MA.4.FR.2.4

Extend previous understanding of multiplication to explore the multiplication of a fraction by a whole number or a whole number by a fraction.

Examples

Example: Shanice thinks about finding the product begin mathsize 12px style 1 fourth cross times 8 end style by imagining having 8 pizzas that she wants to split equally with three of her friends. She and each of her friends will get 2 pizzas since begin mathsize 12px style 1 fourth cross times 8 equals 2 end style.

Example: Lacey thinks about finding the product begin mathsize 12px style 8 cross times 1 fourth end style by imagining having 8 pizza boxes each with one-quarter slice of a pizza left. If she put them all together, she would have a total of 2 whole pizzas since begin mathsize 12px style 8 cross times 1 fourth equals 8 over 4 end style which is equivalent to 2.

Clarifications

Clarification 1: Instruction includes the use of visual models or number lines and the connection to the commutative property of multiplication. Refer to Properties of Operation, Equality and Inequality (Appendix D).

Clarification 2: Within this benchmark, the expectation is not to simplify or use lowest terms.

Clarification 3: Fractions multiplied by a whole number are limited to less than 1. All denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16, 100.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Strand: Fractions
Status: State Board Approved

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))
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.4.FR.2.AP.4: Explore the multiplication of a unit fraction by a whole number (e.g., 3 × 1/4, 2 × 1/6, 5 × 1/2). Denominators limited to 2, 3, 4, 6, 8 or 10.

Related Resources

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

Educational Game

Ice Ice Maybe: An Operations Estimation Game:


This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

Formative Assessments

How Much Sugar?:

Students are asked to multiply a fraction by a whole number to solve a word problem and to represent the product with a visual fraction model.

Type: Formative Assessment

Training for a Race:

Students are asked to multiply an improper fraction by a whole number to solve a word problem and use a visual model or equation to represent the problem.

Type: Formative Assessment

How Many One Fourths?:

Students are asked to multiply a fraction by a whole number and to represent the product with a visual fraction model.

Type: Formative Assessment

Multiplying Fractions by Whole Numbers:

Students are asked to consider an equation involving multiplication of a fraction by a whole number and create a visual fraction model. Additionally, the student is asked to interpret multiplying the number of parts by the whole number.

Type: Formative Assessment

Fractions and Multiples:

Students use a visual fraction model to explain how many one sixths are in begin mathsize 11px style 13 over 6 end style and record their work with an equation.

Type: Formative Assessment

Image/Photograph

Clipart ETC Fractions:

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Type: Image/Photograph

Lesson Plans

Modeling Multiple Groups of Fractions:

In this inquiry lesson students will use a situational story to explore ways to find the total quantity of a fraction multiplied by a whole number using various models.

Type: Lesson Plan

Multiple Bake Sale Cookie Recipes with fractional ingredients:

In this lesson students will explore ways to find the product of mixed numbers multiplied by a whole number using a real-world situation.

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

Looking for Patterns in a Sequence of Fractions:

Students generate and describe a numerical pattern using the multiplication and subtraction of fractions.

Type: Lesson Plan

Exploring Fraction Multiplication:

Students will link multiplication of a whole number times a fraction with repeated addition and fraction circle manipulative. 

Type: Lesson Plan

Modeling Multiplication with Fractions:

Students will relate multiplication strategies with fractions through problem solving situations. This lesson connects prior understanding of multiplication and equal groups to multiplication of fractions.

Type: Lesson Plan

Multiple Bake Sale Cookie Recipes with fractional ingredients PART 1:

In this lesson students are guided through the process of multiplying a whole number and a fraction in a real-world situation.  The lesson uses the number line to explain the process.

Type: Lesson Plan

Multiply Fractions and Whole Numbers with Models:

Students will multiply a whole number by a fraction through set models and problem solving.

Type: Lesson Plan

Volunteering with the Mayor:

The mayor wants to build a new park in town! Volunteer your time and help the mayor design an expense report with a given budget for the new park in this lesson.

Type: Lesson Plan

Original Student Tutorial

Multiplying Fractions with Bake Sale Mania:

Find the total amounts of repeated fraction quantities by multiplying a fraction by a whole number using visual models that represent real-world problems and cookies in this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Tasks

Sugar in six cans of soda:

This task provides a familiar context allowing students to visualize multiplication of a fraction by a whole number. This task could form part of a very rich activity which includes studying soda can labels.

Type: Problem-Solving Task

Connor and Makayla Discuss Multiplication:

The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.

Type: Problem-Solving Task

Tutorial

Multiplying a Fraction by a Whole Number:

In this Khan Academy video visual fraction models are used to represent the multiplication of a whole number times a fraction.

Type: Tutorial

MFAS Formative Assessments

Fractions and Multiples:

Students use a visual fraction model to explain how many one sixths are in begin mathsize 11px style 13 over 6 end style and record their work with an equation.

How Many One Fourths?:

Students are asked to multiply a fraction by a whole number and to represent the product with a visual fraction model.

How Much Sugar?:

Students are asked to multiply a fraction by a whole number to solve a word problem and to represent the product with a visual fraction model.

Multiplying Fractions by Whole Numbers:

Students are asked to consider an equation involving multiplication of a fraction by a whole number and create a visual fraction model. Additionally, the student is asked to interpret multiplying the number of parts by the whole number.

Training for a Race:

Students are asked to multiply an improper fraction by a whole number to solve a word problem and use a visual model or equation to represent the problem.

Original Student Tutorials Mathematics - Grades K-5

Multiplying Fractions with Bake Sale Mania:

Find the total amounts of repeated fraction quantities by multiplying a fraction by a whole number using visual models that represent real-world problems and cookies in this interactive tutorial.

Student Resources

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

Original Student Tutorial

Multiplying Fractions with Bake Sale Mania:

Find the total amounts of repeated fraction quantities by multiplying a fraction by a whole number using visual models that represent real-world problems and cookies in this interactive tutorial.

Type: Original Student Tutorial

Educational Game

Ice Ice Maybe: An Operations Estimation Game:


This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

Problem-Solving Tasks

Sugar in six cans of soda:

This task provides a familiar context allowing students to visualize multiplication of a fraction by a whole number. This task could form part of a very rich activity which includes studying soda can labels.

Type: Problem-Solving Task

Connor and Makayla Discuss Multiplication:

The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.

Type: Problem-Solving Task

Tutorial

Multiplying a Fraction by a Whole Number:

In this Khan Academy video visual fraction models are used to represent the multiplication of a whole number times a fraction.

Type: Tutorial

Parent Resources

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

Image/Photograph

Clipart ETC Fractions:

Illustrations that can be used for teaching and demonstrating fractions. Fractional representations are modeled in wedges of circles ("pieces of pie") and parts of polygons. There are also clipart images of numerical fractions, both proper and improper, from halves to twelfths. Fraction charts and fraction strips found in this collection can be used as manipulatives and are ready to print for classroom use.

Type: Image/Photograph

Problem-Solving Tasks

Sugar in six cans of soda:

This task provides a familiar context allowing students to visualize multiplication of a fraction by a whole number. This task could form part of a very rich activity which includes studying soda can labels.

Type: Problem-Solving Task

Connor and Makayla Discuss Multiplication:

The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.

Type: Problem-Solving Task