Curriculum  /  Math  /  3rd Grade  /  Unit 6: Fractions  /  Lesson 16

Fractions

Lesson 16

Math

Unit 6

3rd Grade

Lesson 16 of 24

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

  • 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

  • 2.MD.A.2

Criteria for Success

  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 partitioned into more pieces will be smaller than pieces of a whole that is partitioned 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 less 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

25-30 minutes

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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Student Response

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Problem 2

a.   Locate and label the points $$\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, $$ and $$\frac{1}{5} $$ on the number line. You can use more than one number line if you wish.

b.   What do you notice? What do you wonder?

Guiding Questions

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Student Response

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References

Illustrative Mathematics Locating Fractions Less than One on the Number Line — Part (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 Fishtank Learning, Inc.

Problem 3

Bryce drew this picture:

Then he said,

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

a.   What was his mistake? Draw a picture that shows why $$ \frac{1}{2}$$ is greater than $$\frac{1}{4}$$.

b.   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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Student Response

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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

15-20 minutes

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

5-10 minutes

Problem 1

Use <, >, or = to compare.

a.   1 half _____ 1 third

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

Student Response

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Problem 2

Annie drank $$1\over 3$$ of a small juice. Enrique drank $$1\over 4$$ of a large juice. Who drank more? Explain your answer in words or pictures. 

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.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Compare fractions with the same numerators by reasoning about the size of their units. Record the results of comparisons with the symbols >, =, or <.

Lesson 17
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Unit Fractions and Building Non-Unit Fractions

Topic B: Fractions on a Number Line

Topic C: Equivalent Fractions

Topic D: Comparing Fractions

Topic E: Line Plots

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