Curriculum  /  Math  /  5th Grade  /  Unit 4: Addition and Subtraction of Fractions/Decimals  /  Lesson 11

Addition and Subtraction of Fractions/Decimals

Lesson 11

Math

Unit 4

5th Grade

Lesson 11 of 17

Objective

Add and subtract more than two fractions.

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.)

Foundational Standards

  • 4.NF.A.1
  • 4.NF.A.2
  • 4.NF.B.3

Criteria for Success

  1. Find a common unit for more than two fractions, ideally (but not necessarily) by finding the least common denominator. 
  2. Add more than two fractions with unlike denominators. 
  3. Subtract more than two fractions with unlike denominators.
  4. Use the properties of addition and subtraction to make a multi-term computation easier (e.g., to add $${{{{1\over3}}}+{3\over5}+{{{2\over3}}}}$$, first add $${{1\over3}}$$ and $${{2\over3}}$$ to make $$1$$, making the computation easier) (MP.7).

Tips for Teachers

  • This lesson provides an opportunity to refer back to the order of operations, particularly that addition and subtraction should be performed simultaneously from left to right. 
  • If you are worried about pacing, you can cut Anchor Task #1 since it doesn’t provide necessary skills or concepts needed to understand the objective that aren’t addressed in the more straightforward computational problems below it. However, it is an engaging way to introduce the idea of adding more than two fractions, which is why it is included. 
  • Note that on the Problem Set, Problem 6 is a partner game that requires two dice. Because of the difficulty of previous problems on the problem set, it’s not especially likely that students will get to this task, but make sure to have the materials ready in case any students do. 
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Anchor Tasks

25-30 minutes

Problem 1

Ancient Egyptians used unit fractions, such as $${{1\over2}}$$ and $${{1\over3}}$$, to represent all fractions. For example, they might write the number $${{{{2\over3}}}}$$ as $${{{1\over2}}}+{1\over6}$$. 

We often think of $${{{{2\over3}}}}$$ as $${{{1\over3}}}+{{{1\over3}}}$$, but the ancient Egyptians would not write it this way because they didn’t use the same unit fraction twice. 

a.   Write each of the following Egyptian fractions as a single fraction:

  1. $${{{1\over2}}}+{{{1\over3}}}$$
  2. $${{{1\over2}}}+{{{1\over3}}}+{1\over5}$$
  3. $${{1\over4}+{1\over5}+{1\over12}}$$

b.   How might the ancient Egyptians have written the fraction we write as $${{3\over4}}$$?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Egyptian Fractions

Egyptian Fractions, accessed on Feb. 8, 2018, 12:52 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.

Problem 2

Solve. Show or explain your work. 

a.   $$\frac{2}{3} + \frac{1}{4} + \frac{1}{2}$$

b.   $$\frac{2}{3} + \frac{1}{5} + \frac{1}{3} + 1 \frac{4}{5}$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 9 — Concept Development

Grade 5 Mathematics > Module 3 > Topic C > Lesson 9 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.
EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 — Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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

Solve. Show or explain your work. 

a.   $$8 \frac{11}{12} - \frac{14}{3} - \frac{9}{4} $$

b.   $$5 \frac{7}{8} - \frac{1}{2} - \frac{7}{8} - 1 \frac{1}{2} $$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 — Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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 4

Solve. Show or explain your work. 

a.   $$6 \frac{3}{4} + \frac{3}{5} - 5 \frac{1}{2}$$

b.   $$2 \frac{5}{6} - \frac{1}{3} + 5 \frac{1}{6} $$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 — Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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 #3. How did you solve? 
  • Look at #5. Was Lucy’s method correct? Can she use it to measure out $${{1\over12}}$$of a cup? What other amounts of water can she measure?
  • Look at #6. What equation did you come up with? Is there more than one correct answer?

Target Task

5-10 minutes

Problem 1

Solve.

$${{2\over3}+{7\over8}-{1\over6}}$$

Student Response

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Problem 2

Solve.

$${{4\over5}-{2\over3}+1{7\over10}}$$

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

Solve two- and multi-step word problems involving addition and subtraction of fractions.

Lesson 12
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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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