Fraction Operations

Lesson 7

Objective

Add two fractions where one denominator is a divisor of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

Materials and Resources

Common Core Standards

Core Standards

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  • 4.NF.B.3.A — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

  • 4.NF.B.3.B — Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Foundational Standards

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  • 4.NF.A.1

Criteria for Success

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  1. Make sense of a three-act task and persevere in solving it (MP.1).
  2. Add fractions where one denominator is a divisor of the other and where the sum is between 1 and 2, by replacing one fraction with an equivalent fraction in such a way as to produce an equivalent sum of fractions with like denominators.
  3. (Optional) Simplify solutions by rewriting them using the largest possible unit.

Tips for Teachers

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  • Lesson 7 goes beyond the explicit expectations of 4.NF.3. However, students will add fractions with denominators of 10 and 100 in Unit 7 (4.NF.5). Thus, today’s lesson is intended to prepare students for that work in Unit 7. The Progressions note that “students might encounter [such] situations, for example using a strip of paper or a tape diagram to reason that $$\frac{1}{3}+\frac{1}{6}=\frac{2}{6}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2}$$” (NF Progression, p. 16).
  • In place of the Problem Set, you might decide to play the following NCTM Illuminations game, Fraction Game. This game can also be converted to a paper version if you don’t want to use the computer version.

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Anchor Tasks

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Problem 1

Act 1: Watch the following video: Black box - Act 1.

What will the sum of $$\frac{1}{2} + \frac{1}{4}$$ be?

Guiding Questions

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References

101Questions Black Box 2

Black Box 2 by is made available on 101Questions under the CC BY 3.0 license. Accessed July 17, 2018, 1:45 p.m..

Modified by The Match Foundation, Inc.
YouTube Video: “Black box - Act 1” by msbritton215

Black box - Act 1 by msbritton215 is made available by YouTube under the Standard YouTube License. Accessed Oct. 23, 2019, 5:27 p.m..

Problem 2

Act 2: Use the following information to solve.

Guiding Questions

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References

101Questions Black Box 2

Black Box 2 by is made available on 101Questions under the CC BY 3.0 license. Accessed July 17, 2018, 1:45 p.m..

Modified by The Match Foundation, Inc.

Problem 3

Act 3: Reveal the answer: Black box - Act 3.

Guiding Questions

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References

101Questions Black Box 2

Black Box 2 by is made available on 101Questions under the CC BY 3.0 license. Accessed July 17, 2018, 1:45 p.m..

Modified by The Match Foundation, Inc.
YouTube Video: “Black box - Act 3” by msbritton215

Black box - Act 3 by msbritton215 is made available by YouTube under the Standard YouTube License. Accessed Oct. 23, 2019, 5:27 p.m..

Problem 4

Solve. Show or explain your work.

a.   $${{1\over2}+{1\over8}}$$

b.   $${{1\over5}+{3\over10}}$$

c.   $${{2\over3}+{1\over6}}$$

d.   $${{3\over4}+{5\over12}}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 21Concept Development

Grade 4 Mathematics > Module 5 > Topic D > Lesson 21 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.
EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 20Concept Development

Grade 4 Mathematics > Module 5 > Topic D > Lesson 20 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Discussion of Problem Set

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  • How did you determine which amounts could have been what Jake added to the jug in #1? 
  • In #2c, did you use sixths as the common denominator? Explain how thirds could be used as the common denominator. 
  • For #5, what strategies did you use to estimate if the sum would be between 0 and 1 or 1 and 2? 
  • Why is it important to have common denominators when adding fractions? 
  • How can you find the sum of two fractions without using a model? 
  • What benefit can you see in expressing a fraction as a mixed number or a mixed number as a fraction?

Target Task

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Solve. Show or explain your work.

1.  $${{5\over8}+{2\over4}=}$$ _____

2.  $${{2\over3}+{7\over12}=}$$ _____

References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 20Exit Ticket, Question #1

Grade 4 Mathematics > Module 5 > Topic D > Lesson 20 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.
EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic D > Lesson 21Exit Ticket, Question #2

Grade 4 Mathematics > Module 5 > Topic D > Lesson 21 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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