# MAFS.4.NF.2.4

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
1. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
2. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
3. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

### Clarifications

Examples of Opportunities for In-Depth Focus

This standard represents an important step in the multi-grade progression for multiplication and division of fractions. Students extend their developing understanding of multiplication to multiply a fraction by a whole number.
General Information
Subject Area: Mathematics
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (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 may only be multiplied by a whole number. Denominators of given fractions are limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.
• Calculator :

None

• Context :

Allowable

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

Daniella fills a container with soil by using a bowl. The bowl holds  cup of soil. Daniella uses 13 full bowls of soil to fill the container.

How many cups of soil does the container hold?

• Difficulty: N/A
• Type: EE: Equation Editor

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 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.4.NF.2.AP.4a: Multiply a fraction by a whole number using a visual fraction model.

## Related Resources

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

## Assessments

Sample 4 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 3 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 2 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 1 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

## Educational Games

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.

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

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

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

Fractions and Multiples:

Students use a visual fraction model to explain how many one sixths are in and record their work with an equation.

Type: Formative Assessment

## Lesson Plans

Birthday Balloon Planner:

Students will develop a model for choosing a balloon party planner and rank them from best to worst.

The students will be able to use prior knowledge of addition of multi-digit whole numbers, multiplication and division facts and concepts, math calculations with money and time, understanding fractions, and problem solving skills to solve a non-routine MEA (Model Eliciting Activity) that requires real-world application of mathematical skills.

Type: Lesson Plan

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

## 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

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

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.

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.

## 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

## STEM Lessons - Model Eliciting Activity

Birthday Balloon Planner:

Students will develop a model for choosing a balloon party planner and rank them from best to worst.

The students will be able to use prior knowledge of addition of multi-digit whole numbers, multiplication and division facts and concepts, math calculations with money and time, understanding fractions, and problem solving skills to solve a non-routine MEA (Model Eliciting Activity) that requires real-world application of mathematical skills.

## MFAS Formative Assessments

Fractions and Multiples:

Students use a visual fraction model to explain how many one sixths are in 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.

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

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 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.

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 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

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 Games

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.

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

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

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.

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.

## 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.