# Cluster 1: Develop understanding of fractions as numbers. (Major Cluster)Archived

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.

General Information
Number: MAFS.3.NF.1
Title: Develop understanding of fractions as numbers. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Number and Operations - Fractions

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.3.NF.1.AP.1a
Identify the number of highlighted parts (numerator) of a given representation (rectangles and circles).
MAFS.3.NF.1.AP.1b
Identify the total number of parts (denominator) of a given representation (rectangles and circles).
MAFS.3.NF.1.AP.1c
Identify the fraction that matches the representation of partitioned rectangles and circles into halves, fourths, thirds, and eighths.
MAFS.3.NF.1.AP.2a
Locate given common unit fractions (i.e., 1/2, 1/4) on a number line or ruler.
MAFS.3.NF.1.AP.3a
Identify equivalent fractions on a number line divided into fourths and halves within 3 units.

## Related Resources

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

## Educational Games

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

Fraction Beach:

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

Crossing the River Online Game (Identifying Fractions):

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

## Formative Assessments

Which Shows One Third?:

Students are shown three circles and asked to select the one that correctly shows one third shaded and explain why the other two do not.

Type: Formative Assessment

What Does One Fifth Mean?:

Students are shown the fraction one fifth and asked to describe what it means.

Type: Formative Assessment

Three Quarters Of The Race:

Students are read a word problem about a student who has run three-fourths of a race and asked to describe what that means.

Type: Formative Assessment

Painting A Wall:

Students are read a word problem about a wall being painted and asked to describe what three-eighths of the wall means.

Type: Formative Assessment

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

How Many Fourths Are In Two Wholes?:

Students are asked to divide two rectangles into fourths and then to consider how many fourths the two wholes represent.

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

Fraction Flyers :

Students will represent fractions between zero and one by completing a number line of their own. Students will use their understanding of fractions between zero and one to design their own number line. Students will then communicate their understanding of representing fractions on a number line through a written proposal.

Type: Lesson Plan

Happy Feet!:

In this chocolately delicious lesson, your students will enjoy learning how to compare fractions and use that mathematical knowledge to create an inventory for a new local shoe store, Happy Feet Footwear. They will also write to express their opinions and provide reasons to justify their opinions.

This lesson suggests using "The Hershey's Milk Chocolate Fraction Book" to help students manipulate and compare fractions and have a great time doing so! What student wouldn't like to use chocolate to help him/her learn?

Type: Lesson Plan

Mystery Strips - Fractional Parts of the Whole:

This problem-solving lesson has students working together in groups to discover that fractions are made up of equal parts of one-whole. In this lesson, students are exposed to equivalent fractions as well as challenged to work beyond unit fractions to discover the fractional part of one-whole that the "mystery strips" represent. This highly engaging lesson takes into account all levels of learners and will challenge even your most advanced students.

Type: Lesson Plan

Parts of a Whole:

In this lesson, students will use area models to partition a whole into equal parts and record the associated fractions that represent the part/s. Students will determine and explain whether or not a given fraction and an area representation match. Various shapes will be used for the area models.

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

Represent and Write Fractions:

Students will demonstrate their understanding of representing and recording fractions using pictures, manipulatives and numbers through an interactive problem solving scenario. Students will create a "picture pie" as an introduction to fractions and also will demonstrate the connection to the numerical form of a fraction and the picture form in a mix-match-mingle game.

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. The students will be able to explain equivalence of fractions based on their pizza exchanges and will be able to compare and order the fractional parts by their size.

Type: Lesson Plan

Fraction Face Off:

In this lesson, students will become familiar with comparing fractions and play a "war" game with fractions.

Type: Lesson Plan

Discovering Fractions:

In this lesson students will make initial discoveries about fractions. Students will work together to explain and record the discoveries they make while using manipulatives to explore fractions.

Type: Lesson Plan

The Human Number Line:

This lesson uses a human number line to help students estimate a fraction's approximate position on the number line between zero and one. It also helps students visualize and understand the relative size of fractions, preparing them to be able to make comparisons.

Type: Lesson Plan

Fraction Name Art:

This lesson is designed to introduce and give students practice with the concept of fractions as part of a set. Students will use their classmates to create fraction statements, play a guessing game with color tiles, and finally write fractional statements about their own Name Art!

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

The "Whole" Deal:

This is an introductory fraction lesson designed to reinforce the idea that fractions are equal parts of one whole. The students will use different pattern blocks as their whole to increase their understanding of fractions in a variety of different representations.

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

"What's the part? What's the whole?":

This lesson provides a conceptual approach to multiplying a fraction times a whole number and a whole number times a fraction.Â  Students are to use an understanding of the meaning of the denominator and numerator to figure out a strategy for finding the solution.Â

Type: Lesson Plan

Fract-o-Bot:

The students will be able to show a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts. The students will be able to show understand a fraction a/b as the quantity formed by a parts of size 1/b. The students will create Fract-O-Bots to meet these two standards and learn about fractions.

Type: Lesson Plan

Fractions Meet Pattern Blocks:

Students will identify the fractional parts of a whole using pattern blocks.

Type: Lesson Plan

Fraction Counting Book:

Students will make a book of fractions by counting by a specified denominator. They will represent the fractions as pictures, in number form, word form, and on a number line.

Type: Lesson Plan

Symmetrical Solutions:

Students will use paper cutout and geoboards to find and create lines of symmetry. Students will have the opportunity to work with a partner and independently.

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 models of fractions, including a human number line. Using a number line, students develop conceptual understanding of fractions. Students use the number line to represent and compare fractions less than one. The activities are engaging and include full participation/engagement of all students. The fractions are limited to positive fractions less than one with a denominator of 2 or 4 including 0 and 1 whole.

Type: Lesson Plan

Making our own fraction manipulatives!:

Students will make and use a set of fraction manipulatives including whole, halves, fourths, and eighths to represent parts of a whole. They may be used later to discover fraction relationships.

Type: Lesson Plan

Fraction Folding - Part 2:

Students will use foldables to create and name fractions. Students will sing a song to learn the terms numerator and denominator. Students will identify how many unit fractions compose a fraction.

Type: Lesson Plan

Match My Fraction:

The students will use pattern blocks to demonstrate fractions and equivalent fractions. They begin by finding and modeling equivalent fractions with pattern blocks, then they are asked to match cards to show the equivalent fractions.

Type: Lesson Plan

Cooking with Fractions:

In this lesson, students will examine real-world recipes and determine if the fractions are less than one or greater than one. Fractions and ingredients are recorded on a chart within the groups. Games are mixed in to make learning interactive and engaging.

Type: Lesson Plan

Comparing Fractions with Pizza:

In this lesson, students will demonstrate their understanding of comparing fractions with the same denominator through engaging problem solving with real-world application to pizza using 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 denominator.

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 have experiences with determining where a given fraction falls in regards to "benchmark" fractions and will practice placing fractions on a number line.

Type: Lesson Plan

Equivalent Fractions: It Means the Same:

In this lesson, students will use models to represent equivalent fractions, including fractions greater than 1, and 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 discover the value of fractions with a numerator of 1. The students will be able to compare the fractions and be able to correctly place them on a number line.

Type: Lesson Plan

Fraction Folding-Part 1:

In this lesson, students will build base knowledge of fractions as parts of a whole. They will differentiate examples and non-examples of fractions. They will label unit fractions.

Type: Lesson Plan

Equivalent Fraction Dominoes:

Students will identify equivalent fractionsÂ to 1/2 using manipulativesÂ and determine what happened to the numerator and denominator when an equivalent fraction was formed.Â  They will practice this idea by identifying equivalent fractions in a domino game.

Type: Lesson Plan

Fraction Measuring With Cuisenaire Rods:

In this lesson students will use Cuisenaire rods to measure distances of different lengths.They will also use and compare fractional amounts to find different ways of naming equivalencies.

Type: Lesson Plan

Students explore the concept of unit fractions. They make sense of the structure of a fraction and make generalizations about unit fractions, and then apply those generalizations when creating a whole from a unit fraction.

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

Twizzle the Fractions!:

In this food-themed lesson students work to understand why fraction comparisons must refer to the same whole to be valid. This lesson covers part "d" of standard MAFS.3.N.F.1.3. (In this standard there are parts a, b,and c.)

Type: Lesson Plan

## Lesson Study Resource Kit

Number and Operations - Fractions Lesson Study Resource Kit â€“ Third Grade:

This lesson study resource kit can be used to guide and support teams of third grade teachers as they engage in lesson study focused on the academic standards in the Number and Operations - Fractions domain.

Type: Lesson Study Resource Kit

## Model Eliciting Activity (MEA) STEM Lesson

Physical Science Unit: Properties Lesson 22 Model Eliciting Activity: Animal Meal Planning:

In this MEA, students will have the opportunity to apply what they learned about physical properties to a realistic problem. 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.

This is a lesson in the Grade 3 Physical Science Unit on Properties. This is a themed unit of SaM-1's adventures at the CPALMS Rehabilitation and Conservation Center.  To see all the lessons in the unit please visit https://www.cpalms.org/page818.aspx .

Type: Model Eliciting Activity (MEA) STEM Lesson

## 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,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

Lesson 22 Video: MEA Animal Meal Planning:

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

Sharing With Fractions:

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

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

## Presentation/Slideshows

Fractions:

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

Introducing Fractions Slideshow- Flowering Fractions:

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

Money in the piggy bank:

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.

Fraction Comparisons With Pictures, Assessment Variation:

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.

Comparing Fractions with the Same Numerators, Assessment Variation:

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.

Comparing Fractions with the Same Denominator, Assessment Variation:

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.

Find 7/4 starting from 1, Assessment Variation:

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.

Find 1/4 Starting from 1, Assessment Version:

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."

Find 1 Starting from 5/3, Assessment Variation:

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."

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 lin

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, 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.

Which is Closer to 1?:

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

Ordering Fractions:

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

Naming the Whole for a Fraction:

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

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).

Equivalent Fractions Pointer:

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.

## 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

## Teaching Idea

Fraction Action:

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

Type: Teaching Idea

## Tutorials

Comparing Fractions on a Number Line and with Rectangular Models:

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

Type: Tutorial

Different Ways to Represent 1 as a Fraction:

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

Type: Tutorial

Understanding Fraction Parts:

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

Fractions:

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

Fractions Introduction:

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

Type: Virtual Manipulative

Build a Fraction:

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

Exploring Fractions:

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

Vectorkids-Fractions:

In this interactive activity users are given pies. Part of the pie is shaded yellow and the total number of pieces is given. The user has to identify the fraction by entering the part divided by the whole. Once the user completes ten problems the score is given.

Type: 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

Fraction Models:

An interactive tool to represent a fraction circle, rectangle, or set model with numerators and denominators ranging from 1 to 100. The decimal and percent equivalents of the created fraction are also displayed.

Type: Virtual Manipulative

Frank and Fran's Fabulous Fractions:

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

## 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,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

Lesson 22 Video: MEA Animal Meal Planning:

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

Sharing With Fractions:

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

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

## Educational Games

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

Fraction Beach:

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

Crossing the River Online Game (Identifying Fractions):

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

Fractions:

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

Introducing Fractions Slideshow- Flowering Fractions:

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

Money in the piggy bank:

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.

Fraction Comparisons With Pictures, Assessment Variation:

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.

Comparing Fractions with the Same Numerators, Assessment Variation:

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.

Comparing Fractions with the Same Denominator, Assessment Variation:

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.

Find 7/4 starting from 1, Assessment Variation:

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.

Find 1 Starting from 5/3, Assessment Variation:

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."

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 lin

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, 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.

Which is Closer to 1?:

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

Ordering Fractions:

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

Naming the Whole for a Fraction:

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

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).

Equivalent Fractions Pointer:

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.

## 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

Comparing Fractions on a Number Line and with Rectangular Models:

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

Type: Tutorial

Different Ways to Represent 1 as a Fraction:

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

Type: Tutorial

Understanding Fraction Parts:

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

Fractions:

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

Fractions Introduction:

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

Type: Virtual Manipulative

Build a Fraction:

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

Exploring Fractions:

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

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

Frank and Fran's Fabulous Fractions:

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

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

## Presentation/Slideshow

Fractions:

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

Money in the piggy bank:

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.

Fraction Comparisons With Pictures, Assessment Variation:

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.

Comparing Fractions with the Same Numerators, Assessment Variation:

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.

Comparing Fractions with the Same Denominator, Assessment Variation:

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.

Find 7/4 starting from 1, Assessment Variation:

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.

Find 1/4 Starting from 1, Assessment Version:

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."

Find 1 Starting from 5/3, Assessment Variation:

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."

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 lin

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, 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.

Which is Closer to 1?:

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

Ordering Fractions:

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

Naming the Whole for a Fraction:

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

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).

## Teaching Idea

Fraction Action:

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

Type: Teaching Idea

## Tutorial

Fractions:

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

Fractions Introduction:

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

Type: Virtual Manipulative

Build a Fraction:

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

Exploring Fractions:

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