# Standard 2: Order and compare fractions and identify equivalent fractions.

General Information
Number: MA.3.FR.2
Title: Order and compare fractions and identify equivalent fractions.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Fractions

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.3.FR.2.AP.1
Compare fractional numbers with the same denominator. Denominators are limited to 2, 3 and 4.
MA.3.FR.2.AP.2
Using a visual model, recognize fractions less than a whole that are equivalent to fractions with denominators of 2, 3 or 4 (e.g., is equivalent to ).

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

## Formative Assessments

Four Fourths:

Students are given a number line scaled by fourths and ask to label the notches.

Type: Formative Assessment

Generating Equivalent Fractions:

Students are given a familiar fraction and asked to generate an equivalent fraction justifying their reasoning.

Type: Formative Assessment

Comparing Fractions:

Students compare two pairs of fractions and record their comparisons using the less than or greater than symbols.

Type: Formative Assessment

The Cake Problem:

Students compare two fractional parts of two different wholes.

Type: Formative Assessment

Equivalent Fractions:

Students determine whether or not fractions are equivalent.

Type: Formative Assessment

Four-Sixths on the Number Line:

Students are asked to use a number line that includes the location of zero and one-sixth to find the location of four-sixths.

Type: Formative Assessment

One-Third on the Number Line:

Students are given four number line diagrams and asked to choose the one that correctly shows the location of one-third.

Type: Formative Assessment

Five-Eighths on the Number Line:

Students are asked to locate five-eighths on a number line that has been anchored by zero and one, but that has not yet been scaled.

Type: Formative Assessment

Three-Fourths on the Number Line:

Students are asked to scale a number line from zero to one so that they can find the location of three-fourths.

Type: Formative Assessment

## Image/Photograph

Clipart ETC Fractions:

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Type: Image/Photograph

## Lesson Plans

Fractions and Civics 3:

Students will conduct surveys, tally results, and represent the data on graphs. In this lesson, students will also represent data in fractions, equivalent fractions and learn how citizens demonstrate civility, cooperation, volunteerism and other civic virtues. Math and Civics are integrated in this lesson plan.

Type: Lesson Plan

Fraction Action!:

This lesson will help students understand that fractions are parts of a whole. The lesson introduces fractional parts using familiar manipulatives.

Type: Lesson Plan

Perfect Pool Plans:

In this Model Eliciting Activity, MEA, students will create a procedure for ranking pool construction companies based on the number of years in business, customer satisfaction, and available pool dimensions. In a “twist,” students will be given information about discounts available by each company. Students will evaluate their procedure for ranking and change it if necessary.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

The Pizza Exchange:

The students will receive paper pizzas that are divided into different fractional parts. They will decorate their pizza, and then make equal trades with classmates to explore equivalence of fractions.

Type: Lesson Plan

Would You Rather?:

This lesson is designed to help students generate rules for comparing fractions. The students will use fraction tiles to discover ways to compare fractions with the same denominator or fractions with the same numerator. They will also begin to use benchmark fractions to help make comparisons and complete inequalities.

Type: Lesson Plan

Would you rather have?:

Would you rather have 2/4 or 6/12 of a Hershey Chocolate Bar? The students will create a fraction tool kit from construction paper to investigate equivalent fractions using rectangular area models.

Type: Lesson Plan

Who has more? Using the size of the fractional part to compare.:

Students explore how they can compare fractions by considering the denominator. Students use real world examples to create models and demonstrate that the size of the piece decreases as the denominator increases.

Type: Lesson Plan

Interactive Fraction Number Lines:

In this lesson students make number lines out of sentence strips to plot, order, and compare fractions with the same denominators.

Type: Lesson Plan

Comparing Fractions:

In this lesson, students will demonstrate their understanding of comparing fractions with the same denominator through engaging problem solving. Students will plot fractions on a numberline, play fraction war and complete a worksheet.

Type: Lesson Plan

Comparing Fractions with Brownies:

Students will demonstrate their understanding of comparing fractions with the same numerator through engaging problem solving using real-world application with brownies as a model. Students will be actively engaged in a fraction war game and "would you rather have" statements to solidify their understanding of comparing fractions with the same numerator.

Type: Lesson Plan

Fractions on a Number line:

In this lesson, students will place fractions on a number line and identify equivalent fractions. Students will explain the definition of equivalent fractions.

Type: Lesson Plan

Equivalent Fractions: It Means the Same:

In this lesson, students will use fold papers to create models to represent equivalent fractions. They will be able to identify representations of equivalence.

Type: Lesson Plan

Comparing and Placing Unit Fractions on a Number Line:

In this lesson, 3rd grade students will compare fractions which have the same numerator and explain their reasoning. The students will be able to compare the fractions by correctly placing them on a number line.

Type: Lesson Plan

Magnified Inches:

This lesson provides a parallel between fraction strips (something students should be familiar with) and measuring length with a ruler past one inch including quarters. This lesson is the follow-up to The Magnified Inch, Resource ID 46593.

Type: Lesson Plan

The Fraction String:

In this lesson students create a model of a number line using string and adding machine tape. Students discover how to partition the string into equal sections, and name the fractional pieces, including fractions greater than 1.

Type: Lesson Plan

The Magnified Inch:

This lesson provides a parallel between fraction strips (something students should be familiar with) and measuring with a ruler up to an inch including quarters.

Type: Lesson Plan

## Original Student Tutorials

Fraction Camp! Fractions Greater Than 1 on a Number Line:

Joey uses his knowledge of fractions to win games at camp by knowing where fractions greater than one are located on number lines, in this interactive tutorial.

Type: Original Student Tutorial

Nature Walk: Fractions Less Than 1 on a Number Line:

Learn to use number lines to represent fractions as Emmy explores nature in this interactive tutorial.

Type: Original Student Tutorial

Finding Fractions at Camp: Fractions on a Number Line:

Joey learns about the location of unit fractions on a number line while at camp in this interactive tutorial.

Type: Original Student Tutorial

Lesson 22 Video: MEA Animal Meal Planning Part 2:

In this video, SaM-1 introduces a part 2 twist to the Model Eliciting Activity (MEA). In the optional twist, students will need to modify their original diet for a senior chimpanzee. The first video provided meal planning information to add to the knowledge students gained throughout the unit to start the challenge.

Type: Original Student Tutorial

Lesson 22 Video: MEA Animal Meal Planning:

In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides meal planning information to add to the knowledge students gained throughout the unit. Students will be asked to develop a varied diet for a chimpanzee at the CPALMS Rehabilitation and Conservation Center based on the color, shape, texture, and hardness of the food.

In the optional twist, students will need to modify their original diet for a senior chimpanzee. The optional twist also has a SaM-1 video to introduce the twist challenge.

Type: Original Student Tutorial

Equal Fractions in Disguise:

Learn how different-sized fractional parts can represent the same amount of a whole, different-sized fractional parts in different orientations can represent the same amount of a whole, and a number line can be used to represent fractional parts of a whole in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Teaching Idea

Exploring Fractions with Pattern Blocks:

Unlock an effective teaching strategy for using pattern blocks to explore fraction concepts in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Comparing Fractions with a Different Whole:

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Comparing Fractions:

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Closest to 1/2:

How students tackle the problem and the amount of work they show on the number line can provide insight into the sophistication of their thinking. As students partition the interval between 0 and 1 into eighths, they will need to recognize that 1/2=4/8. Students who systematically plot every point, even 9/8, which is larger even than 1 may still be coming to grips with the relative size of fractions.

Locating Fractions Greater than One on the Number Line:

The goal of this task is to help students gain a better understanding of fractions and their place on the number line.

Jon and Charlie's Run:

The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.

Find 2/3:

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

Find 1:

This task includes the seeds of several important ideas. Part a presents the student with the opportunity to use a unit fraction to find 1 on the number line. Part b helps reinforce the notion that when a fraction has a numerator that is larger than the denominator, it has a value greater than 1 on the number line.

Ordering Fractions:

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

Locating Fractions Less than One on the Number Line:

In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).

## Virtual Manipulative

Fraction Game:

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

## Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

## Original Student Tutorials

Fraction Camp! Fractions Greater Than 1 on a Number Line:

Joey uses his knowledge of fractions to win games at camp by knowing where fractions greater than one are located on number lines, in this interactive tutorial.

Type: Original Student Tutorial

Nature Walk: Fractions Less Than 1 on a Number Line:

Learn to use number lines to represent fractions as Emmy explores nature in this interactive tutorial.

Type: Original Student Tutorial

Finding Fractions at Camp: Fractions on a Number Line:

Joey learns about the location of unit fractions on a number line while at camp in this interactive tutorial.

Type: Original Student Tutorial

Lesson 22 Video: MEA Animal Meal Planning Part 2:

In this video, SaM-1 introduces a part 2 twist to the Model Eliciting Activity (MEA). In the optional twist, students will need to modify their original diet for a senior chimpanzee. The first video provided meal planning information to add to the knowledge students gained throughout the unit to start the challenge.

Type: Original Student Tutorial

Lesson 22 Video: MEA Animal Meal Planning:

In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides meal planning information to add to the knowledge students gained throughout the unit. Students will be asked to develop a varied diet for a chimpanzee at the CPALMS Rehabilitation and Conservation Center based on the color, shape, texture, and hardness of the food.

In the optional twist, students will need to modify their original diet for a senior chimpanzee. The optional twist also has a SaM-1 video to introduce the twist challenge.

Type: Original Student Tutorial

Equal Fractions in Disguise:

Learn how different-sized fractional parts can represent the same amount of a whole, different-sized fractional parts in different orientations can represent the same amount of a whole, and a number line can be used to represent fractional parts of a whole in this interactive tutorial.

Type: Original Student Tutorial

Comparing Fractions with a Different Whole:

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Comparing Fractions:

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Closest to 1/2:

How students tackle the problem and the amount of work they show on the number line can provide insight into the sophistication of their thinking. As students partition the interval between 0 and 1 into eighths, they will need to recognize that 1/2=4/8. Students who systematically plot every point, even 9/8, which is larger even than 1 may still be coming to grips with the relative size of fractions.

Locating Fractions Greater than One on the Number Line:

The goal of this task is to help students gain a better understanding of fractions and their place on the number line.

Jon and Charlie's Run:

The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.

Find 2/3:

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

Find 1:

This task includes the seeds of several important ideas. Part a presents the student with the opportunity to use a unit fraction to find 1 on the number line. Part b helps reinforce the notion that when a fraction has a numerator that is larger than the denominator, it has a value greater than 1 on the number line.

Ordering Fractions:

The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.

Locating Fractions Less than One on the Number Line:

In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s).

## Virtual Manipulative

Fraction Game:

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

## Image/Photograph

Clipart ETC Fractions:

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Type: Image/Photograph

Comparing Fractions with a Different Whole:

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions.

Comparing Fractions:

The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

Closest to 1/2:

How students tackle the problem and the amount of work they show on the number line can provide insight into the sophistication of their thinking. As students partition the interval between 0 and 1 into eighths, they will need to recognize that 1/2=4/8. Students who systematically plot every point, even 9/8, which is larger even than 1 may still be coming to grips with the relative size of fractions.

Locating Fractions Greater than One on the Number Line:

The goal of this task is to help students gain a better understanding of fractions and their place on the number line.

Jon and Charlie's Run:

The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.

Find 2/3:

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

Find 1:

This task includes the seeds of several important ideas. Part a presents the student with the opportunity to use a unit fraction to find 1 on the number line. Part b helps reinforce the notion that when a fraction has a numerator that is larger than the denominator, it has a value greater than 1 on the number line.