Curriculum  /  Math  /  3rd Grade  /  Unit 6: Fractions  /  Lesson 17

Fractions

Lesson 17

Math

Unit 6

3rd Grade

Lesson 17 of 24

Objective

Compare fractions with the same numerators by reasoning about the size of their units. 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. Compare fractions with the same numerator by using the understanding that when the denominator is larger, the pieces are smaller, and thus when comparing fractions with the same numerators, the fraction with a denominator that is high in value is less than a fraction with a denominator that is low in value (MP.2).
  2. Record the results of comparisons with the symbols >, =, or <.
  3. Justify comparisons of fractions with the same numerator using the reasoning above and/or using an area model or number line (MP.3, MP.5).
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Anchor Tasks

25-30 minutes

Problem 1

LaTonya has 2 equal-sized candy bars. She cut the first candy bar into fourths after lunch and eats three pieces. Later, she cut the second candy bar into sixths after dinner and eats three pieces. Did LaTonya eat the same amount of the first candy bar and second candy bar? If not, did she eat more of the first candy bar or the second one? Show or explain how you know.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 3 Mathematics > Module 5 > Topic F > Lesson 28 — Application Problem

Grade 3 Mathematics > Module 5 > Topic F > Lesson 28 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 2

a.   Who correctly compares the numbers $$\frac{2}{3}$$ and $$\frac{2}{5}$$?

i.  Ben said that $$\frac{2}{3}$$ is greater than $$\frac{2}{5}$$.

ii.  Lee said that $$\frac{2}{3}$$ is equal to $$\frac{2}{5}$$.

iii.  Mia said that $$\frac{2}{3}$$ is less than $$\frac{2}{5}$$.

b.   Compare $$\frac{2}{3}$$ and $$\frac{2}{5}$$ using symbols:

$$\frac{2}{3}$$ _____ $$\frac{2}{5}$$

c.   Choose the two pictures that best compare $$\frac{2}{3}$$ and $$\frac{2}{5}$$.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Fraction Comparisons with Pictures, Assessment Variation

Fraction Comparisons with Pictures, Assessment Variation, accessed on March 19, 2019, 11:11 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.

Problem 3

a.   Choose each statement that is true.

i.  $$\frac{9}{8}$$ is greater than $$\frac{9}{4}$$.

ii.  $$\frac{9}{4}$$ is greater than $$\frac{9}{8}$$.

iii.  $$\frac{9}{8}>\frac{9}{4}.$$

iv.  $$\frac{9}{8}<\frac{9}{4}.$$

v.  $$\frac{9}{4}>\frac{9}{8}$$.

vi.  $$\frac{9}{4}<\frac{9}{8}.$$

vii.  None of these.

b.   $$\frac{9}{8}$$ and $$\frac{9}{4} $$ are shown on the number line. Which is correct?

i. 

ii.

iii. Neither of these.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Comparing Fractions with the Same Numerators, Assessment Variation

Comparing Fractions with the Same Numerators, Assessment Variation, accessed on March 19, 2019, 11:12 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.

Problem Set

15-20 minutes

Discussion of Problem Set

  • If you only know the number of shaded parts, can you tell if fractions are equivalent? Why or why not?
  • Look at the models in #1─4. When comparing fractions, why is it so important that the wholes are the same size?
  • Tell a partner how you used the models in #1─4 to determine greater than, less than, or equal to.
  • Explain a general strategy for comparing fractions with the same numerators.

Target Task

5-10 minutes

Problem 1

Fill in the blank to make the statement true.

$$\frac{3}{4}>\frac{3}{\square}$$

Student Response

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Problem 2

a.   Compare $$5\over 6$$ and $$5\over 8$$. Use <, >, or = to record your comparison.

b.   Explain how you know your answer in Part A is correct. Draw a picture or a number line to support your reasoning.

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 denominators by reasoning about their number of units. Record the results of comparisons with the symbols >, =, or <.

Lesson 18
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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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