Fraction Equivalence and Ordering

Lesson 10

Objective

Compare two fractions using one whole as a benchmark.

Common Core Standards

Core Standards

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  • 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

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  • 3.NF.A.3.D

Criteria for Success

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

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Anchor Tasks

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Problem 1

Mr. and Mrs. Reynolds went for a run. Mr. Reynolds ran for $${{7\over8}}$$ mile. Mrs. Reynolds ran for $${{6\over5}}$$ mile. Who ran farther? Explain how you know.

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic C > Lesson 13Application Problem

Grade 4 Mathematics > Module 5 > Topic C > Lesson 13 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.

Problem 2

Compare the following fractions.

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

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

Guiding Questions

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Problem 3

Compare the following fractions.

a.     $${{9\over8}}$$ and $${{7\over6}}$$

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

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

d.     $${{9\over11}}$$ and $${{5\over7}}$$

Guiding Questions

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Problem Set & Homework

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

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

1.     $${{2\over3}}$$     _______________     $${{5\over4}}$$

2.     $${{4\over5}}$$      _______________    $${{5\over6}}$$

Mastery Response

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