Eureka Math Grade 3 Fluency Modules 5
& 6
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Practice
Eureka Math® Grade 3 Fluency Modules 5–6
VIRGINIA EDITION
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Published by Great Minds PBC. greatminds.org
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ISBN 978-1-64497-891-7
Learn ♦ Practice ♦ Succeed
Eureka Math® student materials for A Story of Units® (K–5) are available in the Learn, Practice, Succeed trio. This series supports differentiation and remediation while keeping student materials organized and accessible. Educators will find that the Learn, Practice, and Succeed series also offers coherent—and therefore, more effective—resources for Response to Intervention (RTI), extra practice, and summer learning.
Learn
Eureka Math Learn serves as a student’s in-class companion where they show their thinking, share what they know, and watch their knowledge build every day. Learn assembles the daily classwork—Application Problems, Exit Tickets, Problem Sets, templates—in an easily stored and navigated volume.
Practice
Each Eureka Math lesson begins with a series of energetic, joyous fluency activities, including those found in Eureka Math Practice. Students who are fluent in their math facts can master more material more deeply. With Practice, students build competence in newly acquired skills and reinforce previous learning in preparation for the next lesson.
Together, Learn and Practice provide all the print materials students will use for their core math instruction.
Succeed
Eureka Math Succeed enables students to work individually toward mastery. These additional problem sets align lesson by lesson with classroom instruction, making them ideal for use as homework or extra practice. Each problem set is accompanied by a Homework Helper, a set of worked examples that illustrate how to solve similar problems.
Teachers and tutors can use Succeed books from prior grade levels as curriculum-consistent tools for filling gaps in foundational knowledge. Students will thrive and progress more quickly as familiar models facilitate connections to their current grade-level content.
Students, families, and educators:
Thank you for being part of the Eureka Math® community, where we celebrate the joy, wonder, and thrill of mathematics. One of the most obvious ways we display our excitement is through the fluency activities provided in Eureka Math Practice
What is fluency in mathematics?
You may think of fluency as associated with the language arts, where it refers to speaking and writing with ease. In prekindergarten through grade 5, the Eureka Math curriculum contains multiple daily opportunities to build fluency in mathematics. Each is designed with the same notion—growing every student’s ability to use mathematics with ease. Fluency experiences are generally fast-paced and energetic, celebrating improvement and focusing on recognizing patterns and connections within the material. They are not intended to be graded.
Eureka Math fluency activities provide differentiated practice through a variety of formats—some are conducted orally, some use manipulatives, others use a personal whiteboard, and still others use a handout and paper-and-pencil format. Eureka Math Practice provides each student with the printed fluency exercises for his or her grade level.
What is a Sprint?
Many printed fluency activities utilize the format we call a Sprint. These exercises build speed and accuracy with already acquired skills. Used when students are nearing optimum proficiency, Sprints leverage tempo to build a low-stakes adrenaline boost that increases memory and recall. Their intentional design makes Sprints inherently differentiated; the problems build from simple to complex, with the first quadrant of problems being the simplest and each subsequent quadrant adding complexity. Further, intentional patterns within the sequence of problems engage students’ higher order thinking skills.
The suggested format for delivering a Sprint calls for students to do two consecutive Sprints (labeled A and B) on the same skill, each timed at one minute. Students pause between Sprints to articulate the patterns they noticed as they worked the first Sprint. Noticing the patterns often provides a natural boost to their performance on the second Sprint.
Sprints can be conducted with an untimed protocol as well. The untimed protocol is highly recommended when students are still building confidence with the level of complexity of the first quadrant of problems. Once all students are prepared for success on the Sprint, the work of improving speed and accuracy with the energy of a timed protocol is often welcome and invigorating.
Where can I find other fluency activities?
The Eureka Math Teacher Edition guides educators in the delivery of all fluency activities for each lesson, including those that do not require print materials. Additionally, the Eureka Digital Suite provides access to the fluency activities for all grade levels, searchable by standard or lesson.
Best wishes for a year filled with aha moments!
Jill Diniz Director of Mathematics Great Minds
Grade 3 Module 5
AMultiply with Seven Build non-unit fractions less than one whole from unit fractions. 1. 1 × 7 = 2. 7 × 1 = 3. 2 × 7 = 4. 7 × 2 = 5. 3 × 7 =
Number Correct:
7 × 3 =
4 × 7 =
BMultiply with Seven 1. 7 × 1 =
Number Correct: Improvement:
AMultiply and Divide by Seven
Number Correct:
Identify and represent shaded and non-shaded parts of one whole as fractions.
Multiply and Divide by Seven
Number Correct: Improvement:
Identify and represent shaded and non-shaded parts of one whole as fractions.
ANumber Correct: Identify Fractions.
A1. 8 × 1 = 2. 1 × 8 = 3. 8 × 2 = 4. 2 × 8 = 5. 8 × 3 = 6. 3 × 8 = 7. 8 × 4 =
4 × 8 =
8 × 5 =
Number Correct:
Multiply with Eight Build and write fractions greater than one whole using unit fractions.
8 × 8 =
8 × 9 =
9 × 8 = 18. 8 × 10 = 19. 10 × 8 =
20. 1 × 8 = 21. 10 × 8 = 22. 2 × 8 =
Number Correct: Improvement:
Multiply with Eight Build and write fractions greater than one whole using unit fractions.
1. 1 × 8 = 2. 8 × 1 = 3. 2 × 8 = 4. 8 × 2 = 5. 3 × 8 =
8 × 3 =
4 × 8 =
8 × 4 =
9 × 8 =
8 × 9 = 18. 10 × 8 = 19. 8 × 10 = 20. 8 × 3 = 21. 1 × 8 = 22. 2 × 8 =
AMultiply and Divide by Eight
1. 2 × 8 =
2. 3 × 8 =
3. 4 × 8 =
4. 5 × 8 =
5. 1 × 8 =
6. 16 ÷ 8 =
7. 24 ÷ 8 =
8. 40 ÷ 8 = 9. 8 ÷ 8 = 10. 32 ÷ 8 = 11. 6 × 8 = 12. 7 × 8 =
13. 8 × 8 = 14. 9 × 8 =
15. 10 × 8 = 16. 64 ÷ 8 =
17. 56 ÷ 8 =
18. 72 ÷ 8 =
19. 48 ÷ 8 =
20. 80 ÷ 8 =
21. ____ × 8 = 40
22. ____ × 8 = 8
Number Correct:
____ × 8 =
____ × 8 = 72
____ × 8 = 64
56 ÷ 8 =
72 ÷ 8 =
48 ÷ 8 =
64 ÷ 8 =
11 × 8 =
88 ÷ 8 =
Compare unit fractions by reasoning about their size using fraction strips.
Multiply and Divide by Eight
1. 1 × 8 =
2. 2 × 8 =
3. 3 × 8 =
4. 4 × 8 =
5. 5 × 8 =
6. 24 ÷ 8 =
7. 16 ÷ 8 = 8. 32 ÷ 8 = 9. 8 ÷ 8 = 10. 40 ÷ 8 = 11. 10 × 8 = 12. 6 × 8 = 13. 7 × 8 = 14. 8 × 8 = 15. 9 × 8 = 16. 56 ÷ 8 =
17. 48 ÷ 8 =
18. 64 ÷ 8 =
19. 80 ÷ 8 =
20. 72 ÷ 8 =
21. ____ × 8 = 8
22. ____ × 8 = 40
Number Correct: Improvement:
____ × 8 = 72
____ × 8 = 56
64 ÷ 8 =
72 ÷ 8 =
48 ÷ 8 =
56 ÷ 8 =
11 × 8 =
8:
Compare unit fractions by reasoning about their size using fraction strips.
A1. 9 × 1 = 2. 1 × 9 = 3. 9 × 2 = 4. 2 × 9 = 5. 9 × 3 = 6. 3 × 9 = 7. 9 × 4 =
4 × 9 =
9 × 5 =
5 × 9 =
Number Correct:
Multiply with Nine Specify the corresponding whole when presented with one equal part.
7 × 9 =
9 × 8 =
8 × 9 =
9 × 9 = 18. 9 × 10 = 19. 10 × 9 = 20. 1 × 9 = 21. 10 × 9 = 22. 2 × 9 =
Number Correct: Improvement:
Multiply with Nine Specify the corresponding whole when presented with one equal part.
1. 1 × 9 = 2. 9 × 1 = 3. 2 × 9 = 4. 9 × 2 = 5. 3 × 9 =
9 × 3 =
4 × 9 =
9 × 4 =
9 × 8 =
9 × 9 = 18. 10 × 9 = 19. 9 × 10 = 20. 9 × 3 = 21. 1 × 9 = 22. 2 × 9 =
AMultiply and Divide by Nine
1. 2 × 9 =
2. 3 × 9 =
3. 4 × 9 =
4. 5 × 9 =
5. 1 × 9 =
6. 18 ÷ 9 =
7. 27 ÷ 9 =
8. 45 ÷ 9 =
9. 9 ÷ 9 =
10. 36 ÷ 9 =
11. 6 × 9 =
12. 7 × 9 =
13. 8 × 9 =
14. 9 × 9 =
15. 10 × 9 =
16. 72 ÷ 9 =
17. 63 ÷ 9 =
18. 81 ÷ 9 =
19. 54 ÷ 9 =
20. 90 ÷ 9 =
21. ____ × 9 = 45
22. ____ × 9 = 9
Number Correct:
____ × 9 = 90
____ × 9 =
____ × 9 = 63
____ × 9 = 81
____ × 9 = 72
63 ÷ 9 =
81 ÷ 9 =
54 ÷ 9 =
72 ÷ 9 = 39. 11 × 9 =
99 ÷ 9 =
12 × 9 =
÷ 9 =
Lesson 14:
Place whole number fractions and fractions between whole numbers on the number line.
BMultiply and Divide by Nine
1. 1 × 9 =
2. 2 × 9 =
3. 3 × 9 =
4. 4 × 9 =
5. 5 × 9 =
6. 27 ÷ 9 =
7. 18 ÷ 9 =
8. 36 ÷ 9 = 9. 9 ÷ 9 =
45 ÷ 9 = 11. 10 × 9 = 12. 6 × 9 = 13. 7 × 9 = 14. 8 × 9 = 15. 9 × 9 =
16. 63 ÷ 9 =
17. 54 ÷ 9 =
18. 72 ÷ 9 =
19. 90 ÷ 9 =
20. 81 ÷ 9 =
21. ____ × 9 = 9
22. ____ × 9 = 45
Number Correct: Improvement:
____ × 9 = 18
____ × 9 = 27
____ × 9 = 36
____ × 9 = 81
____ × 9 = 63
72 ÷ 9 =
81 ÷ 9 =
54 ÷ 9 =
63 ÷ 9 =
11 × 9 =
99 ÷ 9 =
Lesson 14:
Place whole number fractions and fractions between whole numbers on the number line.
ANumber Correct: Divide Practice placing various fractions on the number line.
1. 3 ÷ 3 =
2. 4 ÷ 4 =
3. 5 ÷ 5 =
4. 19 ÷ 19 =
5. 0 ÷ 1 =
6. 0 ÷ 2 =
7. 0 ÷ 3 = 8. 0 ÷ 19 = 9. 6 ÷ 3 = 10. 9 ÷ 3 =
12 ÷ 3 = 12. 15 ÷ 3 =
4 ÷ 2 =
6 ÷ 2 = 15. 8 ÷ 2 = 16. 10 ÷ 2 = 17. 18 ÷ 3 = 18. 12 ÷ 2 = 19. 21 ÷ 3 = 20. 14 ÷ 2 = 21. 20 ÷ 10 = 22. 20 ÷ 2 =
Lesson 15:
÷ 4 =
1. 2 ÷ 2 =
2. 3 ÷ 3 =
3. 4 ÷ 4 = 4. 17 ÷ 17 =
5. 0 ÷ 2 =
6. 0 ÷ 3 = 7. 0 ÷ 4 = 8. 0 ÷ 17 = 9. 4 ÷ 2 = 10. 6 ÷ 2 =
8 ÷ 2 = 12. 10 ÷ 2 = 13. 6 ÷ 3 = 14. 9 ÷ 3 = 15. 12 ÷ 3 = 16. 15 ÷ 3 = 17. 12 ÷ 2 =
18. 18 ÷ 3 = 19. 14 ÷ 2 =
20. 21 ÷ 3 = 21. 20 ÷ 2 = 22. 20 ÷ 10 =
Number Correct: Improvement:
Lesson 15:
Practice placing various fractions on the number line.
÷ 5 =
÷ 4 =
÷ 5 =
÷ 4 =
÷ 5 =
ANumber Correct: Add by
Lesson 19:
Generate simple equivalent fractions by using visual fraction models and the number line.
AAdd by Seven
Number Correct:
21:
Lesson
Add by Eight
21:
Number Correct: Improvement:
Lesson
ASubtract by Seven
Number Correct:
Explain equivalence by manipulating units and reasoning about their size.
Subtract by Seven
Explain equivalence by manipulating units and reasoning about their size.
ASubtract by Eight Compare fractions with the same numerator pictorially.
Number Correct:
1. 18 – 8 = 2. 8 – 8 = 3. 28 – 8 = 4. 9 – 8 = 5. 19 – 8 = 6. 39 – 8 =
10 – 8 =
50 – 8 =
13 – 8 =
23 – 8 =
83 – 8 =
14 – 8 = 20. 24 – 8 = 21. 34 – 8 = 22. 54 – 8 =
1. 8 – 8 = 2. 18 – 8 = 3. 28 – 8 = 4. 9 – 8 = 5. 19 – 8 =
69 – 8 = 7. 10 – 8 =
Subtract by Eight Compare fractions with the same numerator pictorially.
Number Correct: Improvement:
– 8 =
60 – 8 =
13 – 8 =
23 – 8 = 18. 93 – 8 = 19. 14 – 8 = 20. 24 – 8 = 21. 34 – 8 = 22. 74 – 8 =
23:
Multiply.
Lesson 24:
Compare fractions with the same numerator using
or
and use a model to reason about their size.
Multiply.
Grade 3 Module 6
AMultiply or Divide by 6
1. 2 × 6 = 2. 3 × 6 = 3. 4 × 6 = 4. 5 × 6 = 5. 1 × 6 =
Create scaled bar graphs.
Number Correct:
BMultiply or Divide by 6
1. 1 × 6 =
2. 2 × 6 = 3. 3 × 6 = 4. 4 × 6 = 5. 5 × 6 = 6. 18 ÷ 6 =
36 ÷ 6 =
48 ÷ 6 = 19. 60 ÷ 6 = 20. 54 ÷ 6 = 21. ____ × 6 = 6 22. ____ × 6 = 30
Number Correct: Improvement:
Create scaled bar graphs.
Multiply.
Multiply.
Multiply.
Represent measurement data with line plots.
Multiply.
Analyze data to problem solve.
Credits
Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module.
Modules 5–6: Credits
A Story of Units®
Eureka Math helps students truly understand mathematics and connect it to the real world, preparing them to solve problems they have not encountered. Great Minds teachers and mathematicians believe that it is not enough for students to know the process for solving a problem; they need to understand why that process works.
Eureka Math presents mathematics as a story, one that develops from grades PK through 12. In A Story of Units, our elementary curriculum, this sequencing has been joined with methods of instruction that have been proven to work, in this nation and abroad.
Great Minds is here to make sure you succeed with an ever-growing library of resources, including free tip sheets, resource sheets, and full grade-level modules at eureka-math.org.
Sequence of Grade 3 Modules
Module 1: Properties of Multiplication and Division and Solving Word Problems with Units of 2–5 and 10
Module 2: Place Value and Problem Solving with Units of Measure
Module 3: Multiplication and Division with Units of 0, 1, 6–9 and Multiples of 10
Module 4: Multiplication and Area
Module 5: Fractions as Numbers on the Number Line
Module 6: Collecting and Displaying Data
Module 7: Geometry and Measurement Word Problems
On the cover
Vincent van Gogh (1853–1890). The Starry Night. Saint Rémy, June 1889. Oil on canvas, 29 x 36 1/4" (73.7 x 92.1 cm).
Acquired through the Lillie P. Bliss Bequest.
Location: The Museum of Modern Art, New York, NY, U.S.A.
Digital Image © The Museum of Modern Art/Licensed by SCALA/Art Resource, NY
What does this painting have to do with math?
In an effort to take advantage of every opportunity to build students’ cultural literacy, Great Minds features an important work of art or architecture on the cover of each book we publish. We select images that we know students and teachers will love to look at again and again. These works also relate, in visual terms, to ideas taken up in the book. Who can look at the night sky and not think of counting? Or of the shapes that form the constellations? The arrangement of the stars, moon, and planets particularly intrigued Vincent van Gogh, who painted twenty-one images of the sky as seen from his bedroom.
Published by Great Minds PBC