Fraction Operations

Lesson 2

Objective

Decompose non-unit fractions and represent them as a whole number times a unit fraction.

Materials and Resources

Common Core Standards

Core Standards

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  • 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

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  • 3.NF.A.1

  • 3.NF.A.2

Criteria for Success

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  1. 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. 
  2. Decompose a fraction less than or equal to 1 into a multiple of unit fractions, recording the decomposition with an equation. 
  3. Justify decompositions with a visual model, such as a tape diagram or number line.

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Anchor Tasks

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Problem 1

1. Use the first equation below to fill in the blanks for the second equation.

a.   $${2+2+2+2+2=5}$$ groups of $$2$$

b.   $${{1\over4}+{1\over4}+{1\over4}=}$$ ____ groups of ____

2. Replace the right side of the equations above with a numerical expression.

Guiding Questions

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Problem 2

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

Guiding Questions

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Problem 3

Decompose the following fractions into a multiple of unit fractions. Write an equation to record your decomposition.

a.   $${{4\over5}}$$

b.   $${{12\over12}}$$

Guiding Questions

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Discussion of Problem Set

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  • What is an advantage to representing the fractions using multiplication? 
  • What is similar in Problems 3(c), 3(d), and 3(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

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

$${{6\over9}}$$

References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic A > Lesson 3Exit Ticket

Grade 4 Mathematics > Module 5 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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