Curriculum  /  Math  /  4th Grade  /  Unit 4: Fraction Equivalence and Ordering  /  Lesson 13

Fraction Equivalence and Ordering

Lesson 13

Math

Unit 4

4th Grade

Lesson 13 of 15

Objective

Compare two fractions using one whole as a benchmark.

Common Core Standards

Core Standards

  • 4.NF.A.2 — Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Foundational Standards

  • 3.NF.A.3.D

Criteria for Success

  1. Compare fractions to 1.
  2. Understand a benchmark fraction to be a common fraction.
  3. Compare two fractions, one of which is less than a whole and the other of which is greater than a whole, using one as a benchmark (MP.3).
  4. Compare two fractions that are both either greater than or less than a whole by reasoning about their proximity to one (MP.3).
  5. Use the correct symbol (<, >, =) to record a comparison.
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Anchor Tasks

25-30 minutes

Problem 1

For each diagram:

  1. Name a fraction the point represents.
  2. Is that fraction greater than or less than 1?
  3. How far is it from 1?

 

a.   

b.   

c.   

Guiding Questions

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Student Response

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References

Illustrative Mathematics Grade 4 > Unit 2 > Lesson 6 > Activity 1

Grade 4 > Unit 2 > Lesson 6 > Activity 1, accessed on Feb. 18, 2022, 9:43 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 2

a.   Ishmael says he knows $$\frac65$$ is greater than $$\frac78$$ because $$\frac65 \gt 1$$ and $$\frac78 \lt 1$$. Do you agree or disagree? Use the number lines from Anchor Task 1 to support your answer.

b.   Use Ishmael’s strategy to compare the following fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

  1. $${{5\over3}}$$ and $${{9\over10}}$$

  2. $${{4\over5}}$$ and $${{13\over12}}$$

Guiding Questions

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Student Response

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Problem 3

a.   Now Joslyn is comparing $$\frac65$$ and $$\frac43$$. She says that she knows $$\frac65$$ is less than $$\frac43$$ because $$\frac65$$ is $$\frac15$$ more than 1 and $$\frac43$$ is $$\frac13$$ more than 1 and $$\frac13$$ is more than $$\frac15$$. Do you agree or disagree? Use the number lines from Anchor Task 1 to support your answer.

b.   Use any strategy to compare the following fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

  1. $${{3\over4}}$$ and $${{9\over10}}$$

  2. $${{7\over5}}$$ and $${{11\over9}}$$

  3. $${{8\over11}}$$ and $${{13\over16}}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Which containers have enough soda in them to make the punch in #2? How could you tell? 
  • How did you compare the fractions in #3?
  • Who ran the shortest distance in #4? How do you know? 
  • What fraction did you come up with that is close to one? Did anyone else come up with a fraction that is close? Which one is closer? How do you know? Are there possible fractions that are even closer?

Target Task

5-10 minutes

Compare the following fractions by writing <, >, or = in the blank.

a.   $${{2\over3}}$$  _____  $${{5\over4}}$$

b.   $${{4\over5}}$$  _____  $${{5\over6}}$$

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 two fractions using one half as a benchmark.

Lesson 14
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Lesson Map

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

Topic A: Factors and Multiples

Topic B: Equivalent Fractions

Topic C: Comparing and Ordering Fractions

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