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- Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
- Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
- Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
- Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
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.
- Assessment Limits :
Denominators are limited to 2, 3, 4, 6, and 8. Fractions must reference the same whole entity that can be equally partitioned, unless item is assessing MAFS.3.NF.1.3d. Items may not use the term “simplify” or “lowest terms” in directives. Visual models may include number lines and area models. Only whole number marks may be labeled on number lines. - Calculator :
No
- Context :
Allowable
- Test Item #: Sample Item 1
- Question:
For MAFS.3.NF.1.3c:
Select all the fractions that are equivalent to a whole number.
- Difficulty: N/A
- Type: MS: Multiselect
Related Courses
Related Access Points
Related Resources
Educational Game
Formative Assessments
Image/Photograph
Lesson Plans
Model Eliciting Activity (MEA) STEM Lesson
Original Student Tutorials
Problem-Solving Tasks
Student Center Activity
Teaching Idea
Tutorials
Virtual Manipulatives
MFAS Formative Assessments
Students compare two pairs of fractions and record their comparisons using the less than or greater than symbols.
Students are given a familiar fraction and asked to generate an equivalent fraction justifying their reasoning.
Students are asked to divide two rectangles into fourths and then to consider how many fourths the two wholes represent.
Original Student Tutorials Mathematics - Grades K-5
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.
Student Resources
Original Student Tutorials
In this video, SaM-1 introduces a part 2 twist to the Model Eliciting 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 throughout the unit to start the challenge.
Type: Original Student Tutorial
In this video, SaM-1 introduces a Model Eliciting Activity (MEA) challenge for the students. This video provides meal planning information to add to the knowledge students gained throughout 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 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 Game
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
Problem-Solving Tasks
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
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
The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.
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
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
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
Problem-Solving Tasks
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
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
The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.
Type: Problem-Solving Task
Teaching Idea
By making popcorn together with your child you may also introduce the concept of fractions.
Type: Teaching Idea
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
