Addition and Subtraction of Fractions/Decimals

Lesson 4

Math

Unit 4

5th Grade

Lesson 4 of 15

Objective


Add fractions with unlike denominators whose sum is less than 1.

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 add 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, one of which is the least common denominator. 
  4. Add two fractions with unlike denominators whose sum is less than 1 (and therefore does not require regrouping), simplifying the sum if applicable.
  5. Solve one-step word problems involving the addition of two fractions with unlike denominators whose sum is less than 1 (MP.4).

Tips for Teachers


  • Throughout the unit, students are encouraged to use whatever common denominator they like, never forced to use the least common denominator. The Progressions for the Common Core State Standards in Math state, “It is not necessary to find a least common denominator to calculate sums of fractions, and in fact the effort of finding a least common denominator is a distraction from understanding algorithms for adding fractions” (p. 11). 
  • The algorithm for adding fractions with unlike denominators is explicitly discussed in Lesson 6. 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 adding fractions with unlike denominators in Lesson 6, 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 adding fractions with unlike denominators, such as "Wacky Fractions" or "Fraction Addition War", from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.

Lesson Materials

  • Optional: Square-sized paper (1 per student) — Students might not need these depending on their reliance on concrete materials.
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Anchor Tasks


Problem 1

a.   Solve. 

  1. 1 orange + 3 oranges = ___________
  2. 1 child + 3 adults = ___________

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

Guiding Questions

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References

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

Grade 5 Mathematics > Module 3 > Topic B > Lesson 3 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.   $${{1\over2}+{1\over4}}$$

b.   $$\frac{1}{5}+\frac{2}{3}$$

c.   $$\frac{3}{4}+\frac{1}{6}$$

Guiding Questions

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References

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

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

Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use $$\frac{1}{3}$$ of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly $$\frac{1}{6}$$ of a chocolate bar. What fraction of a chocolate bar will Nick and Tasha use in total if they each eat one s’more?

Guiding Questions

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References

Illustrative Mathematics Making S'Mores

Making S'Mores, accessed on Feb. 15, 2018, 12:16 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #1. What fractions are equivalent to $$\frac{4}{9}$$? What fractions are equivalent to $$\frac{2}{6}$$? What equivalent fractions did you use to add these fractions together? 
  • Look at #2. How did you use the number line to figure out the sum? 
  • Look at #6. How did you use an area model to find your answer?
  • Look at #8. 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 sum? 
  • Look at #9. What is the sum of the two fractions you came up with? Was anyone able to find a closer sum? Did anyone get an exact sum of $$\frac{1}{2}$$

Target Task


Problem 1

Solve. Show or explain your work.

 $${{1\over2}+{1\over7}}$$

Problem 2

Carpenters are laying down hardwood floors in a living room. On the first day, they laid down $$\frac{2}{5}$$ of the whole floor. On the second day, they laid down $$\frac{1}{4}$$ of the whole floor. The area model shown can be used to find how much of the whole floor they laid over the two days.

  • How much of the floor did they lay down over the two days?
  • Explain how the area model can be used to answer the question.

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.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 3

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Lesson 5

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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