Fractions

Lesson 21

Objective

Compare unit fractions (a unique case of fractions with the same numerators) by reasoning about the size of their units. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <.

Common Core Standards

Core Standards

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  • 3.NF.A.3.D — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Foundational Standards

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  • 2.MD.A.2

Criteria for Success

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  1. Understand that given a fraction, when its whole is partitioned into more and more parts, the fractional pieces decrease in size and thus pieces of a whole that is split up into more pieces will be smaller than pieces of a whole that is split up into fewer pieces (i.e., when the denominator is larger, the pieces are smaller) (MP.7, MP.8).
  2. Compare unit fractions by using the understanding that when the denominator is larger, the pieces are smaller, and thus a unit fraction with a denominator that is high in value is smaller than a unit fraction with a denominator that is low in value (MP.2).
  3. Record the results of comparisons with the symbols >, =, or <.
  4. Justify comparisons of unit fractions using the reasoning above and/or using an area model or number line (MP.3).
  5. Recognize that comparisons are valid only when the two fractions refer to the same whole (MP.6).

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Anchor Tasks

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Problem 1

Kiana bought two Fruit-by-the-Foot snacks to share with friends. She splits one of them into 3 equal-sized pieces and the other into 8 equal-sized pieces. If Kiana were sharing a piece of Fruit-by-the-Foot with you, which snack would you take a piece from, the 3-piece snack or the 8-piece snack? Explain why.

Guiding Questions

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Problem 2

  1. Mark and label the points $$\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, $$and $$\frac{1}{5} $$ on the number line. Be as exact as possible.

  1. What do you notice? What do you wonder?

Guiding Questions

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References

Illustrative Mathematics Locating Fractions Less than One on the Number LinePart (c)

Locating Fractions Less than One on the Number Line, accessed on March 19, 2019, 11:10 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 3

Bryce drew this picture:

Then he said,

This shows that $$\frac{\mathbf{1}}{\mathbf{4}}$$ is greater than $$\frac{\mathbf{1}}{\mathbf{2}}$$.

  1. What was his mistake? Draw a picture that shows why $$ \frac{1}{2}$$ is greater than $$\frac{1}{4}$$.
  2. Which of these comparisons of $$\frac{1}{4}$$ with $$ \frac{1}{2}$$ are true?

i.  $$\frac{1}{4}>\frac{1}{2}$$

ii.  $$\frac{1}{4}<\frac{1}{2}$$

iii.  $$\frac{1}{4}=\frac{1}{2}$$

iv.  $$\frac{1}{2}>\frac{1}{4}$$

v.  $$\frac{1}{2}<\frac{1}{4}$$

Guiding Questions

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References

Illustrative Mathematics Comparing Fractions with a Different Whole

Comparing Fractions with a Different Whole, accessed on March 28, 2018, 1:21 p.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 Set & Homework

Discussion of Problem Set

  • In #3, how could it be possible that Arnie ate more of his sandwich?
  • How did you decide where to place $$\frac{1}{2}$$ and $$\frac{1}{4}$$ on the number line in #4? Did your number line support or disprove Robert’s statement? Why?
  • What does area have to do with fractions in #6? How did you know the number of slices of pizza would result in pieces with the smallest area? How did you determine how many slices Casey’s pizza would have? How did you compare the slices?
  • What would it require to make Julian’s statement correct in #7?
  • Explain a general strategy for comparing unit fractions.

Target Task

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Problem 1

Use <, >, or = to compare.

a.  1 half _____ 1 third

b.  $$\frac{1}{8}$$ _____ $$\frac{1}{6}$$

Problem 2

Tatiana ate $$\frac{1}{3}$$ of a small carrot. Louis ate $$\frac{1}{4}$$ of a large carrot. Who ate more? Use words and pictures to explain your answer.

References

EngageNY Mathematics Grade 3 Mathematics > Module 5 > Topic C > Lesson 11Exit Ticket, Question #2

Grade 3 Mathematics > Module 5 > Topic C > Lesson 11 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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