Standard #: MAFS.4.NF.2.4 (Archived Standard)


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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
Grade: 4
Domain-Subdomain: Number and Operations - Fractions
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 Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    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 # Question Difficulty Type
Sample Item 1

Daniella fills a container with soil by using a bowl. The bowl holds begin mathsize 12px style 3 over 4 end style cup of soil. Daniella uses 13 full bowls of soil to fill the container.

How many cups of soil does the container hold?

N/A EE: Equation Editor


Related Courses

Course Number1111 Course Title222
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 Resources

Assessments

Name Description
Sample 4 - Fourth Grade Math State Interim Assessment

This is a State Interim Assessment for fourth grade.

Sample 3 - Fourth Grade Math State Interim Assessment

This is a State Interim Assessment for fourth grade.

Sample 2 - Fourth Grade Math State Interim Assessment

This is a State Interim Assessment for fourth grade.

Sample 1 - Fourth Grade Math State Interim Assessment

This is a State Interim Assessment for fourth grade.

Educational Games

Name Description
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.

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.

Formative Assessments

Name Description
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.

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.

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.

Lesson Plans

Name Description
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.

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.

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.

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.

"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. 

Looking for Patterns in a Sequence of Fractions

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

Exploring Fraction Multiplication

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

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.

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.

Multiply Fractions and Whole Numbers with Models

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

Original Student Tutorials

Name Description
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.

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.

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.

Problem-Solving Tasks

Name Description
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

Name Description
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.

Student Resources

Original Student Tutorials

Name Description
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.

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.

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.

Educational Games

Name Description
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.

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.

Problem-Solving Tasks

Name Description
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

Name Description
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.



Parent Resources

Problem-Solving Tasks

Name Description
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.



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