MA.5.AR.1.2

Solve real-world problems involving the addition, subtraction or multiplication of fractions, including mixed numbers and fractions greater than 1.

Examples

Shanice had a sleepover and her mom is making French toast in the morning. If her mom had begin mathsize 12px style 2 1 fourth end style

  loaves of bread and used begin mathsize 12px style 1 1 half end style loaves for the French toast, how much bread does she have left?

Clarifications

Clarification 1: Instruction includes the use of visual models and equations to represent the problem.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 5
Strand: Algebraic Reasoning
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 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.5.AR.1.AP.2a: Solve one-step real-world problems involving addition and subtraction of mixed numbers and fractions greater than one with like denominators.
MA.5.AR.1.AP.2b: Solve one-step real-world problems involving multiplication of unit fractions.

Related Resources

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

Formative Assessments

Maris Has a Party:

Students are given a word problem involving fractions with unlike denominators and are asked to estimate the sum, explain their reasoning, and then determine the sum.

Type: Formative Assessment

Sarah’s Hike:

Students are asked to estimate the difference between two fractional lengths and then calculate the difference.

Type: Formative Assessment

Pizza Party:

Students are asked to solve a word problem by finding the product of two fractions.

Type: Formative Assessment

Just Run:

Students are given a word problem involving subtraction of fractions with unlike denominators. Students are asked to determine if a given answer is reasonable, explain their reasoning, and calculate the answer.

Type: Formative Assessment

Half of a Recipe:

Students are asked to solve a word problem by finding the product of a fraction and a mixed number.

Type: Formative Assessment

Candy at the Party:

Students are asked to solve a word problem by finding the product of two mixed numbers.

Type: Formative Assessment

Box Factory:

Students are asked to solve a word problem by finding the product of two fractions.

Type: Formative Assessment

Baking Cakes:

Students are asked to estimate the sum of two mixed numbers and then calculate the sum.

Type: Formative Assessment

Lesson Plans

Let's Have a Fraction Party!:

In this lesson, students will use addition and subtraction of fractions with unlike denominators to solve word problems involving situations that arise with the children who were invited to a party. They will use fraction strips as number models and connect the algorithm with these real-life word problems.

Type: Lesson Plan

Fractions make the real WORLD problems go round:

In this lesson students will use a graphic organizer to to solve addition and subtraction word problems. Students will create their own word problems in PowerPoint, by using pen and paper, or dry erase boards to help them to connect to and understand the structure of word problems.  

Type: Lesson Plan

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

Real-World Fractions:

This lesson focuses on providing students with real-world experiences where they will be required to multiply fractions. Students will be required to use visual fraction models or equations to represent the problem.  This is a practice and application lesson, not an introductory lesson.

Type: Lesson Plan

Bill of Rights Billboard:

This MEA will deepen students' knowledge of the Bill of Rights through collaborative problem solving. Students are required to analyze data in order to recommend three Amendments to celebrate during a community festival.  They will perform operations with fractions and mixed numbers to recommend advertising options for the festival within a budget.

Type: Lesson Plan

Multiplying a Fraction by a Fraction:

In this lesson, students will solve problems related to training for a marathon to apply and make sense of multiplying fractions. The student will complete a function table to help illustrate patterns in the numerator/denominator relationships. This lesson utilizes the linear model as a concrete representation and moves towards the standard algorithm (a/b) x (c/d) = ac/bd.

Type: Lesson Plan

Are You Ready for a Hurricane?:

This activity allows students to determine the types of items that should be in a hurricane survival kit, use a budget and calculations to determine the items to include in the kit and gain an understanding of hurricanes and the need to prepare for them.

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. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Estimating Fractions Using Benchmark Fractions 0, 1/2, or 1:

In this lesson, students use models (fractions tiles or number lines) to round fractions using benchmark fractions of 0, 1/2, or 1.

Type: Lesson Plan

Garden Variety Fractions:

Students explore the multiplication of a fraction times a fraction through story problems about a garden using models on Geoboards and pictorial representations on grid paper. Students make a connection between their models and the numerical representation of the equation.

Type: Lesson Plan

Discovering Common Denominators:

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

Type: Lesson Plan

Original Student Tutorials

Making Art Part 2: Solving Addition and Subtraction Fraction Word Problems:

Learn to solve addition and subtraction word problems involving fractions with unlike denominators. As you complete this art-themed, interactive tutorial, you'll use visual models, write and solve equations, and check the reasonableness of results based on estimates.

This is part 2 of a two-part series. Click below to open part 1.

Type: Original Student Tutorial

Making Art Part 1: Estimating Adding and Subtracting Fractions Using Benchmarks:

Read word problems and use number lines with benchmarks to solve multi-step problems involving addition and subtraction of fractions with unlike denominators. In this tutorial, you will help Daisy and Angie paint pictures using fractions. 

Type: Original Student Tutorial

Samantha’s Shell-Collecting Adventure:

Learn to interpret data presented on a line plot and use operations on fractions to solve problems involving information presented in line plots as you complete this beach-themed, interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Computing Volume Progression 2:

Students are asked to find the volume of water in a tank that is 3/4 of the way full.

Type: Problem-Solving Task

Computing Volume Progression 3:

Students are asked to find the height of a rectangular prism when given the length, width and volume.

Type: Problem-Solving Task

Painting a Wall:

The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.

Type: Problem-Solving Task

Making Cookies:

This tasks lends itself very well to multiple solution methods. Students may learn a lot by comparing different methods. Students who are already comfortable with fraction multiplication can go straight to the numeric solutions given below. Students who are still unsure of the meanings of these operations can draw pictures or diagrams.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

To Multiply or not to multiply?:

The purpose of this task is to familiarize students with multiplying fractions with real-world questions.

Type: Problem-Solving Task

Salad Dressing:

The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.

Type: Problem-Solving Task

Running to School:

The task could be one of the first activities for introducing the multiplication of fractions.  The task has fractions which are easy to draw and provides a linear situation.  Students benefit from reasoning through the solution to such word problems before they are told that they can be solved by multiplying the fractions; this helps them develop meaning for fraction multiplication.

Type: Problem-Solving Task

Half of a Recipe:

This is the third problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. The first, Running to school, does not require that the unit fractions that comprise 3/4 be subdivided in order to find 1/3 of 3/4. The second task, Drinking Juice, does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2. This task also requires subdivision and involves multiplying a fraction and a mixed number.

Type: Problem-Solving Task

Drinking Juice:

This is the second problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. This task does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2.

Type: Problem-Solving Task

Do These Add Up?:

This task addresses common errors that students make when interpreting adding fractions word problems. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions.

Type: Problem-Solving Task

Teaching Idea

Space Math - Big Moons and Small Planets:

Students use a scale representation of the top 26 small planets and large moons in the solar system to compare their relative sizes to Earth. Students will use simple fractions to solve real world problems.

Type: Teaching Idea

STEM Lessons - Model Eliciting Activity

Are You Ready for a Hurricane?:

This activity allows students to determine the types of items that should be in a hurricane survival kit, use a budget and calculations to determine the items to include in the kit and gain an understanding of hurricanes and the need to prepare for them.

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. Click here to learn more about MEAs and how they can transform your classroom.

Bill of Rights Billboard:

This MEA will deepen students' knowledge of the Bill of Rights through collaborative problem solving. Students are required to analyze data in order to recommend three Amendments to celebrate during a community festival.  They will perform operations with fractions and mixed numbers to recommend advertising options for the festival within a budget.

MFAS Formative Assessments

Baking Cakes:

Students are asked to estimate the sum of two mixed numbers and then calculate the sum.

Box Factory:

Students are asked to solve a word problem by finding the product of two fractions.

Candy at the Party:

Students are asked to solve a word problem by finding the product of two mixed numbers.

Half of a Recipe:

Students are asked to solve a word problem by finding the product of a fraction and a mixed number.

Just Run:

Students are given a word problem involving subtraction of fractions with unlike denominators. Students are asked to determine if a given answer is reasonable, explain their reasoning, and calculate the answer.

Maris Has a Party:

Students are given a word problem involving fractions with unlike denominators and are asked to estimate the sum, explain their reasoning, and then determine the sum.

Pizza Party:

Students are asked to solve a word problem by finding the product of two fractions.

Sarah’s Hike:

Students are asked to estimate the difference between two fractional lengths and then calculate the difference.

Original Student Tutorials Mathematics - Grades K-5

Making Art Part 1: Estimating Adding and Subtracting Fractions Using Benchmarks:

Read word problems and use number lines with benchmarks to solve multi-step problems involving addition and subtraction of fractions with unlike denominators. In this tutorial, you will help Daisy and Angie paint pictures using fractions. 

Making Art Part 2: Solving Addition and Subtraction Fraction Word Problems:

Learn to solve addition and subtraction word problems involving fractions with unlike denominators. As you complete this art-themed, interactive tutorial, you'll use visual models, write and solve equations, and check the reasonableness of results based on estimates.

This is part 2 of a two-part series. Click below to open part 1.

Samantha’s Shell-Collecting Adventure:

Learn to interpret data presented on a line plot and use operations on fractions to solve problems involving information presented in line plots as you complete this beach-themed, interactive tutorial.

Student Resources

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

Original Student Tutorials

Making Art Part 2: Solving Addition and Subtraction Fraction Word Problems:

Learn to solve addition and subtraction word problems involving fractions with unlike denominators. As you complete this art-themed, interactive tutorial, you'll use visual models, write and solve equations, and check the reasonableness of results based on estimates.

This is part 2 of a two-part series. Click below to open part 1.

Type: Original Student Tutorial

Making Art Part 1: Estimating Adding and Subtracting Fractions Using Benchmarks:

Read word problems and use number lines with benchmarks to solve multi-step problems involving addition and subtraction of fractions with unlike denominators. In this tutorial, you will help Daisy and Angie paint pictures using fractions. 

Type: Original Student Tutorial

Samantha’s Shell-Collecting Adventure:

Learn to interpret data presented on a line plot and use operations on fractions to solve problems involving information presented in line plots as you complete this beach-themed, interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Computing Volume Progression 2:

Students are asked to find the volume of water in a tank that is 3/4 of the way full.

Type: Problem-Solving Task

Computing Volume Progression 3:

Students are asked to find the height of a rectangular prism when given the length, width and volume.

Type: Problem-Solving Task

Painting a Wall:

The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.

Type: Problem-Solving Task

Making Cookies:

This tasks lends itself very well to multiple solution methods. Students may learn a lot by comparing different methods. Students who are already comfortable with fraction multiplication can go straight to the numeric solutions given below. Students who are still unsure of the meanings of these operations can draw pictures or diagrams.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

To Multiply or not to multiply?:

The purpose of this task is to familiarize students with multiplying fractions with real-world questions.

Type: Problem-Solving Task

Salad Dressing:

The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.

Type: Problem-Solving Task

Running to School:

The task could be one of the first activities for introducing the multiplication of fractions.  The task has fractions which are easy to draw and provides a linear situation.  Students benefit from reasoning through the solution to such word problems before they are told that they can be solved by multiplying the fractions; this helps them develop meaning for fraction multiplication.

Type: Problem-Solving Task

Half of a Recipe:

This is the third problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. The first, Running to school, does not require that the unit fractions that comprise 3/4 be subdivided in order to find 1/3 of 3/4. The second task, Drinking Juice, does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2. This task also requires subdivision and involves multiplying a fraction and a mixed number.

Type: Problem-Solving Task

Drinking Juice:

This is the second problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. This task does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2.

Type: Problem-Solving Task

Do These Add Up?:

This task addresses common errors that students make when interpreting adding fractions word problems. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions.

Type: Problem-Solving Task

Parent Resources

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

Problem-Solving Tasks

Computing Volume Progression 2:

Students are asked to find the volume of water in a tank that is 3/4 of the way full.

Type: Problem-Solving Task

Computing Volume Progression 3:

Students are asked to find the height of a rectangular prism when given the length, width and volume.

Type: Problem-Solving Task

Painting a Wall:

The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.

Type: Problem-Solving Task

Making Cookies:

This tasks lends itself very well to multiple solution methods. Students may learn a lot by comparing different methods. Students who are already comfortable with fraction multiplication can go straight to the numeric solutions given below. Students who are still unsure of the meanings of these operations can draw pictures or diagrams.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

To Multiply or not to multiply?:

The purpose of this task is to familiarize students with multiplying fractions with real-world questions.

Type: Problem-Solving Task

Salad Dressing:

The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.

Type: Problem-Solving Task

Running to School:

The task could be one of the first activities for introducing the multiplication of fractions.  The task has fractions which are easy to draw and provides a linear situation.  Students benefit from reasoning through the solution to such word problems before they are told that they can be solved by multiplying the fractions; this helps them develop meaning for fraction multiplication.

Type: Problem-Solving Task

Half of a Recipe:

This is the third problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. The first, Running to school, does not require that the unit fractions that comprise 3/4 be subdivided in order to find 1/3 of 3/4. The second task, Drinking Juice, does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2. This task also requires subdivision and involves multiplying a fraction and a mixed number.

Type: Problem-Solving Task

Drinking Juice:

This is the second problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. This task does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2.

Type: Problem-Solving Task

Do These Add Up?:

This task addresses common errors that students make when interpreting adding fractions word problems. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions.

Type: Problem-Solving Task