Standard 2: Build a foundation of addition, subtraction and multiplication operations with fractions.

General Information
Number: MA.4.FR.2
Title: Build a foundation of addition, subtraction and multiplication operations with fractions.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 4
Strand: Fractions

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.4.FR.2.AP.1
Decompose a fraction less than one into a sum of unit fractions with the same denominator (e.g., begin mathsize 12px style 3 over 4 end style = begin mathsize 12px style 1 fourth end style+ begin mathsize 12px style 1 fourth end style + begin mathsize 12px style 1 fourth end style). Denominators limited to 2, 3, 4, 6, 8 or 10. Demonstrate each decomposition with objects, drawings or equations.
MA.4.FR.2.AP.2
Explore adding and subtracting fractions less than one with like denominators. Denominators limited to 2, 3, 4, 6, 8 or 10.
MA.4.FR.2.AP.3
Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using visual models to find equivalent fractions.
MA.4.FR.2.AP.4
Explore the multiplication of a unit fraction by a whole number (e.g., 3 × begin mathsize 12px style 1 fourth end style, 2 × begin mathsize 12px style 1 over 6 end style, 5 × begin mathsize 12px style 1 half end style). 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 topic.

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

Tenths and Hundredths:

Students are asked if an equation involving the sum of two fractions is true or false.  Then students are asked to find the sum of two fractions.

Type: Formative Assessment

Adding Five Tenths:

Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to another fraction with a denominator of 100.

Type: Formative Assessment

Hundredths and Tenths:

Students are asked if an equation is true or false. Then students are asked to find the sum of two fractions.

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

Seven Tenths:

Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to another fraction with a denominator of 100.

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

Adding and Subtracting Mixed Numbers:

Students are given pairs of mixed numbers to either add or subtract.

Type: Formative Assessment

Fraction Word Problems:

Students are asked to solve a word problem that involves subtracting fractions with like denominators. Students then analyze a word problem involving subtraction of unlike unit quantities.

Type: Formative Assessment

Decomposing Three-Fifths:

Students are asked to use a visual fraction model to decompose three-fifths in two different ways.

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

Lessen the Litter:

Students will calculate the total amount of trash at different locations in the community to determine which location has the most trash and explore ways a community can work together to prevent future trash buildup in this integrated lesson plan.

Type: Lesson Plan

Volunteering with the Mayor Part 2:

Volunteering is vital to keeping any community safe, inviting, and running smoothly! In this lesson, students will work together to plan a volunteer project they would like to see happen in their community; as well as, create a budget for their project.

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

The Cookie Jar Wants a New Cookie!:

This lesson asks students to recommend which cookie the owners of The Cookie Jar should add to their menu. Before they make their decision, the students have to convert fractions so they have like denominators. Once they have converted the fractions they will be able to see exactly how many people voted for each cookie and they can factor in that information along with additional cookie facts to make their final recommendation.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Relay Races:

In this lesson, students solve word problems related to races to determine addends of fractions with like denominators that sum to a fraction that is less than or equal to one and has the same denominator as the addends. The focus is on addition, decomposing a fraction into a sum of fractions in more than one way, drawing linear models, and writing equations to represent the problems.

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

Learning to Love Like Denominators:

Students engage in problem solving to explore the addition and subtraction of fractions with like denominators. Students make sense of the structure of addition and subtraction equations with like denominators and make generalizations to move from using manipulatives, pictures and number lines to simply adding or subtracting the numerator.

Type: Lesson Plan

Adding and Subtracting in the Real World with Unit Fractions:

Students will use unit fractions, and counting on or back by unit fractions, to solve addition and subtraction real world problems.

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

Decomposing Fractions:

Using circle fraction manipulative, students will decompose fractions to discover adding fractions with like denominators. 

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

Fractions at the Fair: Equivalent Tenths and Hundredths:

Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial.

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

The Leftover Dessert Dilemma:

Learn how to decompose a fraction into a sum of fractions with common denominators with this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

Perspectives Video: Teaching Ideas

Using Manipulatives to Add Fractions:

Unlock an effective teaching strategy for teaching adding fractions in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Making Connections Between Partitioning Circles and Circle Graphs:

Unlock an effective teaching strategy for connecting partitioning circles and circle graphs in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Decomposing Fractions in Multiple Ways:

Unlock an effective teaching strategy for decomposing fractions in multiple ways in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Exploring Fractions with Pattern Blocks:

Unlock an effective teaching strategy for using pattern blocks to explore fraction concepts in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Adding Tenths and Hundredths:

The purpose of this task is adding fractions with a focus on tenths and hundredths. 

Type: Problem-Solving Task

Making 22 Seventeenths in Different Ways:

This task is a straightforward task related to adding fractions with the same denominator. The main purpose is to emphasize that there are many ways to decompose a fraction as a sum of fractions.

Type: Problem-Solving Task

Expanded Fractions and Decimals:

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task

Writing a Mixed Number as an Equivalent Fraction:

The purpose of this task is to help students understand and articulate the reasons for the steps in the usual algorithm for converting a mixed number into an equivalent fraction. Step two shows that the algorithm is merely a shortcut for finding a common denominator between two fractions. This concept is an important precursor to adding mixed numbers and fractions with like denominators and as such, step two should be a point of emphasis. This task is appropriate for either instruction or formative assessment.

Type: Problem-Solving Task

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

Peaches:

This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes. For this particular task, teachers should anticipate two types of solution approaches: one where students subtract the whole numbers and the fractions separately and one where students convert the mixed numbers to improper fractions and then proceed to subtract.

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

Plastic Building Blocks:

The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task. Two general approaches should be anticipated: one where students calculate exactly how many buckets of blocks the boys have to determine an answer, and one where students compare the given numbers to benchmark numbers.

Type: Problem-Solving Task

Tutorials

Adding Two Fractions with Denominators 10 and 100:

The Khan Academy tutorial video presents a visual fraction model for adding 3/10 + 7/100 .

Type: 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

What Fraction of Spider Eyes are Looking at Me?:

This Khan Academy video uses authentic pictures to present addition of two fractions with common denominators.

Type: Tutorial

Figuring Out How Much of a Pizza is Left:

This Khan Academy video solves two word problems using visual fraction models.

Type: Tutorial

Adding Fractions:

In this web-based tutorial, students learn procedures for adding fractions with like and unlike denominators. The tutorial includes visual representations of the problems using pizzas, animations of the algorithm, and links to related lessons, worksheets, and practice problems.

Type: Tutorial

Virtual Manipulative

Fraction Game:

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

Student Resources

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

Original Student Tutorials

Fractions at the Fair: Equivalent Tenths and Hundredths:

Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial.

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

The Leftover Dessert Dilemma:

Learn how to decompose a fraction into a sum of fractions with common denominators with 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

Adding Tenths and Hundredths:

The purpose of this task is adding fractions with a focus on tenths and hundredths. 

Type: Problem-Solving Task

Making 22 Seventeenths in Different Ways:

This task is a straightforward task related to adding fractions with the same denominator. The main purpose is to emphasize that there are many ways to decompose a fraction as a sum of fractions.

Type: Problem-Solving Task

Expanded Fractions and Decimals:

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task

Writing a Mixed Number as an Equivalent Fraction:

The purpose of this task is to help students understand and articulate the reasons for the steps in the usual algorithm for converting a mixed number into an equivalent fraction. Step two shows that the algorithm is merely a shortcut for finding a common denominator between two fractions. This concept is an important precursor to adding mixed numbers and fractions with like denominators and as such, step two should be a point of emphasis. This task is appropriate for either instruction or formative assessment.

Type: Problem-Solving Task

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

Peaches:

This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes. For this particular task, teachers should anticipate two types of solution approaches: one where students subtract the whole numbers and the fractions separately and one where students convert the mixed numbers to improper fractions and then proceed to subtract.

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

Plastic Building Blocks:

The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task. Two general approaches should be anticipated: one where students calculate exactly how many buckets of blocks the boys have to determine an answer, and one where students compare the given numbers to benchmark numbers.

Type: Problem-Solving Task

Tutorials

Adding Two Fractions with Denominators 10 and 100:

The Khan Academy tutorial video presents a visual fraction model for adding 3/10 + 7/100 .

Type: 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

What Fraction of Spider Eyes are Looking at Me?:

This Khan Academy video uses authentic pictures to present addition of two fractions with common denominators.

Type: Tutorial

Figuring Out How Much of a Pizza is Left:

This Khan Academy video solves two word problems using visual fraction models.

Type: Tutorial

Virtual Manipulative

Fraction Game:

This virtual manipulative allows individual students to work with fraction relationships. (There is also a link to a two-player version.)

Type: Virtual Manipulative

Parent Resources

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

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

Adding Tenths and Hundredths:

The purpose of this task is adding fractions with a focus on tenths and hundredths. 

Type: Problem-Solving Task

Making 22 Seventeenths in Different Ways:

This task is a straightforward task related to adding fractions with the same denominator. The main purpose is to emphasize that there are many ways to decompose a fraction as a sum of fractions.

Type: Problem-Solving Task

Expanded Fractions and Decimals:

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Type: Problem-Solving Task

Writing a Mixed Number as an Equivalent Fraction:

The purpose of this task is to help students understand and articulate the reasons for the steps in the usual algorithm for converting a mixed number into an equivalent fraction. Step two shows that the algorithm is merely a shortcut for finding a common denominator between two fractions. This concept is an important precursor to adding mixed numbers and fractions with like denominators and as such, step two should be a point of emphasis. This task is appropriate for either instruction or formative assessment.

Type: Problem-Solving Task

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

Peaches:

This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes. For this particular task, teachers should anticipate two types of solution approaches: one where students subtract the whole numbers and the fractions separately and one where students convert the mixed numbers to improper fractions and then proceed to subtract.

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

Plastic Building Blocks:

The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task. Two general approaches should be anticipated: one where students calculate exactly how many buckets of blocks the boys have to determine an answer, and one where students compare the given numbers to benchmark numbers.

Type: Problem-Solving Task