MA.3.FR.1.1

Represent and interpret unit fractions in the form 1/n as the quantity formed by one part when a whole is partitioned into n equal parts.

Examples

begin mathsize 11px style 1 fourth end style can be represented as begin mathsize 12px style 1 fourth end style of a pie (parts of a shape), as 1 out of 4 trees (parts of a set) or as begin mathsize 12px style 1 fourth end style on the number line.

Clarifications

Clarification 1: This benchmark emphasizes conceptual understanding through the use of manipulatives or visual models. 
Clarification 2: Instruction focuses on representing a unit fraction as part of a whole, part of a set, a point on a number line, a visual model or in fractional notation.

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

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Fractions
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

Terms from the K-12 Glossary

  • Number line

Vertical Alignment

Previous Benchmarks

Next Benchmarks

Purpose and Instructional Strategies

The purpose of this benchmark is for students to understand that unit fractions are the foundation for all fractions. Second, the purpose is for students to understand that fractions are numbers. This benchmark continues instruction of fractions from Grade 2, where students partitioned circles and rectangles into two, three or four equal-sized parts (MA.2.FR.1.1 and MA.2.FR.1.2). 
  • To activate prior knowledge in Grade 3, instruction should: 
    • Relate how unit fractions build fractions to how whole-number units build whole numbers, and 
    • Show models with non-equal parts as non-examples (MTR.2.1). 
  • Unit fractions are defined as one part when a whole is partitioned in any number of equal parts. It is in this benchmark that students conclude that the greater a unit fraction’s denominator, the greater its number of parts. 
  • Instruction should demonstrate how to represent unit fractions using manipulatives (e.g., fraction strips, circles, relationship rods), visual area models (e.g., partitioned shapes), on a number line, and as 1 object in a set of objects (MTR.2.1, MTR.5.1). 
  • Denominators are limited in Grade 3 to facilitate the visualizing and reasoning required while students plot, compare and identify equivalence in fractions.

Common Misconceptions or Errors

  • Students can misconceive the difference between the meaning of numerators and denominators in fractions. For this reason, it is important for teachers and students to represent unit fractions in multiple ways to understand how they relate to a whole. Representations can be modeled together (e.g., fraction strips side-by-side with number lines, or relationship rods side-by-side with number lines) to help build student understanding. 
  • Students can misconceive that the smaller the denominator, the smaller the piece, or the larger the denominator, the larger the piece. This is due to thinking and reasoning where students worked with whole numbers (the smaller a number, the less it is, or the larger a number, the more it is). To correct this misconception, have students utilize different models, such as fraction bars and number lines, which would provide students opportunities to compare unit fractions and to reason about their sizes. 
  • Students can misconceive that all shapes can be partitioned the same way. To assist with this misconception, have students practice with presenting shapes other than circles, squares or rectangles to prevent students from overgeneralizing that all shapes can be divided the same way.

Strategies to Support Tiered Instruction

  • Teacher represents unit fractions in multiple ways to show understanding of how they relate to a whole. Representations are modeled together (e.g., fraction strips side-by-side with number lines, or relationship rods side-by-side with number lines) to help build understanding. 
fraction strips side-by-side with number lines
  • Instruction includes partitioning shapes into different denominators. 
    • For example, students compare what they notice about partitioning a rectangle into halves versus fourths. Teacher asks students, “What do you notice about the pieces? How can we write what one piece of the rectangle is worth with a fraction?” Instruction includes the vocabulary of numerator and denominator. 
 partitioned shapes into different denominators
  • Instruction includes shapes other than circles and rectangles. Items like pattern blocks allow students to partition shapes like hexagons and rhombi into equal-sized pieces. This prevents students from over-generalizing that all shapes can be divided the same way. 
  • Instruction includes folding and/or cutting premade shapes into different amounts. Students benefit from beginning with halves and fourths, folding the paper in half, and then folding those halves into halves to make fourths. 
    • For example, the teacher asks students, “What do you notice about the shapes? About the size? We now have 4 pieces, Do we have more than we did before?&rdquo The conversation includes the size of the pieces and how that relates to the denominator.

Instructional Tasks

Instructional Task 1 

Terry wants to show the unit fraction 18 using an area model, a number line, and as a set. 
    • Part A. Into how many equal parts should Terry partition his area model? How many of those parts should be shaded? Explain in words. 
    • Part B. Represent 18 using the number line below. 
arrow
    • Part C. Draw a model that represents 18 of a set of juice boxes.

Instructional Items

Instructional Item 1 

Each model shown has been shaded to represent a fraction. Which model shows 14 shaded? 

shaded models

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712040: Access Mathematics Grade 3 (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.3.FR.1.AP.1:

Explore unit fractions in the form begin mathsize 12px style 1 over n end style as the quantity formed by one part when a whole is partitioned into n equal parts. Denominators are limited to 2, 3 and 4.

Related Resources

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

Educational Game

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

Formative Assessments

Unit Fractions:

Students divide a hexagon into two, three, and six equal parts and write the unit fraction representing each part.

Type: Formative Assessment

Two Equal Parts:

Students divide figures into two parts, each having the same area, and write the unit fraction representing each part.

Type: Formative Assessment

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

Halves of an Irregular Polygon:

Students partition an irregular hexagon into two equal parts and describe each part using a unit fraction.

Type: Formative Assessment

Four Parts of the Whole:

Students partition a rectangle into four equal parts and describe each part using a fraction.

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

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

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

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

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

Fractions Meet Pattern Blocks:

Students will identify the fractional parts of a whole using pattern blocks. There is a focus on unit fractions.

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

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

Comparing and Placing Unit Fractions on a Number Line:

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

Type: Lesson Plan

Fraction Folding-Part 1:

In this lesson, students will build the understanding of unit fractions. They will differentiate examples and non-examples of fractional parts of squares. They will label unit fractions and describe unit fractions as those that “build” other fractions.

Type: Lesson Plan

Original Student Tutorials

Partitioning Number Lines in the Neighborhood:

Learn about unit fractions and how to partition number lines to plot unit fractions' locations. Join Nik, Natalia, and their neighborhood friends on a number line fraction finding adventure 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

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

Perspectives Video: Teaching Ideas

Using Manipulatives to Add Fractions:

Unlock an effective teaching strategy for teaching adding fractions in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Making Connections Between Partitioning Circles and Circle Graphs:

Unlock an effective teaching strategy for connecting partitioning circles and circle graphs in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Decomposing Fractions in Multiple Ways:

Unlock an effective teaching strategy for decomposing fractions in multiple ways in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Exploring Fractions with Pattern Blocks:

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

Type: Perspectives Video: Teaching Idea

Problem-Solving Task

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. 

Type: Problem-Solving Task

Virtual Manipulatives

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

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

MFAS Formative Assessments

Four Parts of the Whole:

Students partition a rectangle into four equal parts and describe each part using a fraction.

Halves of an Irregular Polygon:

Students partition an irregular hexagon into two equal parts and describe each part using a unit fraction.

Two Equal Parts:

Students divide figures into two parts, each having the same area, and write the unit fraction representing each part.

Unit Fractions:

Students divide a hexagon into two, three, and six equal parts and write the unit fraction representing each part.

What Does One Fifth Mean?:

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

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.

Original Student Tutorials Mathematics - Grades K-5

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.

Partitioning Number Lines in the Neighborhood:

Learn about unit fractions and how to partition number lines to plot unit fractions' locations. Join Nik, Natalia, and their neighborhood friends on a number line fraction finding adventure in this interactive 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.

Student Resources

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

Original Student Tutorials

Partitioning Number Lines in the Neighborhood:

Learn about unit fractions and how to partition number lines to plot unit fractions' locations. Join Nik, Natalia, and their neighborhood friends on a number line fraction finding adventure 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

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

Educational Game

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

Problem-Solving Task

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. 

Type: Problem-Solving Task

Virtual Manipulatives

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

Fraction Game:

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

Type: Virtual Manipulative

Parent Resources

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

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

Problem-Solving Task

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. 

Type: Problem-Solving Task

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