### 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.

**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 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 $\frac{\text{2}}{\text{8}}$ and $\frac{\text{4}}{\text{8}}$, 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 $\frac{\text{4}}{\text{8}}$ greater than $\frac{\text{2}}{\text{8}}$ .

- 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 $\frac{\text{1}}{\text{2}}$ 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 6/4 and 3/2. Use your number line to determine whether the fractions are equivalent. Justify your argument in words.

### 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 4ths 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 whole number.
- a. $\frac{\text{3}}{\text{3}}$

- b. $\frac{\text{5}}{\text{10}}$

- c. $\frac{\text{8}}{\text{2}}$

- d. $\frac{\text{15}}{\text{7}}$

- e. $\frac{\text{1}}{\text{6}}$

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

## 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