Fractions

Lesson 23

Objective

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

Tips for Teachers

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A number line is a very useful representation to compare fractions, i.e., “given two fractions—thus two points on the number line—the one to the left is said to be smaller and the one to the right is said to be larger” (NF Progression, p. 9). Thus, while Lessons 21 and 22 included tasks related to all models they’ve encountered throughout the unit, Lesson 23’s tasks include contexts or explicit referral to length models (namely, tape diagrams and number lines) in preparation for Lesson 24’s deeper analysis of the benefit of a number line to compare fractions.

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Anchor Tasks

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Problem 1

For the class party, Robin and Shawn each made a loaf of banana bread. Their loaf pans were exactly the same size. Robin sliced her banana bread into 6 equal slices. Shawn also sliced his into 6 equal slices. After the party, Robin had more slices of banana bread left to take home than Shawn did. What fraction of the whole loaf pan might each person take home?

Guiding Questions

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References

San Francisco Unified School District Math Department 3.8 LS3 Day 3 Sharing Brownies Part II StudentSharing Brownies Part II

3.8 LS3 Day 3 Sharing Brownies Part II Student is made available by the San Fransisco Unified School District Math Department as a part of their SFUSD Math Core Curriculum under a CC BY 4.0 license. Accessed March 8, 2019, 4:42 p.m..

Modified by The Match Foundation, Inc.

Problem 2

  1. Choose each statement that is true.

i.  $$\frac{3}{4}$$ is greater than $$\frac{5}{4}$$.

ii.  $$\frac{5}{4}$$ is greater than $$\frac{3}{4}$$.

iii.  $$\frac{3}{4}>\frac{5}{4}.$$

iv.  $$\frac{3}{4}<\frac{5}{4}.$$

v.  $$\frac{5}{4}>\frac{3}{4}.$$

vi.  $$\frac{5}{4}<\frac{3}{4}.$$

vii.  None of these.

  1. $$\frac{3}{4}$$ and $$\frac{5}{4}$$ are shown on the number line. Which is correct?

i.

ii.

 

iii. Neither of these.

Guiding Questions

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References

Illustrative Mathematics Comparing Fractions with the Same Denominator, Assessment Variation

Comparing Fractions with the Same Denominator, Assessment Variation, accessed on March 19, 2019, 11:14 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 & Homework

Discussion of Problem Set

  • If you only know the number of parts, can you tell if fractions are equivalent? Why or why not?
  • In #1, where on the number line are the greater fractions compared to the lesser fractions? Do you think this relationship between a fraction’s size and its location on the number line is true of any pair of fractions? Why or why not?
  • What made the fractions in #2 different from the fractions in #1? Could you still use the same models to compare?
  • What made the fractions in #7 unique? What model did you use to compare them? Is one model more preferable to others? Why or why not?
  • Who was correct in #8? What was incorrect about Gabe’s drawing?
  • Explain a general strategy for comparing fractions with the same numerators.

Target Task

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Problem 1

Fill in the blank to make the statement true.

$$\frac{\square}{6}<\frac{5}{6}$$

Problem 2

Compare $$\frac{11}{8}$$ and $$\frac{7}{8}$$ using <, >, or =. Draw a model to show your thinking.

References

Achievement First Grade 3, Unit 5, Lesson 8 (2017-2018)Exit Ticket

Grade 3, Unit 5, Lesson 8 (2017-2018) is made available by Achievement First as a part of their Open Source web portal under a CC BY 4.0 license. Copyright © 1999-2017 Achievement First. Accessed March 8, 2019, 4:24 p.m..

Modified by The Match Foundation, Inc.

Mastery Response

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