Fraction Operations

Lesson 10

Objective

Convert mixed numbers to fractions greater than 1.

Materials and Resources

Common Core Standards

Core Standards

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  • 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.3.C — Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

  • 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).

Criteria for Success

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  1. Convert from fractions greater than 1 to mixed numbers using a number line or other model. 
  2. Convert from fractions greater than 1 to mixed numbers using the general method, i.e., "by representing the whole number as an equivalent fraction, e.g., $$7\frac{1}{5}=7+\frac{1}{5}=\frac{35}{5}+\frac{1}{5}=\frac{36}{5}$$" (NF Progression, p. 12).

Tips for Teachers

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Before the Problem Set, you could have students play a game to practice converting mixed numbers to fractions greater than 1, such as “Jump Around” or “Sealed Bids" from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.

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Anchor Tasks

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Problem 1

Mrs. Fowler knew that the perimeter of the soccer field was $${{1\over6}}$$ mile. She walked $$2{{{1\over6}}}$$ miles in total. How many times did she walk around the field? Show or explain your work.

Guiding Questions

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Problem 2

Convert the following mixed numbers to fractions greater than 1. Show or explain your work. 

a.   $${3{1\over2}}$$

b.   $${4{1\over4}}$$

c.   $${5{3\over5}}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic E > Lesson 25Concept Development

Grade 4 Mathematics > Module 5 > Topic E > Lesson 25 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.

Problem 3

Ben wrote a mixed number as a fraction $${7{1\over3}}$$. Here is his work:

$$7\frac{1}{3}= 7 + \frac{1}{3}$$ (Step 1)
$$=\left(7\times\frac{3}{3}\right)+\frac{1}{3}$$ (Step 2)
$$=\frac{21}{3}+\frac{1}{3}$$ (Step 3)
$${={22\over3}}$$ (Step 4)

Explain what Ben did in each step.

Guiding Questions

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References

Illustrative Mathematics Writing a Mixed Number as an Equivalent Fraction

Writing a Mixed Number as an Equivalent Fraction, accessed on July 18, 2018, 9:50 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 The Match Foundation, Inc.

Discussion of Problem Set

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  • Did you use the same strategies or different strategies to solve throughout the Problem Set? 
  • How was the work from previous lessons helpful in converting from a mixed number to a fraction greater than 1? 
  • How does the number line help to show the conversion from a mixed number to a fraction greater than 1? 
  • How was #3 related to today’s work? 
  • What mistake did Simone make in #5? What is the correct equivalent fraction? How do you know?

Target Task

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Convert each mixed number to a fraction greater than 1. Show or explain your work.

1.   $${3{1\over4}}$$

2.   $${2{3\over5}}$$

3.   $${4{2\over9}}$$

References

Mastery Response

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