Addition and Subtraction of Fractions/Decimals

Lesson 7

Math

Unit 4

5th Grade

Lesson 7 of 15

Objective


Subtract fractions from fractions less than 2 with unlike denominators.

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 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


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 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 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


Problem 1

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

  1. $$1\frac{2}{3}-\frac{1}{2}$$
  2. $$1\frac{1}{2}-\frac{2}{3}$$

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

Guiding Questions

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Problem 2

a.   Here is Anita’s strategy for finding the value of $$1\frac{1}{4} -\frac{5}{6}$$: “I know 4 × 6 is a common denominator so I’ll use that.” Does Anita’s strategy for finding a common denominator work? Explain or show your thinking and then find the value of $$1\frac{1}{4} -\frac{5}{6}$$.

b.   Estimate the following differences. Then compute using any strategy. 

  1. $$1\frac{3}{5} - \frac{7}{8}$$
  2. $$1\frac{1}{9}-\frac{2}{3}$$
  3. $$1\frac{5}{8}-\frac{7}{12}$$

Guiding Questions

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Problem 3

Karla makes a vegetable stew. She adds an extra $$\frac{3}{4}$$ servings of vegetables to the recipe so that it has a total of $$1\frac{2}{3}$$ servings of vegetables. How many servings of vegetables did the recipe have before Karla added more? 

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • 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


Problem 1

Solve. Show or explain your work. 

$${1{1\over6}-{1\over4}}$$

Problem 2

Rene baked $$1\tfrac{1}{2}$$ dozen cookies, $$\tfrac{2}{3}$$ dozen of which are chocolate chip and the rest are oatmeal raisin. How many dozens of cookies are oatmeal raisin?

Student Response

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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.

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 6

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Lesson 8

Lesson Map

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

Topic A: Addition and Subtraction of Fractions

Topic B: Addition and Subtraction of Decimals

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