Addition and Subtraction of Fractions/Decimals
Lesson 6
Objective
Add fractions with unlike denominators whose sum is less than 2.
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.)
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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
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4.NF.A.2
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4.NF.B.3
Criteria for Success
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- Find common units for fractions with unlike denominators by finding equivalent fractions using a number line, an area model, or using multiplication or division.
- Understand that there is more than one possibility for the common unit used, and use that to optionally find the least common denominator.
- Assess the reasonableness of an answer using number sense and estimation (MP.1).
- 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.
- 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
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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).
Remote Learning Guidance
If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 3 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.
Anchor Tasks
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Problem 1
- Estimate the following sums.
a. $${{1\over3}+{1\over4}}$$
b. $${{1\over2}+{2\over3}}$$
- Solve for the actual sums in #1 above. Are your answers reasonable? Why or why not?
Guiding Questions
References
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
- Estimate whether the following sum will be more or less than 1. Then compute.
$$\frac{4}{5}+\frac{6}{7}$$
- What do you notice about your solution? What do you wonder?
Guiding Questions
Problem 3
- Estimate whether the following sums will be more or less than 1.
a. $$\frac{2}{3}+\frac{4}{5}$$
b. $$\frac{5}{12}+\frac{2}{3}$$
c. $$\frac{1}{6}+\frac{3}{8}$$
- Solve for the actual sums in #1 above. Are your answers reasonable? Why or why not?
Guiding Questions
References
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.Problem Set & Homework
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- Problem Set Answer Key
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- Homework Answer Key
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
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Problem 1
Solve. Show or explain your work.
$${{5\over6}+{1\over3}}$$
References
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
Solve. Show or explain your work.
Patrick drank $${{3\over4}}$$ liter of water Monday before jogging. He drank $${{4\over5}}$$ liter of water after his jog. How much water did Patrick drink altogether?
References
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.Mastery Response
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Additional Practice
Unit Practice
With Fishtank Plus you can access our Daily Word Problem Practice and our content-aligned Fluency Activities created to help students strengthen their application and fluency skills.
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