Fraction Operations

Lesson 9

Math

Unit 5

4th Grade

Lesson 9 of 21

Objective


Convert fractions greater than 1 to mixed numbers.

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.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.

Criteria for Success


  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. 
  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, $$\frac{47}{6}=\frac{42}{6}+\frac{5}{6}=7+\frac{5}{6}=7\frac{5}{6}$$.

Tips for Teachers


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.

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Anchor Tasks


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 Fishtank Learning, 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)
$$=\frac{7}{1}+\frac{1}{5}$$ (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 Fishtank Learning, Inc.

Problem Set


Answer Keys

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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


Write each fraction as an equivalent mixed number.

a.   $${{11\over5}}$$

b.   $${{13\over4}}$$

c.   $${{16\over3}}$$

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.

Extra Practice Problems

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 8

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Lesson 10

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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