| Code |
Description |
| MA.4.FR.2.1: | Decompose a fraction, including mixed numbers and fractions greater than one, into a sum of fractions with the same denominator in multiple ways. Demonstrate each decomposition with objects, drawings and equations.Clarifications:
Clarification 1: Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100. |
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| MA.4.FR.2.2: | Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability.Clarifications:
Clarification 1: Instruction includes the use of word form, manipulatives, drawings, the properties of operations or number lines.
Clarification 2: Within this benchmark, the expectation is not to simplify or use lowest terms. Clarification 3: Denominators are limited to 2, 3, 4, 5, 6, 8, 10, 12, 16 and 100.
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| MA.4.FR.2.3: | Explore the addition of a fraction with denominator of 10 to a fraction with denominator of 100 using equivalent fractions.Clarifications:
Clarification 1: Instruction includes the use of visual models.
Clarification 2: Within this benchmark, the expectation is not to simplify or use lowest terms.
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| 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.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.
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This cluster includes the following access points.
| Access Point Number |
Access Point Title |
| MA.4.FR.2.AP.1: | Decompose a fraction less than one into a sum of unit fractions with the same denominator
(e.g.,  =  + + ). 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 × , 2 ×  , 5 ×  ). Denominators limited to 2, 3, 4, 6, 8 or 10. |
Vetted resources educators can use to teach the concepts and skills in this topic.
| 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. |
| 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. |
| 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. |
| Hundredths and Tenths: | Students are asked if an equation is true or false. Then students are asked to find the sum of two fractions. |
| 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. |
| 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. |
| 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. |
| Fractions and Multiples: | Students use a visual fraction model to explain how many one sixths are in  and record their work with an equation. |
| Adding and Subtracting Mixed Numbers: | Students are given pairs of mixed numbers to either add or subtract. |
| 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. |
| Decomposing Three-Fifths: | Students are asked to use a visual fraction model to decompose three-fifths in two different ways. |
| Name |
Description |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| Looking for Patterns in a Sequence of Fractions: | Students generate and describe a numerical pattern using the multiplication and subtraction of fractions. |
| Decomposing Fractions: | Using circle fraction manipulative, students will decompose fractions to discover adding fractions with like denominators. |
| 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. |
| Name |
Description |
| Adding Tenths and Hundredths: | The purpose of this task is adding fractions with a focus on tenths and hundredths. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Adding Tenths and Hundredths: | The purpose of this task is adding fractions with a focus on tenths and hundredths. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
| Title |
Description |
| Adding Tenths and Hundredths: | The purpose of this task is adding fractions with a focus on tenths and hundredths. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
