Lesson 17 Sprint NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17: Practice placing various fractions on the number line. 203
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Division
1. 3 ÷ 3 = 23. 24 ÷ 3 =
2. 4 ÷ 4 = 24. 16 ÷ 2 =
3. 5 ÷ 5 = 25. 30 ÷ 10 =
4. 19 ÷ 19 = 26. 30 ÷ 3 =
5. 0 ÷ 1 = 27. 27 ÷ 3 =
6. 0 ÷ 2 = 28. 18 ÷ 2 =
7. 0 ÷ 3 = 29. 40 ÷ 10 =
8. 0 ÷ 19 = 30. 40 ÷ 4 =
9. 6 ÷ 3 = 31. 20 ÷ 4 =
10. 9 ÷ 3 = 32. 20 ÷ 5 =
11. 12 ÷ 3 = 33. 24 ÷ 4 =
12. 15 ÷ 3 = 34. 30 ÷ 5 =
13. 4 ÷ 2 = 35. 28 ÷ 4 =
14. 6 ÷ 2 = 36. 40 ÷ 5 =
15. 8 ÷ 2 = 37. 32 ÷ 4 =
16. 10 ÷ 2 = 38. 45 ÷ 5 =
17. 18 ÷ 3 = 39. 44 ÷ 4 =
18. 12 ÷ 2 = 40. 36 ÷ 4 =
19. 21 ÷ 3 = 41. 48 ÷ 6 =
20. 14 ÷ 2 = 42. 63 ÷ 7 =
21. 20 ÷ 10 = 43. 64 ÷ 8 =
22. 20 ÷ 2 = 44. 72 ÷ 9 =
A Number Correct:
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 17 Sprint NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17: Practice placing various fractions on the number line. 204
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Division
1. 2 ÷ 2 = 23. 16 ÷ 2 =
2. 3 ÷ 3 = 24. 24 ÷ 3 =
3. 4 ÷ 4 = 25. 30 ÷ 3 =
4. 17 ÷ 17 = 26. 30 ÷ 10 =
5. 0 ÷ 2 = 27. 18 ÷ 2 =
6. 0 ÷ 3 = 28. 27 ÷ 3 =
7. 0 ÷ 4 = 29. 40 ÷ 4 =
8. 0 ÷ 17 = 30. 40 ÷ 10 =
9. 4 ÷ 2 = 31. 20 ÷ 5 =
10. 6 ÷ 2 = 32. 20 ÷ 4 =
11. 8 ÷ 2 = 33. 30 ÷ 5 =
12. 10 ÷ 2 = 34. 24 ÷ 4 =
13. 6 ÷ 3 = 35. 40 ÷ 5 =
14. 9 ÷ 3 = 36. 28 ÷ 4 =
15. 12 ÷ 3 = 37. 45 ÷ 5 =
16. 15 ÷ 3 = 38. 32 ÷ 4 =
17. 12 ÷ 2 = 39. 55 ÷ 5 =
18. 18 ÷ 3 = 40. 36 ÷ 4 =
19. 14 ÷ 2 = 41. 54 ÷ 6 =
20. 21 ÷ 3 = 42. 56 ÷ 7 =
21. 20 ÷ 2 = 43. 72 ÷ 8 =
22. 20 ÷ 10 = 44. 63 ÷ 9 =
B
Number Correct:
Improvement:
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 17 Problem Set NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17: Practice placing various fractions on the number line. 205
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Name Date
1. Locate and label the following fractions on the number line.
06 6
6 12
6 3
6 9
6
2. Locate and label the following fractions on the number line.
84 6
4 12
4 16
4 4
4
3. Locate and label the following fractions on the number line.
183
143
93 11
3 6
3
1 2 3 4
0 1 2 3
2 3 4 5 6
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 17 Problem Set NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17: Practice placing various fractions on the number line. 206
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4. For a measurement project in math class, students measured the lengths of their pinky fingers. Alex’s measured 2 inches long. Jerimiah’s pinky finger was 7
4 inches long. Whose finger is longer? Draw a
number line to help prove your answer.
5. Marcy ran 4 kilometers after school. She stopped to tie her shoelace at 75 kilometers. Then, she stopped
to switch songs on her iPod at 125
kilometers. Draw a number line showing Marcy’s run. Include her starting and finishing points and the 2 places where she stopped.
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 17 Exit Ticket NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17: Practice placing various fractions on the number line. 207
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Name Date
1. Locate and label the following fractions on the number line.
73
23
43
2. Katie bought 2 one-gallon bottles of juice for a party. Her guests drank 64 gallons of juice. What fraction
of a gallon of juice is left over? Draw a number line to show, and explain your answer.
0 1 2 3
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 17 Homework NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17: Practice placing various fractions on the number line. 208
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Name Date
1. Locate and label the following fractions on the number line.
2. Locate and label the following fractions on the number line.
3. Locate and label the following fractions on the number line.
0 1 2 3
12
42
52
2 3 4
113
63
83
3 4 5 6
204
134
234
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 17 Homework NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17: Practice placing various fractions on the number line. 209
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4. Wayne went on a 4-kilometer hike. He took a break at 43 kilometers. He took a drink of water at 10
3
kilometers. Show Wayne’s hike on the number line. Include his starting and finishing place and the 2 points where he stopped.
5. Ali wants to buy a piano. The piano measures 194
feet long. She has a space 5 feet long for the piano in her house. Does she have enough room? Draw a number line to show, and explain your answer.
4 ft 5 ft
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 18 Problem Set NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 18: Compare fractions and whole numbers on the number line by reasoning about their distance from 0.
215
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Name Date
Place the two fractions on the number line. Circle the fraction with the distance closest to 0. Then, compare using >, <, or =. The first problem is done for you.
0 1
1. 14 3
4
2. 26 3
6
3. 12 1
4
4. 23 2
6
5. 118
74
0 1
0 1
< 0
4 1
4 2
4 3
4 4
4
0 1
1 2
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 18 Problem Set NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 18: Compare fractions and whole numbers on the number line by reasoning about their distance from 0.
216
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6. JoAnn and Lupe live straight down the street from their school. JoAnn walks 56 miles and Lupe walks 7
8
miles home from school every day. Draw a number line to model how far each girl walks. Who walks the least? Explain how you know using pictures, numbers, and words.
7. Cheryl cuts 2 pieces of thread. The blue thread is 54 meters long. The red thread is 4
5 meters long. Draw a
number line to model the length of each piece of thread. Which piece of thread is shorter? Explain how you know using pictures, numbers, and words.
8. Brandon makes homemade spaghetti. He measures 3 noodles. One measures 78 feet, the second is 7
4 feet,
and the third is 42 feet long. Draw a number line to model the length of each piece of spaghetti. Write a
number sentence using <, >, or = to compare the pieces. Explain using pictures, numbers, and words.
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 18 Exit Ticket NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 18: Compare fractions and whole numbers on the number line by reasoning about their distance from 0.
217
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Name Date
Place the two fractions on the number line. Circle the fraction with the distance closest to 0. Then, compare using >, <, or =.
1. 3
5 1
5
2. 12 3
4
3. Mr. Brady draws a fraction on the board. Ken says it’s 23, and Dan said it’s 3
2. Do both of these fractions
mean the same thing? If not, which fraction is larger? Draw a number line to model 23 and 3
2. Use words,
pictures, and numbers to explain your comparison.
0 1
0 1
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 18 Homework NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 18: Compare fractions and whole numbers on the number line by reasoning about their distance from 0.
218
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Name Date
Place the two fractions on the number line. Circle the fraction with the distance closest to 0. Then, compare using >, <, or =.
0 1
1. 13 2
3
2. 46 1
6
3. 14 1
8
4. 45 4
10
5. 86 5
3
0 1
0 1
0 1
1 2
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 18 Homework NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 18: Compare fractions and whole numbers on the number line by reasoning about their distance from 0.
219
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6. Liz and Jay each have a piece of string. Liz’s string is 46 yards long, and Jay’s string is 5
7 yards long. Whose
string is longer? Draw a number line to model the length of both strings. Explain the comparison using pictures, numbers, and words.
7. In a long jump competition, Wendy jumped 910
meters, and Judy jumped 109
meters. Draw a number line to model the distance of each girl’s long jump. Who jumped the shorter distance? Explain how you know using pictures, numbers, and words.
8. Nikki has 3 pieces of yarn. The first piece is 56 feet long, the second piece is 5
3 feet long, and the third piece
is 32 feet long. She wants to arrange them from the shortest to the longest. Draw a number line to model
the length of each piece of yarn. Write a number sentence using <, >, or = to compare the pieces. Explain using pictures, numbers, and words.
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 19 Sprint NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional)
224
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Express Fractions as Whole Numbers
1. 21� = 23. 6
3� =
2. 22� = 24. 3
3� =
3. 42� = 25. 3
1� =
4. 62� = 26. 9
3� =
5. 102� = 27. 16
4� =
6. 82� = 28. 20
4� =
7. 51� = 29. 12
3� =
8. 55� = 30. 15
3� =
9. 105� = 31. 70
10� =
10. 155� = 32. 12
2� =
11. 255� = 33. 14
2� =
12. 205� = 34. 90
10� =
13. 1010� = 35. 30
5� =
14. 5010� = 36. 35
5� =
15. 3010� = 37. 60
10� =
16. 101� = 38. 18
2� =
17. 2010� = 39. 40
5� =
18. 4010� = 40. 80
10� =
19. 84� = 41. 16
2� =
20. 44� = 42. 45
5� =
21. 41� = 43. 27
3� =
22. 124� = 44. 32
4� =
A Number Correct:
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 19 Sprint NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional)
225
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Express Fractions as Whole Numbers
1. 51� = 23. 8
4� =
2. 55� = 24. 4
4� =
3. 105� = 25. 4
1� =
4. 155� = 26. 12
4� =
5. 255� = 27. 12
3� =
6. 205� = 28. 15
3� =
7. 21� = 29. 16
4� =
8. 22� = 30. 20
4� =
9. 42� = 31. 90
10� =
10. 62� = 32. 30
5� =
11. 102� = 33. 35
5� =
12. 82� = 34. 70
10� =
13. 101� = 35. 12
2� =
14. 1010� = 36. 14
2� =
15. 5010� = 37. 80
10� =
16. 3010� = 38. 45
5� =
17. 2010� = 39. 16
2� =
18. 4010� = 40. 60
10� =
19. 63� = 41. 18
2� =
20. 33� = 42. 40
5� =
21. 31� = 43. 36
4� =
22. 93� = 44. 24
3� =
B
Number Correct:
Improvement:
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 19 Problem Set NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional)
226
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Name Date
1. Divide each number line into the given fractional unit. Then, place the fractions. Write each whole as a fraction.
a. halves 32
52
42
b. fourths 94
114
64
c. eighths 248
198
168
2. Use the number lines above to compare the following fractions using >, <, or =.
3
0 3
0 3
0 1 2
64 9
4 3
2 5
2
198
168
42 16
8
248
114
94 19
8
52 9
4
168
32
64 16
8
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 19 Problem Set NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional)
227
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3. Choose a greater than comparison you made in Problem 2. Use pictures, numbers, and words to explain how you made that comparison.
4. Choose a less than comparison you made in Problem 2. Use pictures, numbers, and words to explain a different way of thinking about the comparison than what you wrote in Problem 3.
5. Choose an equal to comparison you made in Problem 2. Use pictures, numbers, and words to explain two ways that you can prove your comparison is true.
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 19 Exit Ticket NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional)
228
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Name Date
1. Divide the number line into the given fractional unit. Then, place the fractions. Write each whole as a fraction.
fourths 24
104
74
2. Use the number line above to compare the following fractions using >, <, or =.
3. Use the number line from Problem 1. Which is larger: 2 wholes or 94? Use words, pictures, and numbers
to explain your answer.
3 0 1 2
34 5
4 7
4 4
4 3 6
4
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 19 Homework NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional)
229
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Name Date
1. Divide each number line into the given fractional unit. Then, place the fractions. Write each whole as a fraction.
a. thirds 63
53
83
b. sixths 106
186
156
c. fifths 145
75
115
2. Use the number lines above to compare the following fractions using >, <, or =.
1 2 3
1 2 3
1 2 3
176
156
73 9
3
115
85
116
53
155
53
136
83
63 12
6
43 8
6
106
33
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 19 Homework NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 19: Understand distance and position on the number line as strategies for comparing fractions. (Optional)
230
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3. Use fractions from the number lines in Problem 1. Complete the sentence. Use words, pictures, or numbers to explain how you made that comparison.
____________ is greater than ____________.
4. Use fractions from the number lines in Problem 1. Complete the sentence. Use words, pictures, or numbers to explain how you made that comparison.
____________ is less than ____________.
5. Use fractions from the number lines in Problem 1. Complete the sentence. Use words, pictures, or numbers to explain how you made that comparison.
____________ is equal to ____________.
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 20 Pattern Sheet NYS COMMON CORE MATHEMATICS CURRICULUM 3 5
Lesson 20: Recognize and show that equivalent fractions have the same size, though not necessarily the same shape.
238
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multiply by 7 (1–5)
Multiply.
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 20 Problem Set NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 20: Recognize and show that equivalent fractions have the same size, though not necessarily the same shape.
239
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Name Date
1. Label what fraction of each shape is shaded. Then, circle the fractions that are equal.
a.
b.
c.
2. Label the shaded fraction. Draw 2 different representations of the same fractional amount.
a.
b.
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 20 Problem Set NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 20: Recognize and show that equivalent fractions have the same size, though not necessarily the same shape.
240
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A B
3. Ann has 6 small square pieces of paper. 2 squares are grey. Ann cuts the 2 grey squares in half with a diagonal line from one corner to the other.
a. What shapes does she have now?
b. How many of each shape does she have?
c. Use all the shapes with no overlaps. Draw at least 2 different ways Ann’s set of shapes might look. What fraction of the figure is grey?
4. Laura has 2 different beakers that hold exactly 1 liter. She pours 12 liter of blue liquid into Beaker A. She
pours 12 liter of orange liquid into Beaker B. Susan says the amounts are not equal. Cristina says they are.
Explain who you think is correct and why.
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 20 Exit Ticket NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 20: Recognize and show that equivalent fractions have the same size, though not necessarily the same shape.
241
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b.
Name Date
1. Label what fraction of the figure is shaded. Then, circle the fractions that are equal.
2. Label the shaded fraction. Draw 2 different representations of the same fractional amount.
a.
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Lesson 20 Homework NYS COMMON CORE MATHEMATICS CURRICULUM 3 5
Lesson 20: Recognize and show that equivalent fractions have the same size, though not necessarily the same shape.
242
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Name Date
1. Label the shaded fraction. Draw 2 different representations of the same fractional amount.
2. These two shapes both show 45.
a. Are the shapes equivalent? Why or why not?
b. Draw two different representations of 45 that are equivalent.
3. Diana ran a quarter mile straight down the street. Becky ran a quarter mile on a track. Who ran more? Explain your thinking.
Diana
Becky
© 2015 Great Minds. eureka-math.orgG3-M5-TE-1.3.0-06.2015
Lesson 20 Template NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 20: Recognize and show that equivalent fractions have the same size, though not necessarily the same shape.
243
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thirds
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