Curriculum  /  Math  /  5th Grade  /  Unit 4: Addition and Subtraction of Fractions/Decimals  /  Lesson 6

Addition and Subtraction of Fractions/Decimals

Lesson 6

Math

Unit 4

5th Grade

Lesson 6 of 17

Objective

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

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.A.2
  • 4.NF.B.3

Criteria for Success

  1. Find common units for fractions with unlike denominators by finding equivalent fractions using a number line, an area model, or using multiplication or division. 
  2. Understand that there is more than one possibility for the common unit used, and use that to optionally find the least common denominator. 
  3. Add two fractions with unlike denominators that require regrouping whose sum is between 1 and 2, simplifying and writing the sum as a mixed number, if applicable.
  4. Assess the reasonableness of an answer using number sense and estimation (MP.1).
  5. Solve one-step word problems involving the addition of two fractions with unlike denominators whose sum is less than 2 (MP.4).

Tips for Teachers

For some problems in this lesson, students may use the computation-specific strategy of making a whole (e.g., $$\frac{2}{5}+\frac{4}{5}=\frac{10}{15}+\frac{12}{15}=\frac{7}{15}+\frac{3}{15}+\frac{12}{15}=\frac{7}{15}+1=1\frac{7}{15}$$). Discussing various strategies and their advantages and disadvantages “provide opportunities for students to compare approaches and justify steps in their computations (MP.3)” (NF Progression, p. 13).

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Anchor Tasks

25-30 minutes

Problem 1

a.   Estimate whether each of the following sums will be more or less than 1.

  1. $${{1\over3}+{1\over4}}$$
  2. $${{1\over2}+{2\over3}}$$

b.   Solve for the actual sums in Part (a) above. 

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic B > Lesson 4 — Concept Development

Grade 5 Mathematics > Module 3 > Topic B > Lesson 4 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

a.   Here is Ragnar’s strategy for finding the value of $$\frac{4}{5}+\frac{6}{7}$$: “I know 5 × 7 is a common denominator so I’ll use that.” Does Ragnar’s strategy for finding a common denominator work? Explain or show your thinking and then find the value of $$\frac{4}{5}+\frac{6}{7}$$.

b.   Estimate the following sums. Then compute using any strategy.

  1. $$\frac{2}{3}+\frac{3}{5}$$
  2. $$\frac{5}{12}+\frac{2}{3}$$
  3. $$\frac{1}{6}+\frac{3}{8}$$

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 5 > Unit 6 > Lesson 10 > Activity 2

Grade 5 > Unit 6 > Lesson 10 > Activity 2, accessed on Feb. 3, 2022, 10:48 a.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 3

Abby buys some coffee beans at the grocery store. She uses $$\frac{3}{4}$$ pounds and has $$\frac{5}{8}$$ pounds left. How much coffee, in pounds, did Abby buy at the grocery store? 

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Look at #3. Did anyone solve without actually adding $${{5\over8}}$$ and $${{1\over2}}$$? How were you able to do that? 
  • Look at #4a. How can you tell, before solving, that the sum is going to be less than $$1$$? 
  • Look at #4c. What do you notice about these fractions? How did that change the way you added?
  • Look at #4d. What do you notice about these fractions? How did that change the way you added? 
  • Look at #8. What is the sum of your two fractions? Was anyone able to come up with a larger sum? How can we ensure we have the largest sum possible? 

Target Task

5-10 minutes

Problem 1

Solve. Show or explain your work.

$${{5\over6}+{1\over3}}$$

Student Response

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Problem 2

Roxanne bought $$2\over5$$ kilograms of raspberries and $$3\over4$$ kilograms of peaches. How much fruit, in kilograms, did Roxanne buy altogether?

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

Subtract fractions from fractions less than 2 with unlike denominators.

Lesson 7
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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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