Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Number:**MAFS.4.NF.1

**Title:**Extend understanding of fraction equivalence and ordering. (Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**4

**Domain-Subdomain:**Number and Operations - Fractions

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Educational Games

## Formative Assessments

## Image/Photograph

## Lesson Plans

## Original Student Tutorials

## Problem-Solving Tasks

## Tutorial

## Virtual Manipulatives

## Student Resources

## Original Student Tutorials

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

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

Learn how to create equivalent fractions and visually see how they are equivalent in this interactive tutorial.

This is part 1 of a 2-part series. Click **HERE **to open Part 2.

Type: Original Student Tutorial

Learn how to find equivalent fractions in a multiplication table in this interactive tutorial.

This is part 2 of a 2 part series. Click **HERE** to open Part 1.

Type: Original Student Tutorial

## Educational Games

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

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

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

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Students will need more opportunities to think about fraction equivalence with different examples and models, but this task represents a good first step.

Type: Problem-Solving Task

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

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

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

The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that. Some students might stop at the second-to-last picture and note that it looks like they ran the same distance, but the explanation is not yet complete at that point.

Type: Problem-Solving Task

## Tutorial

This Khan Academy video illustrates that fraction a/b is equivalent to fraction (a *x* n)/(b x n).

Type: Tutorial

## Virtual Manipulatives

Match shapes and numbers to earn stars in this fractions game.

- Match fractions using numbers and pictures
- make the same fractions using different numbers
- Match fractions in different picture patterns
- Compare fractions using numbers and patterns

Type: Virtual Manipulative

In this activity, you will graphically determine the value of two given fractions represented as points on a number line. You will then graphically find a fraction whose value is between the two given fractions and determine its value.

Type: Virtual Manipulative

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

## Image/Photograph

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

## Problem-Solving Tasks

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

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Students will need more opportunities to think about fraction equivalence with different examples and models, but this task represents a good first step.

Type: Problem-Solving Task

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

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

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

The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that. Some students might stop at the second-to-last picture and note that it looks like they ran the same distance, but the explanation is not yet complete at that point.

Type: Problem-Solving Task

## Virtual Manipulative

Match shapes and numbers to earn stars in this fractions game.

- Match fractions using numbers and pictures
- make the same fractions using different numbers
- Match fractions in different picture patterns
- Compare fractions using numbers and patterns

Type: Virtual Manipulative