# Fraction Equivalence and Ordering

## Objective

Compare two fractions using one half 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.

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• 3.NF.A.3.D

## Criteria for Success

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1. Compare one fraction to ${{{{{{{{{{{{1\over2}}}}}}}}}}}}$
2. Compare two fractions, one of which is less than ${{{{{{{{{{{{1\over2}}}}}}}}}}}}$ and the other of which is greater than ${{{{{{{{{{{{1\over2}}}}}}}}}}}}$, using ${{{{{{{{{{{{1\over2}}}}}}}}}}}}$ as a benchmark (MP.3).
3. Compare two fractions which are both either greater than or less than ${{{{{{{{{{{{1\over2}}}}}}}}}}}}$ by reasoning about their proximity to ${{{{{{{{{{{{1\over2}}}}}}}}}}}}$ (MP.3).
4. Use the correct symbol (<, >, =) to record a comparison.

## Tips for Teachers

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Lesson 9 and Lesson 10 are interchangeable. Lesson 10 may be easier to access for students, since determining whether a fraction is more or less than 1 is generally easier than determining whether a fraction is more or less than $\frac{1}{2}$, so you may decide to switch their order. However, Lesson 10 comes later in the sequence since it previews some work that students will see with fractions greater than 1 in Unit 6 and therefore having Lesson 10 build on Lesson 9 with increasing quantities mirrors a similar progression in Unit 6.

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## Anchor Tasks

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### Problem 1

Show students this Newsweek article, "More Than Half of Medical Advice on 'Dr. Oz' Lacks Proof or Contradicts Best Available Science: Study.

Display just the title, author, and image. Also provide them with this statement, "The research team looked at 80 pieces of medical advice from The Dr. Oz Show, and researchers found no evidence to support 43 of these recommendations."

Do you agree or disagree with the claim in the headline based on the information in the caption? Why or why not?

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic C > Lesson 12Concept Development

Grade 4 Mathematics > Module 5 > Topic C > Lesson 12 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 factions.

a.     ${{4\over10}}$ and ${{5\over8}}$

b.     ${{7\over12}}$ and ${{4\over9}}$

c.      ${{1\over3}}$ and ${{4\over7}}$

#### Guiding Questions

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### Problem 3

Compare the following fractions.

a.   $\frac{4}{6}$ and ${{5\over8}}$

b.   $\frac{5}{12}$ and ${{4\over10}}$

c.   ${{3\over5}}$ and ${{5\over9}}$

d.   ${{1\over3}}$ and ${{3\over7}}$

#### Guiding Questions

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## Problem Set & Homework

#### Discussion of Problem Set

• What did all of the problems in #1 have in common? How did that help with each comparison?
• Which fractions in #2 were greater than ${{{1\over2}}}$? How did you know? Are any of them greater than $1$?
• How did you solve in #3? Which ones were more difficult than others? Why?
• Look at #4. Why do you think this problem was included in today’s lesson?
• What fractions did you find for #5? Was there more than one correct answer?
• How did you solve in #6? Which ones were more difficult than others? Why?
• How did the number line help you to compare in #7c? Which fraction was closer to ${{{1\over2}}}$? How do you know?

## Target Task

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

1.      ${{3\over8}}$    ____________    ${{4\over5}}$

2.      ${{5\over8}}$    ____________    ${{7\over12}}$

### Mastery Response

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