Addition and Subtraction of Fractions/Decimals

Lesson 5

Objective

Subtract fractions from fractions less than 1 with unlike denominators.

Materials and Resources

Common Core Standards

Core Standards

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  • 5.NF.A.1 — Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

  • 5.NF.A.2 — Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Foundational Standards

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  • 4.NF.A.1

  • 4.NF.B.3

Criteria for Success

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  1. Understand that in order to subtract quantities, they must have the same unit (which in the case of fractions, are their denominators). 
  2. Find common units for fractions with unlike denominators by finding equivalent fractions using a number line and an area model (MP.5).
  3. Understand that there is more than one possibility for the common unit used, and use that to optionally find the least common denominator. 
  4. Subtract two fractions with unlike denominators whose sum is less than 1 (and therefore does not require regrouping), simplifying the difference if applicable. 
  5. Solve one-step word problems involving the subtraction of two fractions with unlike denominators whose sum is less than 1 (MP.4).

Tips for Teachers

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  • There are five Anchor Tasks in today’s lesson. However, because the first one just lays a conceptual foundation for adding like units and all the subsequent ones include just a single computation, it should be possible to fit it in a single lesson. 
  • The algorithm for subtracting fractions with unlike denominators is explicitly discussed in Lesson 7. 
  • However, students might uncover it before then, especially since students have used multiplication and division to find equivalent fractions in Grade 4 (4.NF.1) and in Lesson 1. If that does happen, you can discuss it as a class when it comes up naturally and allow students to use it as a strategy before Lesson 7. 
  • For when students get to the generalized algorithm for subtracting fractions with unlike denominators in Lesson 7, it may be helpful for students to see multiple examples of previous problems they’ve completed. Thus, keep anchor charts from the Anchor Tasks in Lessons 4 and 5 up after their instruction.
  • Before the Problem Set, you could have students play a game to practice subtracting fractions with unlike denominators, such as "Wacky Fraction Subtraction" or "Fraction Addition War" (modified to involve subtraction), from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.

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Anchor Tasks

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Problem 1

  1. Solve. 
    1.     3 pencils – 1 pencil = __________
    2.     3 boys – 1 girl = ___________
  2. What do you notice about #1 above? What do you wonder?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 5Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 5 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.

Problem 2

Solve. Show your work with an area model and a number line.

$${{1\over2}-{1\over3}}$$

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 5Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 5 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.

Problem 3

Solve. Show your work with an area model and a number line.

$${{2\over3}-{1\over4}}$$

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 5Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 5 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.

Problem 4

Solve. Show your work with an area model and a number line.

$${{1\over2}-{2\over7}}$$

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 5Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 5 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.

Problem 5

  1. Solve. Show your work with an area model and a number line.

$${{7\over10}-{2\over5}}$$

  1. Is there another common unit that can be used to solve?

Guiding Questions

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Discussion of Problem Set

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  • Look at #2. How did you figure out how far Ben walked?
  • Look at #5. How did you figure out how much larger the pea section was than the carrot section?
  • Look at #7. For part (a), what common denominators did you choose? Why do both of them work? For part (c), how did you solve? What did you get as the difference?

Target Task

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Problem 1

Solve. Show or explain your work.

$${{1\over2}-{1\over7}}$$

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 5Exit Ticket, Question #1

Grade 5 Mathematics > Module 3 > Topic B > Lesson 5 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..

Problem 2

A student has $${{3\over4}}$$ quart of yellow paint in a container. The student uses $${{2\over3}}$$ quart of the yellow paint to make green paint. 

  • How many quarts of yellow paint remain in the container after the student makes the green paint? 
  • Explain how a number line could be used to find your answer.

References

PARCC Released Items Math Spring 2018 Grade 5 Released ItemsQuestion #24, Part B

Math Spring 2018 Grade 5 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed March 15, 2019, 12:26 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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