# MA.4.FR.1.3

Identify and generate equivalent fractions, including fractions greater than one. Describe how the numerator and denominator are affected when the equivalent fraction is created.

### 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.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Fractions
Status: State Board Approved

## Benchmark Instructional Guide

• NA

### Vertical Alignment

Previous Benchmarks

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### 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:

Divide the number line below into enough equal sections so that you can locate and label the point $\frac{\text{2}}{\text{5}}$. Divide the same number line with a different color so that you can locate and label the point $\frac{\text{4}}{\text{10}}$. Discuss what you have learned.

### Instructional Items

Instructional Item 1

Olivia modeled a fraction by shading parts of the rectangle as shown.

Ethan draws a rectangle with the same size to model a fraction equivalent to Olivia’s. Which rectangle could Ethan have drawn?

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

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.FR.1.AP.3: Using a visual model, generate fractions less than a whole that are equivalent to fractions with denominators 2, 3, 4, 6, 8 or 10. Explore how the numerator and denominator are affected when the equivalent fraction is created.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Educational Games

Flower Power: An Ordering of Rational Numbers Game:

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

Fraction Quiz:

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

## Formative Assessments

Equivalent Fractions on a Number Line:

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

Type: Formative Assessment

Equivalence Using A Number Line:

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

Type: Formative Assessment

Eating Cake:

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

Type: Formative Assessment

Are the Fractions Equivalent:

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

Type: Formative Assessment

## Lesson Plans

Majority Rules:

Students will use the benchmark fraction ½ to estimate and compare fractions and make a connection to achieving a simple majority when voting during this integrated lesson.

Type: Lesson Plan

The Alternative Recipe:

The students follow a scaffold model starting with using concrete models of fractions with the fraction tiles to create equivalent fractions, and then by using prior knowledge of multiples to develop the algorithm for creating equivalent fractions.  The algorithm noted here is based on the identity property of multiplying a fraction times a fraction so you are multiplying by 2/2 or 3/3.

Type: Lesson Plan

Create a Quilt - Equivalent Fractions:

In this lesson, students will apply their knowledge of identifying and creating equivalent fractions.  The use of tiles allows a visual check of their equivalent fraction creations using parts of a set.

Type: Lesson Plan

Fraction Land II:

This  is an application lesson for the students’ knowledge of how to identify or create equivalent fractions. After a review, they are expected to multiply or divide to create equivalent fractions.

Type: Lesson Plan

Fraction Land:

This lesson uses paper strips to show equivalent fractions.  It discusses what happens to the denominator and numerator as students learn to multiply to make equivalent fractions. It is part of a series about identifying and creating equivalent fractions. All lessons in the series share the Fraction Land title and are available on CPALMS.

Type: Lesson Plan

"What's the part? What's the whole?":

This lesson provides a conceptual approach to multiplying a fraction times a whole number and a whole number times a fraction.  Students are to use an understanding of the meaning of the denominator and numerator to figure out a strategy for finding the solution.

Type: Lesson Plan

Equivalent Fraction Dominoes:

Students will identify equivalent fractions to 1/2 using manipulatives and determine what happened to the numerator and denominator when an equivalent fraction was formed.  They will practice this idea by identifying equivalent fractions in a domino game.

Type: Lesson Plan

Gettin' Fancy with Fractions:

In this lesson, students engage in problem solving, a fraction sort activity and play the game "Fraction War" to practice and demonstrate understanding of using benchmark quantities when comparing fractions with different numerators and denominators.  This lesson is not intended as initial instruction on using benchmark quantities to compare fractions.  Instead, it may be useful for skill reinforcement, student engagement, and formative assessment of skill mastery.  Parts of this lesson could be revisited periodically as students build comfort and mastery comparing fractions.

Type: Lesson Plan

The Brownie Breakdown:

This lesson demonstrates the relationships between equivalent fractions and the size of the pieces that represent the fractions. The lesson moves from concrete activities to pictorial representations. The lesson begins by using a pan of brownies to represent equivalent fractions. The brownies will help to engage students as the lesson moves from the concrete to the pictorial representation of equivalent fractions.

Type: Lesson Plan

Chocolate Fractions:

Chocolate bars will be used to introduce equivalent fractions. Students will find patterns for equivalent fractions through the concrete-representational-abstract process.

Type: Lesson Plan

Equivalent Fraction Dominoes:

Students will identify equivalent fractions to 1/2 using manipulatives and determine what happened to the numerator and denominator when an equivalent fraction was formed.  They will practice this idea by identifying equivalent fractions in a domino game.

Type: Lesson Plan

Fraction Measuring With Cuisenaire Rods:

In this lesson, students will use Cuisenaire rods to measure lengths and generate equivalent fractions. This is a concrete way to introduce how to generate equivalent fractions by finding patterns in the numerators and denominators.

Type: Lesson Plan

Party Entertainment:

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

Type: Lesson Plan

## Original Student Tutorials

Equivalent Fractions Part 1: Sharing at the Shelter:

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

Equivalent Fractions, Part 2: Patterns in the Multiplication Table:

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

## Perspectives Video: Teaching Ideas

Exploring Fractions with Pattern Blocks:

Unlock an effective teaching strategy for using pattern blocks to explore fraction concepts in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Using Manipulatives to Create Stem and Leaf Plots:

Unlock an effective teaching strategy for teaching stem and leaf plots in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Explaining Fraction Equivalence with Pictures:

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.

Running Laps:

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.

## Tutorial

Equivalent Fractions: Visual Models:

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

Type: Tutorial

## Virtual Manipulative

Fraction Game:

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

Type: Virtual Manipulative

## STEM Lessons - Model Eliciting Activity

Party Entertainment:

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

Are the Fractions Equivalent:

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

Eating Cake:

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

Equivalence Using A Number Line:

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

Equivalent Fractions on a Number Line:

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

Equivalent Fractions Part 1: Sharing at the Shelter:

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.

Equivalent Fractions, Part 2: Patterns in the Multiplication Table:

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

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Equivalent Fractions Part 1: Sharing at the Shelter:

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

Equivalent Fractions, Part 2: Patterns in the Multiplication Table:

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

Flower Power: An Ordering of Rational Numbers Game:

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

Fraction Quiz:

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

Explaining Fraction Equivalence with Pictures:

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.

Running Laps:

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.

## Tutorial

Equivalent Fractions: Visual Models:

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

Type: Tutorial

## Virtual Manipulative

Fraction Game:

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

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.