Addition and Subtraction of Fractions/Decimals

Lesson 7

Objective

Subtract fractions from fractions less than 2 with unlike denominators.

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 a number line, an area model, or 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. Subtract two fractions with unlike denominators that require regrouping whose whole is between 1 and 2, simplifying and writing the sum as a mixed number, if applicable.
  5. Solve one-step word problems involving the subtraction of two fractions with unlike denominators whose whole is less than 2 (MP.4).

Tips for Teachers

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For some problems in this lesson, students may use a computation-specific strategy. For example, students might think of a computation as an unknown-addend problem and use an addition strategy to solve (including the simplifying strategy of making a whole, e.g., to solve $$1\frac{3}{5}-\frac{7}{8}=1\frac{24}{40}-\frac{35}{40}$$, a student might add $$\frac{35}{40}+\frac{5}{40}=1$$ and $$1+\frac{24}{40}=1\frac{24}{40}$$, so the difference is $$\frac{5}{40}+\frac{24}{40}=\frac{29}{40}$$). Students might also use a simplifying strategy like going down over a whole (e.g., $$1\frac{24}{40}-\frac{24}{40}-\frac{11}{40}=1-\frac{11}{40}=\frac{29}{40}$$). 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).

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Anchor Tasks

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Problem 1

  1. Estimate the following differences. 

a. $$1\frac{2}{3}-\frac{1}{2}$$

b. $$1\frac{1}{2}-\frac{2}{3}$$

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

Guiding Questions

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Problem 2

  1. Estimate whether the following difference will be more or less than 1. Then compute.

$${1{4\over5}-{5\over6}}$$

  1. What do you notice about your solution? What do you wonder?

Guiding Questions

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Problem 3

  1. Estimate whether the following differences will be more or less than 1. 

a. $$1\frac{3}{5}-\frac{7}{8}$$

b. $$1\frac{2}{3}-\frac{5}{6}$$

c. $$1\frac{5}{8}-\frac{5}{12}$$

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

Guiding Questions

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Discussion of Problem Set

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  • Look at #2. I got $${{2\over6}}$$ as an answer, so I think none of the options are correct. Do you agree or disagree?
  • Look at #4b and #4d. What made these problems different from the rest? What strategy did you use to solve? 
  • Look at #5. How did you figure out how much orange juice Meiling has left? 
  • Look at #6. Is Lucy’s method correct? Can you use it to measure $${{1\over12}}$$ of a cup? What other measurements can you make?
  • Look at #7. What do you notice about the answer in comparison to the similar problem yesterday? Why is that? 

Target Task

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Problem 1

Solve. Show or explain your work. 

 $${1{1\over6}-{1\over4}}$$

Problem 2

Solve. Show or explain your work.

Tara baked $$1\frac{1}{2}$$ dozen cookies. She sold $$\frac{2}{3}$$ dozen of the cookies she made. How many dozens of cookies does Tara have remaining?

References

EngageNY New York State Testing Program Grade 5 Common Core Mathematics Test Released Questions June 2017Question #2

From EngageNY.org of the New York State Education Department. New York State Testing Program Grade 5 Common Core Mathematics Test Released Questions June 2017. Internet. Available from https://www.engageny.org/resource/released-2017-3-8-ela-and-mathematics-state-test-questions/file/150271; accessed Dec. 5, 2017, 3:55 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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