MA.4.FR.1.4

Plot, order and compare fractions, including mixed numbers and fractions greater than one, with different numerators and different denominators.

Examples

begin mathsize 12px style 1 2 over 3 greater than 1 1 fourth end style because begin mathsize 12px style 2 over 3 end style is greater than begin mathsize 12px style 1 half end style and begin mathsize 12px style 1 half end style is greater than begin mathsize 12px style 1 fourth end style.

Clarifications

Clarification 1: When comparing fractions, instruction includes using an appropriately scaled number line and using reasoning about their size.

Clarification 2: Instruction includes using benchmark quantities, such as 0, begin mathsize 12px style 1 fourth end style, begin mathsize 12px style 1 half end style, begin mathsize 12px style 3 over 4 end style and 1, to compare fractions.

Clarification 3: Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.

Clarification 4: Within this benchmark, the expectation is to use symbols (<, > or =).

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Strand: Fractions
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.FR.1.AP.4a: Explore mixed numbers and fractions greater than one.
MA.4.FR.1.AP.4b: Using visual models, compare fractions less than one with different numerators and different denominators. Denominators limited to 2, 3, 4, 6, 8 or 10.

Related Resources

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

Educational Games

Flower Power: An Ordering of Rational Numbers Game:


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Type: Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Formative Assessments

Corn Farms:

Students compare two fractions with unlike denominators in the context of a word problem and record the comparison using an inequality symbol.

Type: Formative Assessment

Comparing Fractions Using Benchmark Fractions:

Students compare two fractions using benchmark fractions on a number line and record the comparison using the less than or greater than symbol.

Type: Formative Assessment

Comparing Four-Fifths and Three-Fourths:

Students consider the correctness of a model for comparing four-fifths to three-fourths.

Type: Formative Assessment

Compare Fractions:

Students are given three sets of fractions to compare and are asked to record the comparisons using the less than, greater than, or equal to symbols.

Type: Formative Assessment

Lesson Plans

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

Type: Lesson Plan

Fractions: Let's Compare:

The lesson is an application and extension of fraction comparison strategies, not an introduction.  While the beginning of the lesson has a review, the situational stories require students to read and analyze carefully.

Type: Lesson Plan

Wondrous Water Parks:

This activity requires students to apply their knowledge of unit conversions, speed calculation, and comparing fractions to solve the problem of which water park their class should choose to go on for their 5th grade class trip.

Type: Lesson Plan

Out of Order?:

This lesson is a way for students to use benchmark fractions to get a conceptual understanding of comparing and ordering fractions.

Type: Lesson Plan

Fraction Line-up!:

Students will model and compare fraction pairs by writing an inequality.  

Type: Lesson Plan

Gettin' Fancy with Fractions:

In this lesson, students engage in problem solving, a fraction sort activity and play the game "Fraction War" to practice and demonstrate understanding of using benchmark quantities when comparing fractions with different numerators and denominators.  This lesson is not intended as initial instruction on using benchmark quantities to compare fractions.  Instead, it may be useful for skill reinforcement, student engagement, and formative assessment of skill mastery.  Parts of this lesson could be revisited periodically as students build comfort and mastery comparing fractions.

Type: Lesson Plan

Looking for Patterns in a Sequence of Fractions:

Students generate and describe a numerical pattern using the multiplication and subtraction of fractions.

Type: Lesson Plan

Ordering Fractions:

Students work in groups to arrange sets of fraction cards from least to greatest using multiple strategies.  Fractions include those greater than one.

Type: Lesson Plan

Original Student Tutorials

Comparing Fractions with Square Foot Gardens Part 2:

Use equivalent fractions to compare fractions in this garden-themed, interactive tutorials

This is Part 2 in a two-part series. Click to open Part 1,  “Mama’s Pizza, Butterflies, & Comparing Fractions.”

Type: Original Student Tutorial

Mama's Pizza, Butterflies, and Comparing Fractions Part 1:

Help a family settle an argument about who got the most pizza and which butterfly was longer by comparing fractions using benchmarks and area models, in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Listing fractions in increasing size:

The fractions for this task have been carefully chosen to encourage and reward different methods of comparison. The first solution judiciously uses each of the following strategies when appropriate: comparing to benchmark fractions, finding a common denominator, finding a common numerator. The second and third solution shown use only either common denominators or numerators. Teachers should encourage multiple approaches to solving the problem. This task is mostly intended for instructional purposes, although it has value as a formative assessment item as well.

Type: Problem-Solving Task

Comparing two different pizzas:

The focus of this task is on understanding that fractions, in an explicit context, are fractions of a specific whole. In this this problem there are three different wholes: the medium pizza, the large pizza, and the two pizzas taken together. This task is best suited for instruction. Students can practice explaining their reasoning to each other in pairs or as part of a whole group discussion.

Type: Problem-Solving Task

Comparing Sums of Unit Fractions:

The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size.

Type: Problem-Solving Task

Using Benchmarks to Compare Fractions:

This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two. In Melissa's example, she chooses 1/4 as being larger than 1/5 and smaller than 2/7.

Type: Problem-Solving Task

Tutorial

Comparing Fractions:

This tutorial for student audiences will assist learners with a further understanding that fractions are a way of showing part of a whole. Yet some fractions are larger than others. So this tutorial will help to refresh the understanding for the comparison of fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

STEM Lessons - Model Eliciting Activity

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

Wondrous Water Parks:

This activity requires students to apply their knowledge of unit conversions, speed calculation, and comparing fractions to solve the problem of which water park their class should choose to go on for their 5th grade class trip.

MFAS Formative Assessments

Compare Fractions:

Students are given three sets of fractions to compare and are asked to record the comparisons using the less than, greater than, or equal to symbols.

Comparing Four-Fifths and Three-Fourths:

Students consider the correctness of a model for comparing four-fifths to three-fourths.

Comparing Fractions Using Benchmark Fractions:

Students compare two fractions using benchmark fractions on a number line and record the comparison using the less than or greater than symbol.

Corn Farms:

Students compare two fractions with unlike denominators in the context of a word problem and record the comparison using an inequality symbol.

Original Student Tutorials Mathematics - Grades K-5

Comparing Fractions with Square Foot Gardens Part 2:

Use equivalent fractions to compare fractions in this garden-themed, interactive tutorials

This is Part 2 in a two-part series. Click to open Part 1,  “Mama’s Pizza, Butterflies, & Comparing Fractions.”

Mama's Pizza, Butterflies, and Comparing Fractions Part 1:

Help a family settle an argument about who got the most pizza and which butterfly was longer by comparing fractions using benchmarks and area models, in this interactive tutorial.

Student Resources

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

Original Student Tutorials

Comparing Fractions with Square Foot Gardens Part 2:

Use equivalent fractions to compare fractions in this garden-themed, interactive tutorials

This is Part 2 in a two-part series. Click to open Part 1,  “Mama’s Pizza, Butterflies, & Comparing Fractions.”

Type: Original Student Tutorial

Mama's Pizza, Butterflies, and Comparing Fractions Part 1:

Help a family settle an argument about who got the most pizza and which butterfly was longer by comparing fractions using benchmarks and area models, in this interactive tutorial.

Type: Original Student Tutorial

Educational Games

Flower Power: An Ordering of Rational Numbers Game:


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Type: Educational Game

Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Type: Educational Game

Problem-Solving Tasks

Listing fractions in increasing size:

The fractions for this task have been carefully chosen to encourage and reward different methods of comparison. The first solution judiciously uses each of the following strategies when appropriate: comparing to benchmark fractions, finding a common denominator, finding a common numerator. The second and third solution shown use only either common denominators or numerators. Teachers should encourage multiple approaches to solving the problem. This task is mostly intended for instructional purposes, although it has value as a formative assessment item as well.

Type: Problem-Solving Task

Comparing two different pizzas:

The focus of this task is on understanding that fractions, in an explicit context, are fractions of a specific whole. In this this problem there are three different wholes: the medium pizza, the large pizza, and the two pizzas taken together. This task is best suited for instruction. Students can practice explaining their reasoning to each other in pairs or as part of a whole group discussion.

Type: Problem-Solving Task

Comparing Sums of Unit Fractions:

The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size.

Type: Problem-Solving Task

Using Benchmarks to Compare Fractions:

This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two. In Melissa's example, she chooses 1/4 as being larger than 1/5 and smaller than 2/7.

Type: Problem-Solving Task

Tutorial

Comparing Fractions:

This tutorial for student audiences will assist learners with a further understanding that fractions are a way of showing part of a whole. Yet some fractions are larger than others. So this tutorial will help to refresh the understanding for the comparison of fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

Listing fractions in increasing size:

The fractions for this task have been carefully chosen to encourage and reward different methods of comparison. The first solution judiciously uses each of the following strategies when appropriate: comparing to benchmark fractions, finding a common denominator, finding a common numerator. The second and third solution shown use only either common denominators or numerators. Teachers should encourage multiple approaches to solving the problem. This task is mostly intended for instructional purposes, although it has value as a formative assessment item as well.

Type: Problem-Solving Task

Comparing two different pizzas:

The focus of this task is on understanding that fractions, in an explicit context, are fractions of a specific whole. In this this problem there are three different wholes: the medium pizza, the large pizza, and the two pizzas taken together. This task is best suited for instruction. Students can practice explaining their reasoning to each other in pairs or as part of a whole group discussion.

Type: Problem-Solving Task

Comparing Sums of Unit Fractions:

The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size.

Type: Problem-Solving Task

Using Benchmarks to Compare Fractions:

This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two. In Melissa's example, she chooses 1/4 as being larger than 1/5 and smaller than 2/7.

Type: Problem-Solving Task

Tutorial

Comparing Fractions:

This tutorial for student audiences will assist learners with a further understanding that fractions are a way of showing part of a whole. Yet some fractions are larger than others. So this tutorial will help to refresh the understanding for the comparison of fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial