Curriculum  /  Math  /  5th Grade  /  Unit 4: Addition and Subtraction of Fractions/Decimals  /  Lesson 8

Addition and Subtraction of Fractions/Decimals

Lesson 8

Math

Unit 4

5th Grade

Lesson 8 of 17

Objective

Add fractions with unlike denominators whose sum is greater 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 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, including mixed numbers, with unlike denominators that require regrouping whose sum is greater than 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 more than 2 (MP.4).

Tips for Teachers

  • “Calculations with mixed numbers provide opportunities for students to compare approaches and justify steps in their computations (MP.3)” (NF Progression, p. 13). In general, given the Grade 4 instruction on this content, it’s unlikely that students will rewrite mixed numbers as “improper” fractions and add but instead will add like units and then regroup where necessary. For the problems that require regrouping, you should at least go through this strategy of adding like units and regrouping when necessary since this is a universal strategy. Students may also use computation-specific strategies, which are listed below.   
  • For some problems in this lesson, students may use the computation-specific strategy of making a whole, e.g., $$2\frac{8}{10}+1\frac{5}{10}=3\frac{8}{10}+ \frac{5}{10}=3\frac{8}{10}+\frac{2}{10}+\frac{3}{10}=4+\frac{3}{10}=4\frac{3}{10}$$.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

25-30 minutes

Problem 1

a.   Estimate which two whole numbers each of the following sums will be in between.

  1. $${2{1\over5}+1{1\over2}}$$
  2. $${2{4\over5}+1{1\over2}}$$

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

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 10 — Concept Development

Grade 5 Mathematics > Module 3 > Topic C > Lesson 10 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.   Estimate the following sums. Determine whether the actual sum will be more or less than the estimated sum. Be prepared to explain your reasoning.

  1. $${3{5\over7}+6{2\over3}}$$
  2. $${3{1\over4}+4{7\over8}}$$
  3. $${15{1\over6}+8{7\over10}}$$

b.   Solve for the actual sums in Part (a) above. Are your answers reasonable? Why or why not?

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 10 — Concept Development

Grade 5 Mathematics > Module 3 > Topic C > Lesson 10 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

It takes Wei $$2\frac{7}{10}$$ hours to clean her home. It takes Bernard $$1\frac{3}{4}$$ more hours to clean his home than it takes Wei. How long does it take Bernard to clean his home?

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 10 — Concept Development

Grade 5 Mathematics > Module 3 > Topic C > Lesson 10 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. What was wrong with options A through C? How could you change them to be correct?
  • Look at #5. What two ways did you solve? Are there other ways you could have solved? Could you have used the strategy of making 1? Why or why not?
  • Look at #6. How did you solve? Did anyone make a whole with two of their addends? 
  • Look at #6. What is the sum of your two fractions? Was anyone able to come up with a larger sum? What if you used fractions greater than 1 for the fractional part of each mixed number? Why do you think it is that we don’t usually write numbers in that way?

Target Task

5-10 minutes

Problem 1

Solve. Show or explain your work.

$${2{5\over8}+4{2\over3}}$$

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

Sang needs $$3\tfrac{1}{2}$$ feet of string to make a necklace and $$2\tfrac{1}{4}$$ feet of string left. How much string, in feet, did Sang have before making the necklace?

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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 greater than 2 with unlike denominators.

Lesson 9
icon/arrow/right/large

Lesson Map

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

Topic A: Addition and Subtraction of Fractions

Topic B: Addition and Subtraction of Decimals

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free