Fraction Operations

Lesson 9

Objective

Convert fractions greater than 1 to mixed numbers.

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. Determine which two whole numbers a fraction greater than 1 lies between. 
  2. Convert from fractions greater than 1 to mixed numbers using a number line or other model. 
  3. Convert from fractions greater than 1 to mixed numbers using the general method involving the Grade 4.NBT skill of finding quotients and remainders. For example, $$\frac{47}{6}=\frac{(7\times6)+5}{6}=\frac{7\times6}{6}+\frac{5}{6}=7+\frac{5}{6}=7\frac{5}{6}$$(NF Progression, p. 13).

Tips for Teachers

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Before the Problem Set, you could have students play a game to practice converting fractions greater than one to mixed numbers, such as the "Converting Mixed Numbers Game: Pin the Fraction on the Number Line (whole-group version)” from Games with Fraction Strips and Fraction Cards on The Max Ray Blog.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

Ms. Giordano, a high school soccer coach, tells her players to run between $$3$$ and $$4$$ miles every week over the summer in preparation for the fall season. Kayla runs $${{1\over2}}$$ mile every day. Will Kayla run enough each week for Ms. Giordano? How do you know? 

Guiding Questions

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Problem 2

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

a.   $${{8\over3}}$$

b.   $${{15\over4}}$$

c.   $${{32\over6}}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic E > Lesson 24Concept Development

Grade 4 Mathematics > Module 5 > Topic E > Lesson 24 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

Alice wrote the fraction $${{36\over5}}$$ as a mixed number. Here is her work:

$$\frac{36}{5} = \frac{35}{5} + \frac{1}{5}$$ (Step 1)
$$=\left(7\times\frac{5}{5}\right)+\frac{1}{5}$$ (Step 2)
$${=7+{1\over5}}$$ (Step 3)
$${=7{1\over5}}$$ (Step 4)

Explain what Alice 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.

Problem Set & Homework

Discussion of Problem Set

  • What is $${{13\over5}}$$ written as a mixed number? How did the tape diagram in #1 help you figure that out? 
  • How can drawing a number line help you when converting a fraction to a mixed number? 
  • How was #3 related to today’s work? How is it related to the work we did with quotients and remainders? 
  • In #4, which fractions were the easiest for you to convert? Which were the most challenging? Why? 
  • What mistake did Rex make in #5? What is the correct equivalent fraction? How do you know?

Target Task

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

1.   $${{17\over5}}$$

2.   $${{19\over3}}$$

3.   $${{11\over4}}$$

References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic E > Lesson 24Exit Ticket

Grade 4 Mathematics > Module 5 > Topic E > Lesson 24 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.

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