Fraction Operations

Lesson 2

Math

Unit 5

4th Grade

Lesson 2 of 21

Objective


Decompose fractions as a sum of fractions with the same denominator in more than one way.

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.
  • 4.NF.B.4.A — Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

Foundational Standards

  • 3.NF.A.1
  • 3.NF.A.2

Criteria for Success


  1. Decompose a fraction less than or equal to 1 into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation. 
  2. Justify decompositions with a visual model, such as a tape diagram or number line.
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Anchor Tasks

25-30 minutes


Problem 1

Lin later found a $$\frac34$$-cup measuring cup. Show how she could use the $$\frac34$$ and $$\frac14$$ measuring cups to measure the right amount of each ingredient below.

a.   $$\frac34$$ cups sugar

b.   1 cup butter

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 4 Unit 3 Lesson 7 Activity 1

Grade 4 Unit 3 Lesson 7 Activity 1, accessed on March 17, 2022, 3:49 p.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

On each number line, draw two “jumps” to show how to use sixths to make a sum of $$\frac66$$. Then, write an equation to represent each combination of jumps.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Math Grade 4 Unit 3 Lesson 8 Activity 1"Sum of Jumps"

Math Grade 4 Unit 3 Lesson 8 Activity 1, accessed on March 18, 2022, 10:17 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 3

a.   Use different combinations of tenths to make a sum of $$\frac{9}{10}$$.

  1. $$\frac{9}{10}$$ = ___ + ___ + ___ + ___ + ___
  2. $$\frac{9}{10}$$ = ___ + ___ + ___ + ___
  3. $$\frac{9}{10}$$ = ___ + ___ + ___
  4. $$\frac{9}{10}$$ = ___ + ___

b.   Write different ways to use fifths to make a total of $$\frac 55$$. How many can you think of? Write an equation for each combination.

c.   Is it possible to write any fraction with a denominator of 8 as a sum of other eighths? Explain or show your reasoning.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 4 Unit 3 Lesson 7 Activity 2

Grade 4 Unit 3 Lesson 7 Activity 2, accessed on March 17, 2022, 3:56 p.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 Set

15-20 minutes


Discussion of Problem Set

  • How else could you have decomposed any of the number lines in #2? (You could choose to discuss specific parts based on what’s best for your students.)
  • Why does #3(a) start with “$${1 =}$$” as opposed to a fraction? What equivalent fraction could we use instead of $$1$$?
  • What other decompositions could have been possible answers in #4? 
  • In #5, how would you record the fraction’s decomposition into unit fractions? How can you draw parentheses around a certain number of unit fractions to model another decomposition you wrote (e.g., $$\left({1\over8}+{1\over8}\right)+\left({1\over8}+{1\over8}\right) + {1\over8}$$ to model $${2\over8}+{2\over8}+{1\over8}$$)? 
  • Did anyone write a multiplication equation for any part of #5? What is the equation?
  • What relationship does the unit fraction have with the number of units in a whole? 
  • How did you decompose numbers in earlier grades? How is that similar to and different from how you decomposed fractions today? 

Target Task

5-10 minutes


Decompose the following fraction in three different ways. Record the decompositions with equations.

$${{7\over8}}$$

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Next

Add and subtract fractions within 1 with the same units.

Lesson 3
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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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