B. –44 C. 44 D. 56 Write an integer for the situation. stock market down 56 points (over Lesson 2-1)
  26. 26. 5Min 2-2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –3 B. –0.3 C. 0.3 D. 3 Write an integer for the situation. a score of 3 (over Lesson 2-1)
  27. 27. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 2-3 A. 75 B. 25 C. 0.75 D. 0.25 Write an integer for the situation. a bank deposit of $25 (over Lesson 2-1)
  28. 28. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 2-4 A. –|19| B. –19 C. |19| D. 19 Evaluate |–19|. (over Lesson 2-1)
  29. 29. 5Min 2-5 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. 14 B. 10 C. –10 D. –14 Evaluate |12| + |– 2|. (over Lesson 2-1)
  30. 30. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 2-6 A. –8 B. –4 C. 4 D. 8 Find | k | – | m | if k = –6 and m = –2. (over Lesson 2-1)
  31. 31. Lesson 2 MI/Vocab <ul><li>Compare and order integers. </li></ul>
  32. 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. 33. Lesson 2 KC 1 Interactive Lab: Comparing and Ordering Integers
  34. 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.
  35. 35. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 2 CYP1 A. < B. > C. = D. none of the above Replace ● with < or > to make –3 ● –6 a true sentence.
  36. 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. 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
  38. 38. Lesson 2 CYP2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –3, –6, 7, –12 B. –12, –6, –3, 7 C. –12, 7, –6, –3 D. –3, –6, 7, –12 The lowest temperatures on a given day in four cities in the United State are listed in the table. Which of the following lists the temperatures in order from coolest to warmest?
  39. 39. End of Lesson 2
  40. 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
  41. 41. <ul><li>A </li></ul><ul><li>B </li></ul>5Min 3-1 A. < B. > Use < or > in –21 __ –15 to make a true sentence. (over Lesson 2-2)
  42. 42. <ul><li>A </li></ul><ul><li>B </li></ul>5Min 3-2 A. < B. > Use < or > in 5 __ –5 to make a true sentence. (over Lesson 2-2)
  43. 43. <ul><li>A </li></ul><ul><li>B </li></ul>5Min 3-3 A. < B. > Use < or > in 0 __ –1 to make a true sentence. (over Lesson 2-2)
  44. 44. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 3-4 A. 7, 4, 0, –1, –6 B. –1, –6, 0, 4, 7 C. 0, –1, 4, –6, 7 D. –6, –1, 0, 4, 7 Order 7, –1, 0, 4, –6 from least to greatest. (over Lesson 2-2)
  45. 45. 5Min 3-5 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. You can tell that 8 numbers in the set are greater than 0, and 1 number is less than 0 B. You can tell that 8 numbers in the set are greater than 0, and 2 numbers are less than 0 C. You can tell that 8 numbers in the set are less than 0, and 1 number is greater than 0 D. You can tell that 8 numbers in the set are less than 0, and 2 numbers are greater than 0 If 0 is the second smallest number in a set of 10 integers, what can you conclude about the other 9 numbers? (over Lesson 2-2)
  46. 46. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 3-6 A. 0 < –7 B. –3 > 6 C. –2 > –5 D. 1 < –4 Which of the following is a true sentence? (over Lesson 2-2)
  47. 47. Lesson 3 MI/Vocab <ul><li>coordinate plane </li></ul><ul><li>x -axis </li></ul><ul><li>y -axis </li></ul><ul><li>origin </li></ul><ul><li>quadrant </li></ul><ul><li>Graph points on a coordinate plane. </li></ul><ul><li>ordered pair </li></ul><ul><li>x -coordinate </li></ul><ul><li>y -coordinate </li></ul>
  48. 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. 49. Lesson 3 KC 1
  50. 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.
  51. 51. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 3 CYP1 A. (–3, –1); Quadrant III B. (2, 1); Quadrant I C. (3, 1); Quadrant I D. (3, –1); Quadrant IV Write the ordered pair that names point M . Then name the quadrant in which the point is located.
  52. 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.
  53. 53. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 3 CYP2 Graph and label the point G (–2, –4). A. B. C. D. G G G G
  54. 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
  55. 55. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 3 CYP3 A. Quadrant I B. Quadrant II C. Quadrant III D. Quadrant IV GEOGRAPHY Use the map of Utah. In which quadrant is Tremonton located.
  56. 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
  57. 57. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 3 CYP4 A. Tremonton B. Vernal C. Bluff D. Cedar City Name a city from the map of Utah that is located in Quadrant III.
  58. 58. End of Lesson 3
  59. 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
  60. 60. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 4-1 A. (3, 3), I B. (3, –3), II C. (3, 3), III D. (3, –3), IV Refer to the graph. Name the ordered pair for the point C . Then identify the quadrant in which the point C lies. (over Lesson 2-3)
  61. 61. 5Min 4-2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. (–3, 2), III B. (2, –3), I C. (2, –3), II D. (–3, 2), II Refer to the graph. Name the ordered pair for the point L . Then identify the quadrant in which the point L lies. (over Lesson 2-3)
  62. 62. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 4-3 A. (3, –3), I B. (3, –3), IV C. (–3, 3), I D. (–3, 3), IV Refer to the graph. Name the ordered pair for the point S . Then identify the quadrant in which the point S lies. (over Lesson 2-3)
  63. 63. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 4-4 Which choice shows the graph of the point W (4, –2)? (over Lesson 2-3) A. B. C. D.
  64. 64. 5Min 4-5 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Which choice shows the graph of the point N (–3, 0)? (over Lesson 2-3) A. B. C. D.
  65. 65. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 4-6 A. (–5, –3) B. (5, –3) C. (5, 3) D. (–5, 3) Which ordered pair is 5 units left and 3 units up from the origin? (over Lesson 2-3)
  66. 66. Lesson 4 MI/Vocab <ul><li>opposites </li></ul><ul><li>additive inverse </li></ul><ul><li>Add integers. </li></ul>
  67. 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. 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.
  69. 69. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 4 CYP1 A. –7 B. –3 C. 3 D. 7 Find –5 + (–2).
  70. 70. Lesson 4 KC 1
  71. 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
  72. 72. Lesson 4 CYP2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –46 B. –8 C. 8 D. 46 Find –27 + (–19).
  73. 73. Lesson 4 KC 2
  74. 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.
  75. 75. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 4 CYP3 A. –8 B. –4 C. 4 D. 12 Find 6 + (–2).
  76. 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.
  77. 77. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 4 CYP4 A. –8 B. 2 C. 8 D. 15 Find –3 + 5.
  78. 78. Lesson 4 KC 3
  79. 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.
  80. 80. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 4 CYP5 A. –14 B. –4 C. 4 D. 14 Find 5 + (–9).
  81. 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.
  82. 82. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 4 CYP6 A. –10 B. –4 C. 4 D. 10 Find 7 + (–3).
  83. 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
  84. 84. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 4 CYP7 A. –21 B. –11 C. 6 D. 16 Find 5 + (–11) + (–5).
  85. 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.
  86. 86. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 4 CYP8 A. –12 + (–9); –21 B. –12 + 9; –3 C. 12 + (–9); 3 D. 12 + 9; 21 During an hour trading baseball cards with his friends, Kyle increases the size of his collection by 12 cards and then loses nine cards. Write an addition sentence to describe this situation. Then find its sum.
  87. 87. End of Lesson 4
  88. 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
  89. 89. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 5-1 A. 8 B. 0 C. –4 D. –8 Add –4 + 4. (over Lesson 2-4)
  90. 90. 5Min 5-2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –15 B. –1 C. 1 D. 15 Add 8 + (–7). (over Lesson 2-4)
  91. 91. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 5-3 A. –8 B. –2 C. 2 D. 8 Add –3 + (–5). (over Lesson 2-4)
  92. 92. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 5-4 A. –50 – (–10) = –60 B. –50 + 10 = –40 C. 50 – 10 = 40 D. 50 – (–10) = 60 Write an addition expression to describe the situation. Then find its sum. A bird flies up 50 feet and swoops back down 10 feet. (over Lesson 2-4)
  93. 93. 5Min 5-5 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –14 + 10 = 4 B. –14 + 10 = –4 C 14 – 10 = 4 D. 14 + 10 = 24 Write an addition expression to describe the situation. Then find its sum. Teresa loses $14 at poker, then wins $10. (over Lesson 2-4)
  94. 94. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 5-6 A. –12 B. –6 C. 6 D. 12 Evaluate x + y if x = –3 and y = –9. (over Lesson 2-4)
  95. 95. Lesson 5 MI/Vocab <ul><li>Subtract integers. </li></ul>
  96. 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. 97. Lesson 5 KC 1 Interactive Lab: Subtracting Positive and Negative Integers
  98. 98. Lesson 5 Ex1 Subtract Positive Integers Find 2 – 15. 2 – 15 = 2 + (–15) To subtract 15, add –15. = –13 Simplify. Answer: –13
  99. 99. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 5 CYP1 A. –34 B. –8 C. 8 D. 34 Find 13 – 21.
  100. 100. Lesson 5 Ex2 Subtract Positive Integers Find –13 – 8. Answer: –21 – 13 – 8 = –13 + (–8) To subtract 8, add –8. = –21 Simplify.
  101. 101. Lesson 5 CYP2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –20 B. –2 C. 2 D. 20 Find –9 – 11.
  102. 102. Lesson 5 Ex3 Subtract Negative Integers Find 12 – (–6). Answer: 18 12 – (–6) = 12 + 6 To subtract –6, add 6. = 18 Simplify.
  103. 103. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 5 CYP3 A. –13 B. –5 C. 5 D. 13 Find 9 – (–4).
  104. 104. Lesson 5 Ex4 Find –21 – (–8). Answer: –13 Subtract Negative Integers – 21 – (–8) = –21 + 8 To subtract –8, add 8. = –13 Simplify.
  105. 105. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 5 CYP4 A. –23 B. –11 C. 11 D. 23 Find 17 – (–6).
  106. 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.
  107. 107. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 5 CYP5 A. –10 B. –2 C. 2 D. 10 ALGEBRA Evaluate m – n if m = –6 and n = 4.
  108. 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.
  109. 109. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 5 CYP6 A. –26 B. –4 C. 4 D. 26 TEMPERATURE On a particular day in Anchorage, Alaska, the high temperature was 15ºF and the low temperature was –11ºF. What is the difference between these two temperatures for that day?
  110. 110. End of Lesson 5
  111. 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
  112. 112. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 6-1 A. –9 B. –1 C. 1 D. 9 Subtract 4 – (–5). (over Lesson 2-5)
  113. 113. 5Min 6-2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –48 B. –20 C. 20 D. 48 Subtract –14 – 34. (over Lesson 2-5)
  114. 114. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 6-3 A. –53 B. –37 C. 37 D. 53 Subtract –45 – (–8). (over Lesson 2-5)
  115. 115. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 6-4 A. 4 B. 2 C. –2 D. –4 Evaluate c – b for b = 3, and c = –1. (over Lesson 2-5)
  116. 116. 5Min 6-5 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. 11 B. 7 C. –7 D. –11 Evaluate 9 – a for a = –2. (over Lesson 2-5)
  117. 117. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 6-6 A. –7 B. –1 C. 1 D. 7 What is –4 subtracted from –3? (over Lesson 2-5)
  118. 118. Lesson 6 MI/Vocab <ul><li>Multiply integers. </li></ul>
  119. 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. 120. Lesson 6 KC 1
  121. 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.
  122. 122. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 6 CYP1 A. –15 B. –2 C. 2 D. 15 Find 3(–5).
  123. 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.
  124. 124. Lesson 6 CYP2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –35 B. 2 C. 12 D. 35 Find –5(7).
  125. 125. Lesson 6 KC 2
  126. 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.
  127. 127. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 6 CYP3 A. –28 B. –11 C. 11 D. 28 Find –4(–7).
  128. 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.
  129. 129. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 6 CYP4 A. –25 B. –10 C. 10 D. 25 Find (–5) 2 .
  130. 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.
  131. 131. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 6 CYP5 A. 84 B. –14 C. 14 D. –84 Find –7(–3)(–4).
  132. 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.
  133. 133. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 6 CYP6 A. –$468 B. $468 C. –$84 D. $84 RETIREMENT Mr. Rodriguez has $78 deducted from his pay every month and placed in a savings account for his retirement. What integer represents a change in his savings account for these deductions after six months?
  134. 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.
  135. 135. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 6 CYP7 A. –48 B. –4 C. 0 D. 48 ALGEBRA Evaluate xyz if x = –6, y = –2, and z = 4.
  136. 136. End of Lesson 6
  137. 137. Lesson 7 Menu Five-Minute Check (over Lesson 2-6) Main Idea California Standards Example 1: Look For a Pattern
  138. 138. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 7-1 A. $40,000 B. $36,505 C. $42,500 D. $44,000 Tonya gets a job that pays $35,000 per year. She is promised a $1,500 raise each year. At this rate, what will her salary be in 5 years? Solve the problem by looking for a pattern. (over Lesson 2-6)
  139. 139. 5Min 7-2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. 4 inches B. 3 inches C. 6 inches D. 1.5 inches A ball that is dropped from the top of a building bounces 48 inches up the first bounce, 24 inches up the second bounce, and 12 inches up the third bounce. At this rate, who far up will the ball bounce on a fifth bounce? (over Lesson 2-6)
  140. 140. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 7-3 A. 576,000 B. 9,600 C. 1,152,000 D. 288,000 Hummingbird wing-beats are about 80 per second. At this rate, how many times does a hummingbird beat its wings in 2 hours? (over Lesson 2-6)
  141. 141. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 7-4 A. 3 hours B. 4 hours C. 4.5 hours D. 3.75 hours Kendra created a 5-day study schedule for her exams. The table shows the number of hours she studies in the first three days. If the pattern continues, how many hours will she study on the fifth day? (over Lesson 2-6)
  142. 142. Lesson 7 MI/Vocab <ul><li>Solve problems by looking for a pattern. </li></ul>
  143. 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. 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. 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
  146. 146. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 7 CYP1 A. 3.5 mi B. 15 mi C. 16.5 mi D. 19.5 mi RUNNING Samuel ran 2 miles on his first day of training to run a marathon. On the third day, Samuel increased the length of his run by 1.5 miles. If this pattern continues for every other day, how many miles will Samuel run on the 27th day?
  147. 147. End of Lesson 7
  148. 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
  149. 149. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 8-1 A. 26 B. 16 C. –105 D. –125 Multiply 21(–5). (over Lesson 2-7)
  150. 150. 5Min 8-2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. 28 B. 3 C. –3 D. –28 Multiply –7(–4). (over Lesson 2-7)
  151. 151. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 8-3 A. –81 B. –18 C. 18 D. 81 Multiply (–9) 2 . (over Lesson 2-7)
  152. 152. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 8-4 A. 1,233 B. 1,105 C. 441 D. 265 Evaluate the expression 9( x 2 + y 2 ) for x = –4 and y = 11. (over Lesson 2-7)
  153. 153. 5Min 8-5 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –44 B. –15 C. 15 D. 44 Find the product of – x and y if x = –4, and y = 11. (over Lesson 2-7)
  154. 154. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>5Min 8-6 A. –38 m B. –24 m C. –24 + m D. –24 + 3 m What is –3(8 m ) simplified? (over Lesson 2-7)
  155. 155. Lesson 8 MI/Vocab <ul><li>Divide integers. </li></ul>
  156. 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. 157. Lesson 8 KC 1
  158. 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.
  159. 159. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 8 CYP1 A. –4 B. 4 C. 27 D. 45 Find 36 ÷ (–9).
  160. 160. Lesson 8 Ex2 Dividing Integers with Different Signs Answer: –11 The integers have different signs. The quotient is negative. Find
  161. 161. Lesson 8 CYP2 <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>A. –5 B. 5 C. 36 D. 54
  162. 162. Lesson 8 KC 2
  163. 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.
  164. 164. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 8 CYP3 A. –32 B. –16 C. –3 D. 3 Find –24 ÷ (–8).
  165. 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.
  166. 166. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 8 CYP4 A. –63 B. 63 C. 7 D. –7 ALGEBRA Evaluate g ÷ h if g = –21 and h = –3.
  167. 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?
  168. 168. <ul><li>A </li></ul><ul><li>B </li></ul><ul><li>C </li></ul><ul><li>D </li></ul>Lesson 8 CYP5 A. –20ºF B. –4ºF C. 12ºF D. 4ºF WEATHER The temperature at 4:00 P.M. was 52ºF. By 8:00 P.M. , the temperature had gone down to 36ºF. What is the average change in temperature per hour?
  169. 169. Lesson 8 CS 1
  170. 170. End of Lesson 8
  171. 171. CR Menu Image Bank Math Tools Adding Integers Comparing and Ordering Integers Subtracting Positive and Negative Integers
  172. 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. 173. IB 2
  174. 174. IB 3
  175. 175. IB 4
  176. 176. End of Custom Shows This slide is intentionally blank.

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