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Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Standard #: MAFS.3.NF.1.1Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 3
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Develop understanding of fractions as numbers. (Major Cluster) -

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.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
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.
  • 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.
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.
  • What Does One Fifth Mean? # Students are shown the fraction one fifth and asked to describe what it means.
  • 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.
  • 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.
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.
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.
  • Parts of a Whole # In this lesson, students will recognize a whole partitioned into equal parts and represent the unit fraction as 1/b. Students will learn to represent one equal-sized piece (numerator) of the partitioned whole (denominator) as a number in standard, numeral-word, and word form.
  • Fraction Action! # This lesson will help students understand that fractions are parts of a whole. The lesson introduces fractional parts using familiar manipulatives.
  • 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.
  • 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!
  • The "Whole" Deal # In this lesson, students will extend their understanding of unit and non-unit fractions by using different pattern blocks to represent one whole and then determining the fractional part the other pattern blocks represent.
  • "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.  Students are to use an understanding of the meaning of the denominator and numerator to figure out a strategy for finding the solution. 
  • Fractions Meet Pattern Blocks # Students will identify the fractional parts of a whole using pattern blocks. There is a focus on unit fractions.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
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.
  • 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.
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.
Problem-Solving Tasks
  • 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. 
  • 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.
Student Center Activity
  • Edcite: Mathematics Grade 3 # 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.
Teaching Idea
  • Fraction Action # By making popcorn together with your child you may also introduce the concept of fractions.
Tutorials
  • 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.
  • 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.
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.
  • 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
  • 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.
  • Fraction Game # This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)
  • 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.
MFAS Formative Assessments
  • 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.
  • 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.
  • 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
  • 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.
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