# Fraction Equivalence and Ordering

## 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.

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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.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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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.

#### 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 ${{13\over12}}$

### 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 ${{5\over7}}$

## 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?

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

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

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

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