Addition and Subtraction of Fractions/Decimals

Lesson 8

Objective

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

Materials and Resources

Common Core Standards

Core Standards

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  • 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

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  • 4.NF.A.1

  • 4.NF.A.2

  • 4.NF.B.3

Criteria for Success

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  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. Assess the reasonableness of an answer using number sense and estimation (MP.1). 
  4. 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.
  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

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  • “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, whereas making a whole is more computation-specific. The computation-specific possibilities are listed below.  
  • For some problems in this lesson, students may use the computation-specific strategy of making a whole, e.g., $$2\frac{8}{10}+1\frac{5}{10}=3\frac{8}{10}+ \frac{5}{10}=3\frac{8}{10}+\frac{2}{10}+\frac{3}{10}=4+\frac{3}{10}=4\frac{3}{10}$$.

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Anchor Tasks

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Problem 1

  1. Estimate the following sums.

a.  $${2{1\over5}+1{1\over2}}$$

b.  $${2{4\over5}+1{1\over2}}$$

  1. Solve for the actual sums in #1 above. Are your answers reasonable? Why or why not?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 10Concept 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 The Match Foundation, Inc.

Problem 2

  1. Estimate the following sums. Determine whether the actual sum will be more or less than the estimated sum. 

a.  $${2{2\over3}+5{2\over5}}$$

b.  $${3{5\over7}+6{2\over3}}$$

  1. Solve for the actual sums in #1 above. Are your answers reasonable? Why or why not?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 10Concept 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 The Match Foundation, Inc.

Problem 3

  1. Estimate the following sum. Determine whether the actual sum will be more or less than the estimated sum.

a.   $${3{1\over2}+4{7\over8}}$$

b.   $${15{5\over6}+7{9\over10}}$$

  1. Solve for the actual sums in #1 above. Are your answers reasonable? Why or why not?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 10Concept 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 The Match Foundation, Inc.

Discussion of Problem Set

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  • 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

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Problem 1

Solve. Show or explain your work.

$${4{5\over7}+3{3\over4}}$$

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 10Exit Ticket, Question #2

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..

Problem 2

Solve. Show or explain your work.

Jean needs $${2{1\over2}}$$ cups of flour to make sugar cookies and $${3{1\over4}}$$ cups of flour to make peanut butter cookies. What is the total number of cups of flour that Jean will need to make both kinds of cookies?

References

Massachusetts Department of Elementary and Secondary Education Spring 2016 Grade 5 Mathematics TestQuestion Stem #12

Spring 2016 Grade 5 Mathematics Test is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed Dec. 5, 2017, 3:53 p.m..

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