Fraction Operations

Lesson 1

Math

Unit 5

4th Grade

Lesson 1 of 21

Objective


Decompose fractions as a sum of unit fractions and as a multiple of 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.
  • 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 unit fractions, recording the decomposition with an equation. 
  2. Understand that repeated addition expressions can be more efficiently represented using multiplication and use that understanding to transition from decompositions of fractions as a sum of unit fractions to a multiple of unit fractions. 
  3. Decompose a fraction less than or equal to 1 into a multiple of unit fractions, recording the decomposition with an equation. 
  4. Justify decompositions with a visual model, such as a tape diagram or number line. 

Tips for Teachers


  • Throughout the unit, students will rely on tape diagrams and number lines to represent fraction operations. They won’t be formally introduced to the use of an area model to perform these operations until Grade 5, where they are particularly useful for helping to find a common unit when the units are unrelated to one another (e.g., 5 and 7, where they share no common factors). However, if students naturally choose to represent these computations with an area model or gravitate toward them, their use should not be discouraged.
  • Before the Problem Set, you could have students play around with manipulatives to decompose fractions into a sum of unit fractions or non-unit fractions, similar to Joe Schwartz’s blog post “Building Towers”. Just make sure students are building fractions less than or equal to 1. If you don’t have fraction towers or even fraction tiles, you can create them from paper.
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Anchor Tasks

25-30 minutes


Problem 1

Lin is learning to make cookies using a family recipe. She has only one measuring cup that measures $$\frac1 4$$ cup. Show how Lin could use the cup to measure the amount of each ingredient below.

a.   $$\frac 3 4$$ 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, 10:23 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.

Problem 2

Decompose the fraction represented below into a sum of unit fractions and a multiple of that unit fraction. Record the decompositions with equations.

Guiding Questions

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Student Response

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Problem 3

Decompose the following fractions into a sum of unit fractions and a multiple of that unit fraction, recording each with an equation. 

a.   $$\frac{4}{5}$$

b.   $$\frac{3}{3}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • What is similar in Problems 2(c), 2(d), and 2(e)? What is different? 
  • Are you surprised to see multiplication equations with products less than 1? Why? 
  • How is multiplying fractions like multiplying whole numbers?

Target Task

5-10 minutes


Decompose the following fraction as a sum of unit fractions as well as a multiple of unit fractions. Record the decompositions with equations.

$$\frac69$$

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.

Before the Problem Set, you could have students play around with manipulatives to decompose fractions into a sum of unit fractions or non-unit fractions, similar to Joe Schwartz’s blog post “Building Towers”. Just make sure students are building fractions less than or equal to 1. If you don’t have fraction towers or even fraction tiles, you can create them from paper.

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.

Next

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

Lesson 2
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Lesson Map

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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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