# Fraction Equivalence and Ordering

## Objective

Compare and order fractions using various strategies.

## Common Core Standards

### Core Standards

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• 4.NF.A — Extend understanding of fraction equivalence and ordering.

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• 3.NF.A.3

## Criteria for Success

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1. Order a set of fractions using various strategies by comparing two fractions in the set at a time.
2. Choose the strategy that would be most efficient to compare two fractions (MP.3, MP.5).
3. Use the correct symbol (<, >, =) to record a comparison.

## Tips for Teachers

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Lesson 11 is intended to address the cluster level expectations for 4.NF.A, including, “ordering…fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100."

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Would you rather have ${{4\over9}}$${{2\over3}}$${{5\over7}}$, or ${{3\over4}}$ of your favorite pie? Show or explain your reasoning.

### Problem 2

This activity is designed for pairs of students. It uses a set of cards (use Fraction Cards). Instructions for the activity are as follows:

1. Deal out the cards evenly so that each person has half of the deck. Each person should place their stack face down in front of them.
2. Each player turns up a card at the same time.
1. The player with the greater fraction takes both cards and puts them on the bottom of their stack of cards. Students can use any method to compare them. If they disagree, they should discuss until reaching a consensus, drawing a model if necessary.
2. If the fractions are equivalent, then each person deals three cards facedown and turns the fourth one face up to compare. The person with the larger second fraction takes all of the cards that have been dealt out. If the fractions are again equivalent, then another three are dealt facedown and the fourth face up to be compared. (This can continue as long as it needs to.)
3. The game is over when one player has all of the cards.

#### References

Illustrative Mathematics Comparing Fractions using Benchmarks Game

Comparing Fractions using Benchmarks Game, accessed on March 23, 2018, 11:22 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 The Match Foundation, Inc.

## Problem Set & Homework

#### Discussion of Problem Set

• Look at #1 & #4. How did you decide which strategy to use to compare the fractions? What were some things you looked for before deciding on a strategy?
• How did you order the fractions in #3? How did you go about doing so?
• Look at #6. Do you agree with Melissa’s reasoning? How is it different from some of the strategies we’ve used in previous lessons? How is it similar?
• Look at #7. How did you figure out what the numerators could be?

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Order the following fractions from smallest to largest:

${{3\over8},{1\over3},{5\over9},{2\over5}}$