Curriculum  /  Math  /  5th Grade  /  Unit 4: Addition and Subtraction of Fractions/Decimals  /  Lesson 5

Addition and Subtraction of Fractions/Decimals

Lesson 5

Math

Unit 4

5th Grade

Lesson 5 of 17

Objective

Subtract fractions from fractions less than 1 with unlike denominators.

Common Core Standards

Core Standards

  • 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

  • 4.NF.A.1
  • 4.NF.B.3

Criteria for Success

  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 where the minuend 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 where the minuend is less than 1 (MP.4).

Tips for Teachers

  • 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 then. 
  • Keep anchor charts from the Anchor Tasks in Lessons 4 and 5 up after their instruction. 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. 
  • 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

25-30 minutes

Problem 1

a.   Solve. 

  1. 3 pencils – 1 pencil = __________
  2. 3 animals – 1 dog = ___________

b.   What do you notice about Part (a) above? What do you wonder?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 5 — Concept 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 Fishtank Learning, Inc.

Problem 2

Solve. Show or explain your work. 

a.   $${{1\over2}-{1\over8}}$$

b.   $$\frac{2}{3}-\frac{1}{5}$$

c.   $$\frac{5}{9}-\frac{2}{6}$$

Guiding Questions

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Student Response

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Problem 3

Bandi has $$\frac{2}{3}$$ cups of flour. He uses $$\frac{1}{4}$$ cups of flour for a recipe. How much flour, in cups, does Bandi have left?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 5 — Concept 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 Fishtank Learning, Inc.

Problem Set

15-20 minutes

Discussion of Problem Set

  • 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

5-10 minutes

Problem 1

Solve. Show or explain your work.

$$\frac{1}{2}-\frac{1}{5}$$

Student Response

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Problem 2

Parth has $$3\over4$$ cups of sugar. He uses $$2\over3$$ cups of sugar to make cookies.

  • How many cups of sugar does Parth have left after he makes the cookies? 
  • Explain how a number line could be used to find your answer.

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Add fractions with unlike denominators whose sum is less than 2.

Lesson 6
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Addition and Subtraction of Fractions

Topic B: Addition and Subtraction of Decimals

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