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.3.NF.1

**Title:**Develop understanding of fractions as numbers. (Major Cluster)

**Type:**Cluster

**Subject:**Mathematics - Archived

**Grade:**3

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

## Related Standards

## Related Access Points

## Access Points

## Related Resources

## Educational Games

## Educational Software / Tool

## Formative Assessments

## Image/Photograph

## Lesson Plans

## Lesson Study Resource Kit

## Model Eliciting Activity (MEA) STEM Lesson

## Original Student Tutorials

## Presentation/Slideshows

## Problem-Solving Tasks

## Student Center Activity

## Teaching Idea

## Tutorials

## Virtual Manipulatives

## Student Resources

## Original Student Tutorials

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

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

In this video,Â SaM-1 introduces a part 2 twist to the Model ElicitingÂ 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 throughoutÂ the unit to start the challenge.

Â

Type: Original Student Tutorial

In this video,Â SaM-1 introduces a Model ElicitingÂ Activity (MEA) challenge for the students. This video provides meal planning information to add to the knowledge students gained throughoutÂ 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

Learn to name or identify fractions, especially unit fractions, and justify the fractional value using an area model in this pizza-themed, interactive tutorial.

Type: Original Student Tutorial

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

## Educational Games

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

In this interactive Flash game, students are challenged to identify a fraction from a picture of a group of objects or from a geometric diagram, or they are asked to create a diagram or picture given a common fraction. Motivation is provided by earning buckets of sand to built a sand castle.

Type: Educational Game

## Educational Software / Tool

This interactive, online game is a fun way for students to practice identifying fractions. In this lesson students identify fractions to help a man hop his way across a river.

Type: Educational Software / Tool

## Presentation/Slideshows

This is an accessible, easy-to-read book introducing fractions. It can be downloaded in PowerPoint, Impress, and Flash formats. For struggling or non-readers the book can be read aloud in a variety of voices. All of the books on the Tar Heel Reader site can be used with the Intellikeys keyboard with a custom overlay, a touch screen, and/or 1-3 switches. The text and background colors can be modified for students with visual impairments.

Type: Presentation/Slideshow

This online resource is a story of a girl and her father planting flowers that your children and you interact with. Help them fill in the fractions as they practice dividing the garden up for their flowers!

Type: Presentation/Slideshow

## Problem-Solving Tasks

This task is designed to help students focus on the whole that a fraction refers. It provides a context where there are two natural ways to view the coins. While the intent is to deepen a student's understanding of fractions, it does go outside the requirements of the standard.

Type: Problem-Solving Task

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Type: Problem-Solving Task

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Type: Problem-Solving Task

This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.

Type: Problem-Solving Task

Part (a) of the standard is about representing unit fractions and part (b) is about representing fractions in terms of unit fractions. The tasks require attention to the whole when thinking about fractions; on a number line, the whole is the interval from 0 to 1.

Type: Problem-Solving Task

Part (a) of the standard is about representing unit fractions and part (b) is about representing fractions in terms of unit fractions. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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, a critical aspect for meeting standard 3.NF.2b. 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.

Type: Problem-Solving Task

The purpose of this task is for students to identify which fraction is closest to the whole number 1.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.

Type: Problem-Solving Task

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).

Type: Problem-Solving Task

In this activity, students highlight portions of circles or squares that are equivalent to a given fraction. As the student highlights sections, a pointer on a number line between zero and one updates so they can see when they are close or equal to the given fraction. This activity allows students to explore equivalent fractions by making it necessary that each of the three fractions have a different denominator but have the fractions be equal. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Problem-Solving Task

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorials

In this Khan Academy video four fractions are compared by plotting them on a number line and drawing models.

Type: Tutorial

Use fraction models and a number line to represent 1 as a fraction.

Type: Tutorial

Students will view a video that explains that a fraction is the quantity formed by 1 part when a whole is partitioned into equal parts. Students will then have opportunities to practice this concept with assorted problems and are given immediate feedback as to the accuracy of their responses.

Type: Tutorial

This tutorial for student audiences reviews basic introductory information on fractions. Students will review that a fraction is part of a whole, a fraction is less than 1 whole thing, but more than 0, how to determine pieces of a whole and how to write fractions.

Type: Tutorial

## Virtual Manipulatives

This virtual manipulative offers activities that allow the learner to explore fractions by building fractions, making equivalent fractions, and matching fractions.

Type: Virtual Manipulative

This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.

Some of the sample learning goals can be:

- Build equivalent fractions using numbers and pictures.
- Compare fractions using numbers and patterns
- Recognize equivalent simplified and unsimplified fractions

Type: 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

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

Type: Virtual Manipulative

This online slideshow is another way to introduce parts of a whole to your class.

This lesson could be presented to the whole class or completed by students independently.

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

## Presentation/Slideshow

This is an accessible, easy-to-read book introducing fractions. It can be downloaded in PowerPoint, Impress, and Flash formats. For struggling or non-readers the book can be read aloud in a variety of voices. All of the books on the Tar Heel Reader site can be used with the Intellikeys keyboard with a custom overlay, a touch screen, and/or 1-3 switches. The text and background colors can be modified for students with visual impairments.

Type: Presentation/Slideshow

## Problem-Solving Tasks

This task is designed to help students focus on the whole that a fraction refers. It provides a context where there are two natural ways to view the coins. While the intent is to deepen a student's understanding of fractions, it does go outside the requirements of the standard.

Type: Problem-Solving Task

Type: Problem-Solving Task

Type: Problem-Solving Task

Type: Problem-Solving Task

Part (a) of the standard is about representing unit fractions and part (b) is about representing fractions in terms of unit fractions. The tasks require attention to the whole when thinking about fractions; on a number line, the whole is the interval from 0 to 1.

Type: Problem-Solving Task

Part (a) of the standard is about representing unit fractions and part (b) is about representing fractions in terms of unit fractions. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."

Type: Problem-Solving Task

Part (a) of the standard is about representing unit fractions and part (b) is about representing fractions in terms of unit fractions. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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, a critical aspect for meeting standard 3.NF.2b. 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.

Type: Problem-Solving Task

The purpose of this task is for students to identify which fraction is closest to the whole number 1.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.

Type: Problem-Solving Task

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).

Type: Problem-Solving Task

## Teaching Idea

By making popcorn together with your child you may also introduce the concept of fractions.

Type: Teaching Idea

## Tutorial

This tutorial for student audiences reviews basic introductory information on fractions. Students will review that a fraction is part of a whole, a fraction is less than 1 whole thing, but more than 0, how to determine pieces of a whole and how to write fractions.

Type: Tutorial

## Virtual Manipulatives

This virtual manipulative offers activities that allow the learner to explore fractions by building fractions, making equivalent fractions, and matching fractions.

Type: Virtual Manipulative

This virtual manipulative will help the students to build fractions from shapes and numbers to earn stars in this fraction lab. To challenge the children there are multiple levels, where they can earn lots of stars.

Some of the sample learning goals can be:

- Build equivalent fractions using numbers and pictures.
- Compare fractions using numbers and patterns
- Recognize equivalent simplified and unsimplified fractions

Type: 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