# MAFS.5.NF.1.1

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
General Information
Subject Area: Mathematics
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Use equivalent fractions as a strategy to add and subtract fractions. (Major Cluster) -

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.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :

Fractions greater than 1 and mixed numbers may be included. Expressions may have up to three terms. Least common denominator is not necessary to calculate sums or differences of fractions. Items may not use the terms “simplify” or “lowest terms.” For given fractions in items, denominators are limited to 1-20. Items may require the use of equivalent fractions to find a missing term or part of a term.

• Calculator :

No

• Context :

No context

Sample Test Items (3)

## Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond (current))
5020120: STEM Lab Grade 5 (Specifically in versions: 2016 - 2022 (current), 2022 and beyond)
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.5.NF.1.AP.1a: Add and subtract fractions with like denominators with sums greater than 1 represented by mixed numbers using visual fraction models.
MAFS.5.NF.1.AP.1b: Add or subtract fractions with unlike denominators within one whole unit on a number line.

## Related Resources

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

## Assessments

Sample 3 - Fifth Grade Math State Interim Assessment:

This is a State Interim Assessment for fifth grade.

Type: Assessment

Sample 1 - Fifth Grade Math State Interim Assessment:

This is a State Interim Assessment for fifth grade.

Type: Assessment

## 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

Adding More Fractions with Unlike Denominators:

Type: Formative Assessment

Students are asked to add two pairs of fractions with unlike denominators.

Type: Formative Assessment

Subtracting More Fractions:

Students are asked to subtract improper fractions and mixed numbers with unlike denominators.

Type: Formative Assessment

Subtracting Fractions:

Students are asked to subtract fractions with unlike denominators.

Type: Formative Assessment

## Lesson Plans

Aaron and Anya's Discovery: Adding Fractions with Unlike Denominators:

In this situational story, Aaron and Anya find several pieces of ribbon/cord of varying fractional lengths. They decide to choose 3 pieces and make a belt. All of the fractions have different denominators; students have to determine common denominators in order to add the fractional pieces. After students successfully add three fractional pieces, they make a belt and label it with their fractional pieces.

Type: Lesson Plan

Babysitter's Club Fun with Fractions MEA:

In this MEA, students will apply their knowledge of adding, subtracting, and comparing fractions with like and unlike denominators. Babysitters 'R Us will require students to analyze data in the form of fractional units of time in order to select the best babysitter for the Cryin' Ryan family.

Type: Lesson Plan

Using Models to Add Fractions with Unlike Denominators:

This lesson is specific to adding fractions with unlike denominators. It requires students to already have a working knowledge of adding fractions with common denominators, and equivalent fractions. Subtracting fractions with unlike denominators will follow in a subsequent lesson, as the two should be taught on separate days.

Type: Lesson Plan

Adding and Subtracting Mixed Numbers with Unlike Denominators:

This lesson helps fifth graders combine their understanding of adding and subtracting fractions with unlike denominators, finding equivalent fractions, and adding and subtracting mixed numbers with like denominators to move on to adding and subtracting mixed numbers with unlike denominators.

Type: Lesson Plan

Discovering Common Denominators:

Students use pattern blocks to represent fractions with unlike denominators. Students discover that they need to convert all the pattern blocks to the same shape in order to add them. Therefore, they find and use common denominators for the addition of fractions.

Type: Lesson Plan

## Original Student Tutorial

Adding Potions with Unlike Fractions Part 1:

Explore how to add fractions less than one with unlike denominators in this magical, interactive tutorial.

Type: Original Student Tutorial

Mixed Numbers with Unlike Denominators:

The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting. The two primary ways one can expect students to add are converting the mixed numbers to fractions greater than 1 or adding the whole numbers and fractional parts separately. It is good for students to develop a sense of which approach would be better in a particular context.

Making S'Mores:

The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context.

Jog-A-Thon:

The purpose of this task is to present students with a situation where it is natural to add fractions with unlike denominators; it can be used for either assessment or instructional purposes. Teachers should anticipate two types of solutions: one where students calculate the distance Alex ran to determine an answer, and one where students compare the two parts of his run to benchmark fractions.

Finding Common Denominators to Subtract:

Part (a) of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. Part (b) does not ask students to do it in more than one way; the purpose is to give them an opportunity to choose a denominator and possibly compare with another student who chose a different denominator. The purpose of part (c) is to help students move away from a reliance on drawing pictures. Students can draw a picture if they want, but this subtraction problem is easier to do symbolically, which helps students appreciate the power of symbolic notation.

Part (a) of this task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator. Part (b) does not ask students to solve the given addition problem in more than one way. Instead, the purpose of this question is to give students an opportunity to choose a denominator and possibly to compare their solution method with another student who chose a different denominator.  The purpose of part (c) is to give students who are ready to work symbolically a chance to work more efficiently.

Egyptian Fractions:

One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions.

## Student Center Activity

Fractions Jigsaw:

This problem provides students an opportunity to find equivalent fractions and carry out some simple additions and subtractions of fractions in a context that may challenge and motivate students. Users need to download, print, and cut-out the fraction jigsaw. Then, they must arrange the square pieces right-side up so that the edges that touch contain equivalent fractions. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, and ideas for extension and support.

Type: Student Center Activity

## Teaching Idea

Kahn Academy video - How to add and subtract fractions with like and unlike denominators.

Type: Teaching Idea

## Tutorials

Creating Common Denominators:

This tutorial explores the addition and subtraction of fractions with unlike denominators. Performing these operations on fractions with unlike denominators requires the creation of a 'common' denominator. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd).

Type: Tutorial

Least Common Denominators:

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases. Sometimes when finding a common denominator, an unnecessarily large common denominator is created (a/b x c/d = ad + bc/bd). This chapter explains how to find the smallest possible common denominator. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

In this web-based tutorial, students learn procedures for adding fractions with like and unlike denominators. The tutorial includes visual representations of the problems using pizzas, animations of the algorithm, and links to related lessons, worksheets, and practice problems.

Type: Tutorial

Subtracting Fractions:

In this web-based tutorial, students learn procedures for subtracting fractions. The tutorial includes visual representations of the problems using pizzas, animations of the algorithm, and links to related lessons, worksheets, and practice problems.

Type: Tutorial

## Virtual Manipulatives

Fractions - Adding (with Unlike Denominators):

This resource from the National Library of Virtual Manipulatives shows students how to rename fractions to have a common denominator and then add them. It is appealing because it visually engages the students by showing them what happens to a unit (a rectangle is used here) as the denominator increases or decreases. As the denominator increases or decreases, the partitions are shown accordingly, and the effect on the numerator is shown as well. This is a convenient, visual way to show students how to manipulate fractions for adding.

Type: 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

Diffy Virtual Manipulative:

Diffy is a virtual manipulative that allows students to practice their subtraction facts with whole numbers, integers, fractions, decimals, or money. It is a puzzle of sorts with four black numbers placed at the corners of a black square. The first goal is to fill in the four blanks in the blue circles in the middle of each side of the black square.

Type: Virtual Manipulative

## STEM Lessons - Model Eliciting Activity

Babysitter's Club Fun with Fractions MEA:

In this MEA, students will apply their knowledge of adding, subtracting, and comparing fractions with like and unlike denominators. Babysitters 'R Us will require students to analyze data in the form of fractional units of time in order to select the best babysitter for the Cryin' Ryan family.

## MFAS Formative Assessments

Students are asked to add two pairs of fractions with unlike denominators.

Adding More Fractions with Unlike Denominators:

Subtracting Fractions:

Students are asked to subtract fractions with unlike denominators.

Subtracting More Fractions:

Students are asked to subtract improper fractions and mixed numbers with unlike denominators.

## Original Student Tutorials Mathematics - Grades K-5

Adding Potions with Unlike Fractions Part 1:

Explore how to add fractions less than one with unlike denominators in this magical, interactive tutorial.

## Student Resources

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

## Original Student Tutorial

Adding Potions with Unlike Fractions Part 1:

Explore how to add fractions less than one with unlike denominators in this magical, interactive tutorial.

Type: Original Student Tutorial

## 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

Mixed Numbers with Unlike Denominators:

The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting. The two primary ways one can expect students to add are converting the mixed numbers to fractions greater than 1 or adding the whole numbers and fractional parts separately. It is good for students to develop a sense of which approach would be better in a particular context.

Making S'Mores:

The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context.

Jog-A-Thon:

The purpose of this task is to present students with a situation where it is natural to add fractions with unlike denominators; it can be used for either assessment or instructional purposes. Teachers should anticipate two types of solutions: one where students calculate the distance Alex ran to determine an answer, and one where students compare the two parts of his run to benchmark fractions.

Finding Common Denominators to Subtract:

Part (a) of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. Part (b) does not ask students to do it in more than one way; the purpose is to give them an opportunity to choose a denominator and possibly compare with another student who chose a different denominator. The purpose of part (c) is to help students move away from a reliance on drawing pictures. Students can draw a picture if they want, but this subtraction problem is easier to do symbolically, which helps students appreciate the power of symbolic notation.

Part (a) of this task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator. Part (b) does not ask students to solve the given addition problem in more than one way. Instead, the purpose of this question is to give students an opportunity to choose a denominator and possibly to compare their solution method with another student who chose a different denominator.  The purpose of part (c) is to give students who are ready to work symbolically a chance to work more efficiently.

Egyptian Fractions:

One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions.

## Tutorials

Creating Common Denominators:

This tutorial explores the addition and subtraction of fractions with unlike denominators. Performing these operations on fractions with unlike denominators requires the creation of a 'common' denominator. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd).

Type: Tutorial

Least Common Denominators:

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases. Sometimes when finding a common denominator, an unnecessarily large common denominator is created (a/b x c/d = ad + bc/bd). This chapter explains how to find the smallest possible common denominator. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

## Virtual Manipulatives

Fractions - Adding (with Unlike Denominators):

This resource from the National Library of Virtual Manipulatives shows students how to rename fractions to have a common denominator and then add them. It is appealing because it visually engages the students by showing them what happens to a unit (a rectangle is used here) as the denominator increases or decreases. As the denominator increases or decreases, the partitions are shown accordingly, and the effect on the numerator is shown as well. This is a convenient, visual way to show students how to manipulate fractions for adding.

Type: 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

Diffy Virtual Manipulative:

Diffy is a virtual manipulative that allows students to practice their subtraction facts with whole numbers, integers, fractions, decimals, or money. It is a puzzle of sorts with four black numbers placed at the corners of a black square. The first goal is to fill in the four blanks in the blue circles in the middle of each side of the black square.

Type: Virtual Manipulative

## Parent Resources

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

Mixed Numbers with Unlike Denominators:

The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting. The two primary ways one can expect students to add are converting the mixed numbers to fractions greater than 1 or adding the whole numbers and fractional parts separately. It is good for students to develop a sense of which approach would be better in a particular context.

Making S'Mores:

The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context.

Jog-A-Thon:

The purpose of this task is to present students with a situation where it is natural to add fractions with unlike denominators; it can be used for either assessment or instructional purposes. Teachers should anticipate two types of solutions: one where students calculate the distance Alex ran to determine an answer, and one where students compare the two parts of his run to benchmark fractions.

Finding Common Denominators to Subtract:

Part (a) of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. Part (b) does not ask students to do it in more than one way; the purpose is to give them an opportunity to choose a denominator and possibly compare with another student who chose a different denominator. The purpose of part (c) is to help students move away from a reliance on drawing pictures. Students can draw a picture if they want, but this subtraction problem is easier to do symbolically, which helps students appreciate the power of symbolic notation.

Part (a) of this task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator. Part (b) does not ask students to solve the given addition problem in more than one way. Instead, the purpose of this question is to give students an opportunity to choose a denominator and possibly to compare their solution method with another student who chose a different denominator.  The purpose of part (c) is to give students who are ready to work symbolically a chance to work more efficiently.

Egyptian Fractions:

One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions.

## Tutorials

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

Subtracting Fractions:

In this web-based tutorial, students learn procedures for subtracting fractions. The tutorial includes visual representations of the problems using pizzas, animations of the algorithm, and links to related lessons, worksheets, and practice problems.

Type: Tutorial

## Virtual Manipulatives

Fractions - Adding (with Unlike Denominators):

This resource from the National Library of Virtual Manipulatives shows students how to rename fractions to have a common denominator and then add them. It is appealing because it visually engages the students by showing them what happens to a unit (a rectangle is used here) as the denominator increases or decreases. As the denominator increases or decreases, the partitions are shown accordingly, and the effect on the numerator is shown as well. This is a convenient, visual way to show students how to manipulate fractions for adding.

Type: Virtual Manipulative

Diffy Virtual Manipulative:

Diffy is a virtual manipulative that allows students to practice their subtraction facts with whole numbers, integers, fractions, decimals, or money. It is a puzzle of sorts with four black numbers placed at the corners of a black square. The first goal is to fill in the four blanks in the blue circles in the middle of each side of the black square.

Type: Virtual Manipulative