MAFS.5.NF.2.6Archived Standard

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
General Information
Subject Area: Mathematics
Grade: 5
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide 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 Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
    Assessed with: MAFS.5.NF.2.4 

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.

Related Resources

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

Formative Assessments

Pizza Party:

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

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

Lesson Plans

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

Wazzup Charter Schools Playground Dilemma MEA:

This Model Eliciting Activity (MEA) is written at a 5th grade level. The Wazzup Charter School MEA provides students with an engineering problem in which they must work as a team to design a procedure to select the best type of surface for a playground at a charter school.

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

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

Original Student Tutorials

Buffy's Bakery Part 4- Multiplying a Fraction by a Whole: Standard Algorithm:

Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.

This is part 4 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Buffy’s Bakery Part 3: Using Models to Multiply a Fraction by a Whole Number:

Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.

This is part 3 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Buffy's Bakery Part 2: Multiplying Fractions:

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

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

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

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

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.

Wazzup Charter Schools Playground Dilemma MEA:

This Model Eliciting Activity (MEA) is written at a 5th grade level. The Wazzup Charter School MEA provides students with an engineering problem in which they must work as a team to design a procedure to select the best type of surface for a playground at a charter school.

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.

MFAS Formative Assessments

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.

Pizza Party:

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

Original Student Tutorials Mathematics - Grades K-5

Buffy’s Bakery Part 3: Using Models to Multiply a Fraction by a Whole Number:

Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.

This is part 3 of a 4-part series. Click below to open other tutorials in the series.

Buffy's Bakery Part 2: Multiplying Fractions:

Buffy's Bakery Part 4- Multiplying a Fraction by a Whole: Standard Algorithm:

Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.

This is part 4 of a 4-part series. Click below to open other tutorials in the series.

Student Resources

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

Original Student Tutorials

Buffy's Bakery Part 4- Multiplying a Fraction by a Whole: Standard Algorithm:

Help Buffy multiply fractions by whole numbers using the standard algorithm in addition to visual fraction models in this bakery-themed, interactive tutorial.

This is part 4 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Buffy’s Bakery Part 3: Using Models to Multiply a Fraction by a Whole Number:

Help Buffy the Baker multiply a fraction by a whole using models in this sweet interactive tutorial.

This is part 3 of a 4-part series. Click below to open other tutorials in the series.

Type: Original Student Tutorial

Buffy's Bakery Part 2: Multiplying Fractions:

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

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

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

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

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

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