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Examples
Example: The fractions
and 
can be identified as equivalent using number lines.
Example: The fractions 
and 
can be identified as not equivalent using a visual model.
Clarifications
Clarification 1: Instruction includes identifying equivalent fractions and explaining why they are equivalent using manipulatives, drawings, and number lines.Clarification 2: Within this benchmark, the expectation is not to generate equivalent fractions.
Clarification 3: Fractions are limited to fractions less than or equal to one with denominators of 2, 3, 4, 5, 6, 8, 10 and 12. Number lines must be given and scaled appropriately.
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 identify equivalent fractions both on appropriately scaled number lines and on area models, and to justify how they know (MTR.2.1, MTR.4.1).
- Instruction should prioritize tasks that allow for students to reason why fractions are equivalent using the models instead of the algorithm. Students are not expected to generate equivalent fractions until Grade 4 (MTR.2.1).
Common Misconceptions or Errors
- Students can be confused that when numerators are the same in fractions, larger denominators represent smaller pieces, and smaller denominators represent larger pieces
Strategies to Support Tiered Instruction
- Instruction includes opportunities to use concrete models and drawings to solidify understanding of fraction equivalence. Students use models to describe why fractions are equivalent or not equivalent when referring to the same-size whole.
- For example, when looking at and , conversation includes that both fraction 88 models are the same size, so when comparing them we are comparing the same size whole. Students can see that 2 out of the 8 are shaded in the first model and 4 out of the 8 are shaded in the second model, making the greater than .
- Instruction includes opportunities to use concrete models and drawings to solidify understanding of fraction equivalence. Students use models to describe why fractions are equivalent or not equivalent when referring to the same-size whole. Instruction includes partitioning shapes with halves, thirds, and fourths and then comparing the pieces used.
- For example, students partition a shape into halves.
- Conversation includes observations about the shape partitioned into two equal pieces. The teacher models writing the fractional parts of so that students can make the connection of the denominator representing the number of pieces. Students then practice partitioning shapes into thirds and fourths for this same understanding.
Instructional Tasks
Instructional Task 1
- Plot the fractions 2/4 and 1/2. Use your number line to determine whether the fractions are equivalent. Justify your argument in words.
Instructional Task 2
- Use a visual model to prove why 6 eighths is equivalent to 3 fourths.
Instructional Task 3
- The fractions 3/4 and 9/12 are equivalent.
Part A. Describe how a visual model will show that these fractions are equivalent.
Part B. Describe how a number line will show that these fractions are equivalent.
Instructional Items
Instructional Item 1
- Use the area models below to determine whether the fractions they represent are equivalent.
- a. The model shows that 2 sixths and 2 fourths are equivalent because the area models each have 2 shaded parts.
- b. The model shows that 2 sixths and 2-fourths are equivalent because the area models show the size of the shaded parts are equal when the size of each whole is the same.
- c. The model shows that 2 sixths and 2-fourths are not equivalent because 2 sixths is greater than 2-fourths when the size of each whole is the same.
- d. The model shows that 2 sixths and 2-fourths are not equivalent because the area models show the size of the shaded parts are not equal when the size of each whole is the same.
Instructional Item 2
- Select all the fractions that are equivalent to a one-half.
- a.
- b.
- c.
- d.
- e.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Image/Photograph
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Idea
Problem-Solving Tasks
Virtual Manipulative
MFAS Formative Assessments
Students are given a familiar fraction and asked to generate an equivalent fraction justifying their reasoning.
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
Problem-Solving Tasks
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
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.
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
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
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
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.
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
