### Clarifications

*Clarification 1:*Instruction includes the use of manipulatives, visual models, number lines or equations.

*Clarification 2: *Instruction includes recognizing how the numerator and denominator are affected when equivalent fractions are generated.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**4

**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

- NA

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to begin generating equivalent fractions. This work builds on identifying equivalent fractions in grade 3 (MA.3.FR.2.2) and builds the foundation for adding and subtracting fractions with unlike denominators in grade 5 (MA.5.FR.2.1).- For instruction, students should use multiple models to develop an understanding of equivalent fractions (MTR.2.1). Students can use area models, set models, number lines, and equations to determine and generate equivalent fractions.
- Area Model

- Number Lines

- Instruction should focus on reasoning about how the numerator and denominators are affected when equivalent fractions are generated.
- Reasoning about the size of a fraction using benchmark fractions helps solidify students’ understanding of the size of the fraction.
- Instruction includes fractions equal to and greater than one.

### Common Misconceptions or Errors

- Students may think that when generating equivalent fractions, they need to multiply or divide only the numerator or only denominator, such as changing $\frac{\text{3}}{\text{4}}$ to $\frac{\text{3}}{\text{8}}$.

### 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 $\frac{\text{2}}{\text{5}}$ and $\frac{\text{4}}{\text{10}}$, conversation includes that both fraction models are the same size. So, when comparing them, we are comparing the same size whole. Students should be able to see that 2 out of the 5 are shaded in the first model and 4 out of the 10 are shaded in the second model, making the $\frac{\text{2}}{\text{5}}$ equal to $\frac{\text{4}}{\text{10}}$.

- Instruction includes fraction tiles or fraction kits to physically place and see equivalent fractions of a model. Students line up fraction tiles and begin to make observations about equivalence. One-half is equivalent to 2 one-fourth pieces. Students then notice that those pieces are equivalent to 4 one-eighth pieces. Once students have this understanding, then they can begin to rename fractions.
- Example:

### Instructional Tasks

*Instructional Task 1* (MTR.4.1)

### Instructional Items

*Instructional Item 1 *

**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

## Educational Games

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Teaching Ideas

## Problem-Solving Tasks

## Tutorial

## Virtual Manipulative

## STEM Lessons - Model Eliciting Activity

In this MEA, students will decide which entertainer an owner of an entertainment company should hire. They will base their decisions on information provided on resumes. Students will calculate the cost of hiring the entertainer (multiplication of whole numbers) as well as compare the statistics of their talent competitions and attendance turn-out (comparing fractions). Students will write letters to the owner of the entertainment company ranking the entertainers and providing explanation and justification of their strategy for doing so.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

## MFAS Formative Assessments

Students partition squares to model two fractions and then determine if the fractions are equivalent.

Students draw a visual fraction model to determine whether two fractions are equivalent.

Students use a number line to explain that one-half is equivalent to two-fourths.

Students scale number lines to locate given fractions, find equivalent fractions, and explain the relationship between equivalent fractions.

## Original Student Tutorials Mathematics - Grades K-5

Learn how to create equivalent fractions and visually see how they are equivalent in this interactive tutorial.

This is part 1 of a 2-part series. Click **HERE **to open Part 2.

Learn how to find equivalent fractions in a multiplication table in this interactive tutorial.

This is part 2 of a 2 part series. Click **HERE** to open Part 1.

## Student Resources

## Original Student Tutorials

Learn how to create equivalent fractions and visually see how they are equivalent in this interactive tutorial.

This is part 1 of a 2-part series. Click **HERE **to open Part 2.

Type: Original Student Tutorial

Learn how to find equivalent fractions in a multiplication table in this interactive tutorial.

This is part 2 of a 2 part series. Click **HERE** to open Part 1.

Type: Original Student Tutorial

## Educational Games

This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

Type: 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

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Students will need more opportunities to think about fraction equivalence with different examples and models, but this task represents a good first step.

Type: Problem-Solving Task

The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that. Some students might stop at the second-to-last picture and note that it looks like they ran the same distance, but the explanation is not yet complete at that point.

Type: Problem-Solving Task

## Tutorial

This Khan Academy video illustrates that fraction a/b is equivalent to fraction (a *x* n)/(b x n).

Type: Tutorial

## 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

## Problem-Solving Tasks

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Students will need more opportunities to think about fraction equivalence with different examples and models, but this task represents a good first step.

Type: Problem-Solving Task

The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that. Some students might stop at the second-to-last picture and note that it looks like they ran the same distance, but the explanation is not yet complete at that point.

Type: Problem-Solving Task