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# Lesson 1 (Unit Rates)

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• 1. Name Numeracy Skill Builder: Long Division Write any remainders as fractions and reduce. Date 3 25 8 506 6 1227 4 8030 Objectives 1. Find a Unit Rate 2. Compare by using Unit 1 1 1 1 Rates 8 63 204 2007 3 4 2 2 Concept 1: Find a Unit Rate Basic Proficient Advanced I need 24 dollars for 6 sandwiches. I need 18 cups of flour for 8 loaves of I need 2 teaspoons of salt for 60 Find and reduce the unit rate. bread. Find and reduce the unit rate. cookies. Find and reduce the unit rate. 1 1 4 dollars per sandwich 2  cups per loaf  teaspoon per cookie 4 30 Concept 2: Compare by using Unit Rates Basic Proficient Advanced Andrew drives 150 miles in 4 hours. Andrew drives 120 miles in 2 hours. Andrew drives 228 miles in 4 hours. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours. Who drives faster? Who drives faster and by how much? 1 1 1 A : 60 mph E : 65  mph A : 57 mph E : 56  mph 37  miles per hour 3 5 2 4 Erika drives faster. Andrew  drives faster by mph 5
• 2. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours. Who drives faster? Who drives faster and by how much? Test Prep 3 Work / Explanation 1. Which number is the additive inverse of - ? 5 A 5 C 3 Additive inverse = opposite. - 3 5 ( )+( )=0 B - 5 D 3 Change the sign. 3 5 3 2. Which number is the multiplicative inverse of - ? 5 Multiplicative inverse = reciprocal. A 5 C 3 3 - 5 ( )•( )=1 B 5 D 3 Flip the fraction. - 3 5
• 3. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours. Who drives faster? Who drives faster and by how much? Test Prep 3 Work / Explanation 1. Which number is the additive inverse of - ? 5 A 5 C 3 Additive inverse = opposite. - 3 5 ( )+( )=0 B - 5 D 3 Change the sign. 3 5 3 2. Which number is the multiplicative inverse of - ? 5 Multiplicative inverse = reciprocal. A 5 C 3 3 - 5 ( )•( )=1 B 5 D 3 Flip the fraction. - 3 5
• 4. How fast does he drive? Erika drives 196 miles in 3 hours. Erika drives 281 miles in 5 hours. Who drives faster? Who drives faster and by how much? Test Prep 3 Work / Explanation 1. Which number is the additive inverse of - ? 5 A 5 C 3 Additive inverse = opposite. - 3 5 ( )+( )=0 B - 5 D 3 Change the sign. 3 5 3 2. Which number is the multiplicative inverse of - ? 5 Multiplicative inverse = reciprocal. A 5 C 3 3 - 5 ( )•( )=1 B 5 D 3 Flip the fraction. - 3 5
• 5. Which one should I buy?
• 6. 24.12 ounces 36.5 ounces
• 7. 24.12 ounces 36.5 ounces .331 24.12 7.99
• 8. 24.12 ounces 36.5 ounces .331 24.12 7.99 Each ounce costs 33.1 cents
• 9. 24.12 ounces 36.5 ounces .331 .247 24.12 7.99 36.5 8.99 Each ounce costs 33.1 cents
• 10. 24.12 ounces 36.5 ounces .331 .247 24.12 7.99 36.5 8.99 Each ounce costs 33.1 cents Each ounce costs 24.7 cents
• 11. 24.12 ounces 36.5 ounces .331 .247 24.12 7.99 36.5 8.99 Each ounce costs 33.1 cents Each ounce costs 24.7 cents
• 12. 24.12 ounces 36.5 ounces .331 .247 24.12 7.99 36.5 8.99 Each ounce costs 33.1 cents Each ounce costs 24.7 cents
• 13. Main Concept Unit Rates
• 14. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. =
• 15. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet =
• 16. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents
• 17. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents
• 18. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole?
• 19. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 5 8
• 20. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 1 5 8
• 21. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 1 5 8 −5
• 22. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 1 5 8 −5 3
• 23. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 3 1 5 8 −5 3
• 24. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet = 5 presents more or less than 1 whole? 3 15 5 8 −5 3
• 25. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet 3 = 1 5 presents 5 more or less than 1 whole? 3 15 5 8 −5 3
• 26. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet 3 feet = 1 5 presents 5 present more or less than 1 whole? 3 15 5 8 −5 3
• 27. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet 3 feet 3 = 1 = 1 5 presents 5 present 5 more or less than 1 whole? 3 15 5 8 −5 3
• 28. Find Unit Rate I need 8 feet of wrapping paper to wrap 5 presents. 8 feet 3 feet 3 = 1 = 1 feet per present 5 presents 5 present 5 more or less than 1 whole? 3 15 5 8 −5 3
• 29. Find Unit Rate I run 3 miles in 21 minutes. =
• 30. Find Unit Rate I run 3 miles in 21 minutes. 3 miles =
• 31. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes
• 32. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes
• 33. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole?
• 34. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole? 3 21
• 35. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole? 3 ÷3 21
• 36. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole? 3 ÷3 21 ÷3
• 37. Find Unit Rate I run 3 miles in 21 minutes. 3 miles = 21 minutes more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
• 38. Find Unit Rate I run 3 miles in 21 minutes. 3 miles 1 = 21 minutes 7 more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
• 39. Find Unit Rate I run 3 miles in 21 minutes. 3 miles 1 mile = 21 minutes 7 minute more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
• 40. Find Unit Rate I run 3 miles in 21 minutes. 3 miles 1 mile 1 = = 21 minutes 7 minute 7 more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
• 41. Find Unit Rate I run 3 miles in 21 minutes. 3 miles 1 mile 1 = = mile per minute 21 minutes 7 minute 7 more or less than 1 whole? 3 ÷3 1 = 21 ÷3 7
• 42. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? =
• 43. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars =
• 44. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months
• 45. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months
• 46. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months more or less than 1 whole?
• 47. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months more or less than 1 whole? 3 400
• 48. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 more or less than 1 whole? 3 400
• 49. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 more or less than 1 whole? 3 400 −3
• 50. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 more or less than 1 whole? 3 400 −3 1
• 51. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 more or less than 1 whole? 3 400 −3 10
• 52. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 more or less than 1 whole? 3 400 −3 10
• 53. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 more or less than 1 whole? 3 400 −3 10 −9
• 54. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 more or less than 1 whole? 3 400 −3 10 −9 1
• 55. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 more or less than 1 whole? 3 400 −3 10 −9 10
• 56. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 3 more or less than 1 whole? 3 400 −3 10 −9 10
• 57. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9
• 58. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 13 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
• 59. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars = 3 months 1 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
• 60. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars 133 1 = 3 months 3 1 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
• 61. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars 133 1 dollars = 3 months 3 month 1 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
• 62. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars 133 1 dollars 1 = = 133 3 months 3 month 1 3 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
• 63. Find Unit Rate To answer a “how fast” question, use a unit rate. I save 400 dollars every 3 months. How fast is my bank account growing? 400 dollars 133 1 dollars 1 dollars per = = 133 3 months 3 month 1 3 month 13 3 3 more or less than 1 whole? 3 400 −3 10 −9 10 −9 1
• 64. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. I spend \$265 every 4 weeks. Find the unit rate. A tree grows 4 inches in 12 years. How fast is it growing? I drive 228 miles in 5 hours. How fast am I driving?
• 65. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. 1 1 cups per cake 2 I spend \$265 every 4 weeks. Find the unit rate. A tree grows 4 inches in 12 years. How fast is it growing? I drive 228 miles in 5 hours. How fast am I driving?
• 66. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. 1 1 cups per cake 2 I spend \$265 every 4 weeks. Find the unit rate. 1 66 dollars per week 4 A tree grows 4 inches in 12 years. How fast is it growing? I drive 228 miles in 5 hours. How fast am I driving?
• 67. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. 1 1 cups per cake 2 I spend \$265 every 4 weeks. Find the unit rate. 1 66 dollars per week 4 A tree grows 4 inches in 12 years. How fast is it growing? 1 inch per year 3 I drive 228 miles in 5 hours. How fast am I driving?
• 68. Find Unit Rate I need 3 cups of sugar for 2 cakes. Find the unit rate. 1 1 cups per cake 2 I spend \$265 every 4 weeks. Find the unit rate. 1 66 dollars per week 4 A tree grows 4 inches in 12 years. How fast is it growing? 1 inch per year 3 I drive 228 miles in 5 hours. How fast am I driving? 3 45 miles per hour 5
• 69. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster?
• 70. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha
• 71. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters = 40 seconds
• 72. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 40 seconds 5
• 73. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5
• 74. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan
• 75. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan 110 meters = 50 seconds
• 76. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan 110 meters 1 = 2 50 seconds 5
• 77. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan 110 meters 1 = 2 meters per second 50 seconds 5
• 78. Comparing Quantities Samantha ran 96 meters in 40 seconds. Juan ran 110 meters in 50 seconds. Who ran faster? Samantha 96 meters 2 = 2 meters per second 40 seconds 5 Juan 110 meters 1 = 2 meters per second 50 seconds 5 They were very close, but Samantha ran faster by 1/5 of a meter every second.
• 79. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
• 80. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
• 81. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
• 82. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? 2 1 Tomato:  inch per month Pepper:  inch per month 5 2 Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
• 83. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? 2 1 Tomato:  inch per month Pepper:  inch per month 5 2 Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job?
• 84. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? 2 1 Tomato:  inch per month Pepper:  inch per month 5 2 Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job? 1 3 Francisco: 9  dollars per hour Jasmine: 8  dollars per hour 4 4
• 85. Comparing Quantities Noemi ran 105 meters in 30 seconds. Mirian ran 112 meters in 40 seconds. Who ran faster? 1 4 Noemi: 3  metersper second Mirian: 2  metersper second 2 5 My tomato plants grow 4 inches in 10 months. My pepper plants grow 3 inches in 6 months. Which grows faster? 2 1 Tomato:  inch per month Pepper:  inch per month 5 2 Francisco earned \$74 in 8 hours. Jasmine earned \$105 in 12 hours. Who has a better paying job? 1 3 Francisco: 9  dollars per hour Jasmine: 8  dollars per hour 4 4