Fraction Operations

Lesson 8

Math

Unit 5

4th Grade

Lesson 8 of 21

Objective


Decompose and compose non-unit fractions greater than two as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction. 

Common Core Standards


Core Standards

  • 4.NF.B.3.B — Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Foundational Standards

  • 3.NF.A.1
  • 3.NF.A.2

Criteria for Success


  1. Decompose a fraction greater than 2 written as a mixed number or a fraction into a sum of unit fractions, recording the decomposition with an equation. 
  2. Decompose a fraction greater than 2 written as a mixed number or a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation. 
  3. Decompose a fraction greater than 2 written as a mixed number or a fraction into a multiple of unit fractions, recording the decomposition with an equation. 
  4. Compose a fraction written as a sum of unit fractions, as a sum of non-unit fractions with the same denominator, or as a multiple of a unit fraction.
  5. Use decompositions of fractions as a sum of unit fractions or a multiple of a unit fraction to understand the equivalence between a mixed number and a fraction greater than 1. 
  6. Justify decompositions and compositions with a visual model, such as a tape diagram or number line.
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Anchor Tasks


Problem 1

There are a few more ingredients in Lin’s family recipe for cookies, listed below. Write an addition equation and a multiplication equation to show how she can use the $$\frac14$$-cup measure to measure the amount of each ingredient below.

a.   $$\frac94$$ cups chocolate chips

b.   $$2\frac34$$ cup flour

Guiding Questions

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References

Illustrative Mathematics Grade 4 Unit 3 Lesson 7 Activity 1"Barley Soup"

Grade 4 Unit 3 Lesson 7 Activity 1 ("Activity 1: Barley Soup"), accessed on March 18, 2022, 10:07 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

Decompose each of the following fractions as a sum of unit fractions, a multiple of a unit fraction, and a sum of non-unit fractions. 

a.   $${{8\over2}}$$

b.   $$3\frac{1}{4}$$

c.   $${{12\over5}}$$

Guiding Questions

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Problem 3

Compose each of the following expressions.

a.   $${{1\over3}+{1\over3}+{1\over3}+{1\over3}+{1\over3}+{1\over3}}$$

b.   $${{3\over5}+{2\over5}+{6\over5}}$$

c.   $$12\times\frac{1}{4}$$

d.   $$9\times\frac{1}{2}$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Which equations were incorrect in #1? How did you change those equations to make them correct? 
  • How is your work in #1(a) related to your work in #4(c)? How is adding like unit fractions related to multiplying unit fractions? 
  • Look at #2 and #4. Is there a way to tell when the product will be a whole number before multiplying? Explain your thinking. 

Target Task


Problem 1

Decompose the following fractions as a sum of unit fractions and a multiple of a unit fraction.

a.   $${{10\over2}}$$

b.   $${2{3\over4}}$$

Student Response

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Problem 2

Compose the following fractions. 

a.   $${{1\over3}+{1\over3}+{1\over3}+{1\over3}+{1\over3}+{1\over3}+{1\over3}+{1\over3}+{1\over3}}$$

b.   $${18\times{1\over5}}$$

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

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

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Lesson 7

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Lesson 9

Lesson Map

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

Topic A: Building, Adding, and Subtracting Fractions Less Than or Equal to 1

Topic B: Building, Adding, and Subtracting Fractions Less Than 2

Topic C: Building, Adding, and Subtracting Fractions Greater Than or Equal to 2

Topic D: Multiplication of Fractions

Topic E: Line Plots

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