Addition and Subtraction of Fractions/Decimals

Lesson 11

Objective

Add and subtract more than two fractions. 

Materials and Resources

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

?

  • Find a common unit for more than two fractions, ideally (but not necessarily) by finding the least common denominator since it means the computation is more manageable with larger units (i.e., smaller denominators). 
  • Add more than two fractions with unlike denominators. 
  • Subtract more than two fractions with unlike denominators.
  • 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 in tandem 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 master 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. 

Fishtank Plus

Subscribe to Fishtank Plus to unlock access to additional resources for this lesson, including:

  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package

 

Anchor Tasks

?

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. 

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

i.     $${{{1\over2}}}+{{{1\over3}}}$$

ii.   $${{{1\over2}}}+{{{1\over3}}}+{1\over5}$$

iii.  $${{1\over4}+{1\over5}+{1\over12}}$$

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

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

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

b.     $${{2\over3}+{1\over5}+{1\over3}+1{4\over5}}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 9Concept 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 The Match Foundation, Inc.
EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14Concept 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 The Match Foundation, Inc.

Problem 3

Solve. Show or explain your work. 

a.     $${8{11\over12}-{14\over3}-{9\over4}}$$

b.     $${5{7\over8}-{1\over2}-{7\over8}-1{1\over2}}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14Concept 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 The Match Foundation, Inc.

Problem 4

Solve. Show or explain your work. 

a.     $${6{3\over4}+{3\over5}-5{1\over2}}$$

b.     $${2{5\over6}-{1\over3}+{1\over6}}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14Concept 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 The Match Foundation, Inc.

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

?

Problem 1

Solve.

 $${{3\over4}+{4\over5}-{7\over10}}$$

References

PARCC Mathematics Practice Tests Grade 5 Mathematics Paper-Based Practice TestQuestion Stem #26

Grade 5 Mathematics Paper-Based Practice Test from Mathematics Practice Tests is made available by Partnership for Assessment of Readiness for College and Careers. © Copyright 1998 - 2015 Pearson Education, Inc. or its affiliate(s). All rights reserved. Accessed Feb. 5, 2018, 12:11 p.m..

Problem 2

Solve.

$${8{4\over5}-{2\over3}+3{7\over10}}$$

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14Exit Ticket, Question #2

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 The Match Foundation, Inc.

Mastery Response

?

Create a free account or sign in to view Mastery Response