# Fraction Equivalence and Ordering

## Objective

Compare two fractions with related numerators or related denominators by finding common units or number of units.

## 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 two fractions with the same numerators or denominators using visual models (MP.3, MP.5).
2. Understand that fractions are said to have a common numerator when they have the same number of units. Fractions are said to have a common denominator when they have the same sized units.
3. Compare two fractions where one numerator is a factor of the other numerator by replacing one fraction with an equivalent one to compare them with like numerators (MP.3).
4. Compare two fractions where one denominator is a factor of the other denominator by replacing one fraction with an equivalent one to compare them with like denominators (MP.3).
5. Use the correct symbol (< , >, =) to record a comparison.
6. Understand that comparisons are valid only when the two fractions refer to the same whole.

## Tips for Teachers

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• The supporting work of gaining familiarity with factors and multiples (4.OA.4) supports this major work of comparing fractions with related numerators or denominators by finding common units or number of units, since students must recognize that the fractions’ numerators or denominators share a common factor to be able to utilize this strategy.
• As mentioned in Lesson 1, there are no problems in this Problem Set, or any hereafter, that are related to the idea that “comparisons are valid only when the two fractions refer to the same whole” (4.NF.2). This is because this is also part of the third-grade expectations regarding fraction equivalence and comparison, so students should have mastered this idea already. However, if they would benefit from some additional practice, a list of potential resources can be found in the Tips for Teachers for Lesson 1.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Below are measurements of ribbon in feet. For each pair of ribbons, determine which one is longer. Show or explain how you know.

a.     ${{3\over4}}$ ft. and ${{1\over4}}$ ft.

b.    ${{5\over12}}$ ft. and ${{5\over6}}$ ft.

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic C > Lesson 14Concept Development

Grade 4 Mathematics > Module 5 > Topic C > Lesson 14 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.
North Carolina Department of Public Instruction 5.NF TasksComparing Fractions

5.NF Tasks from the 3-5 Formative Instructional and Assessment Tasks for the Standards in Mathematics, made available by the North Carolina Department of Public Instruction (NCDPI) Elementary Mathematics Consultants and their public school partners under the CC BY-NC-SA 3.0 license. Accessed Feb. 8, 2018, 12:51 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Compare the following fractions.

a.       ${{2\over3}}$ and ${{7\over9}}$

b.      ${{7\over10}}$ and ${{3\over5}}$

### Problem 3

Compare the following fractions.

a.     ${{9\over10}}$ and ${{3\over8}}$

b.      ${{2\over3}}$ and ${{4\over5}}$

## Problem Set & Homework

#### Discussion of Problem Set

• How did the tape diagrams help you to determine which statements were true in #1?
• What values did you choose to support Phil’s claim? What about to show that it’s not always true? Was there more than one correct choice for either or both parts?
• #4a, 4d, and 4f can be compared using different types of reasoning. Explain the reasoning you used for each.
• How did you determine whether the first comparison in #5 was true or false?
• How can you determine whether you can make common numerators or common denominators when comparing fractions?

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

1.     ${{2\over5}}$      ________________     ${{3\over10}}$

2.     ${{4\over3}}$      ________________    ${{12\over10}}$

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic C > Lesson 14Exit Ticket, Question #1

Grade 4 Mathematics > Module 5 > Topic C > Lesson 14 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.

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