Standard #: MAFS.3.NF.1.2 (Archived Standard)


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Understand a fraction as a number on the number line; represent fractions on a number line diagram.
  1. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
  2. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.


Remarks


Example of Opportunities for In-Depth Focus

Developing an understanding of fractions as numbers is essential for future work with the number system. It is critical that students at this grade are able to place fractions on a number line diagram and understand them as a related component of their ever- expanding number system.

Fluency Expectations or Examples of Culminating Standards

Students fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3.NBT.1.2 a relatively small and incremental expectation.

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
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :
    Denominators are limited to 2, 3, 4, 6, and 8. Number lines in MAFS.3.NF.1.2b items may extend beyond 1. Only whole number marks may be labeled on number lines.
    Calculator :

    No

    Context :

    No context



Sample Test Items (4)

Test Item # Question Difficulty Type
Sample Item 1

Which number line is divided into thirds?

 

N/A MC: Multiple Choice
Sample Item 2

Which fraction is represented by the total length marked on the number line shown?

N/A EE: Equation Editor
Sample Item 3

What fraction is represented by the length marked on the number line shown?

N/A EE: Equation Editor
Sample Item 4

Only for MAFS.3.NF.1.2b:

What fraction is represented by point A on the number line shown?

N/A EE: Equation Editor


Related Courses

Course Number1111 Course Title222
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 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 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))


Related Resources

Formative Assessments

Name Description
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.

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.

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.

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.

Lesson Plans

Name Description
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.

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.

The Human Number Line

In this lesson, students will create a human number line by estimating a fraction's approximate location on the number line between zero and one. This lesson helps students visualize fractions’ relative distance from 0 in order to order and compare fractions and engages them in justifying their thinking.

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.

Interactive Fraction Number Lines

In this lesson students make number lines out of sentence strips to plot, order, and compare fractions with the same denominators.

Fractions on a Number line

In this lesson, students will place fractions on a number line and identify equivalent fractions. Students will explain the definition of equivalent fractions.

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.

Original Student Tutorials

Name Description
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.

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.

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.

Problem-Solving Tasks

Name Description
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.

Find 2/3

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

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. 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.

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).

Student Center Activity

Name Description
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.

Virtual Manipulative

Name Description
Fraction Game

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

Student Resources

Original Student Tutorials

Name Description
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.

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.

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.

Problem-Solving Tasks

Name Description
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.

Find 2/3:

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

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. 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.

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).

Student Center Activity

Name Description
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.

Virtual Manipulative

Name Description
Fraction Game:

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



Parent Resources

Problem-Solving Tasks

Name Description
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.

Find 2/3:

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

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. 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.

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).



Printed On:4/30/2025 7:35:57 AM
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