More than Just Lines on a Map: Best Practices for U.S Bike Routes
Lesson 1 (Unit Rates)
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
15. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
=
16. Find Unit Rate
I need 8 feet of wrapping paper to wrap 5 presents.
8 feet
=
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
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?
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?
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
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
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?
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
1
5 8
−5
3
25. 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
26. 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
27. 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
28. 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
29. 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
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
34. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes
more or less than 1 whole?
35. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes
more or less than 1 whole?
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
37. Find Unit Rate
I run 3 miles in 21 minutes.
3 miles
=
21 minutes
more or less than 1 whole?
3 ÷3
21 ÷3
38. 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
39. 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
40. 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
41. 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
42. 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
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?
=
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
=
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
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?
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
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
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
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
1
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
1
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
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
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
1
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
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
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
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
13 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
=
3 months
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
=
3 months 3 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
=
3 months 3 month 1
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
= = 133
3 months 3 month 1 3
13 3 3
more or less than 1 whole? 3 400
−3
10
−9
10
−9
1
64. 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
65. 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?
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.
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?
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?
69. 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
72. Comparing Quantities
Samantha ran 96 meters in 40 seconds. Juan ran 110
meters in 50 seconds. Who ran faster?
Samantha
96 meters
=
40 seconds
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
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
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
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
=
50 seconds
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
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
79. 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.
80. 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?
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?
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?
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
86. 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
