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.
Related Standards
Related Access Points
Access Points
Related Resources
Educational Games
Formative Assessments
Lesson Plans
Original Student Tutorials
Problem-Solving Tasks
Professional Development
Teaching Ideas
Tutorials
Student Resources
Original Student Tutorials
Learn to divide whole numbers by unit fractions as you help Allie and Cameron create equal shares of candy and prizes for guests at a carnival in this interactive tutorial.
Type: Original Student Tutorial
Solve real-world word problems involving dividing a unit fraction by a whole number and dividing a whole number by a unit fraction using number lines in this chocolate-themed, interactive tutorial.
This is part 2 of a 2-part series. Click HERE to open "Chocolate Shop Challenge Part 1: Dividing Unit Fractions and Whole Numbers Using Fraction Bar Models"
Click HERE to open the related tutorial, "David Divides Desserts: Divide a Unit Fraction by a Whole Number"
Type: Original Student Tutorial
Divide unit fractions by whole numbers and divide whole numbers by unit fractions in this chocolate-themed, interactive tutorial.
This is part 1 of a 2-part series. Click HERE to open "Chocolate Shop Challenge Part 2: Dividing Unit Fractions and Whole Numbers Using Number Lines"
Type: Original Student Tutorial
Learn to solve word problems involving division of a unit fraction by a whole number by using models, expressions, equations, and strategic thinking in this interactive, dessert-themed tutorial.
Type: Original Student Tutorial
Learn how to divide a unit fraction by a whole number to share yummy picnic goodies equally in this interactive tutorial.
Type: Original Student Tutorial
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
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
Help Buffy the Baker multiply fractions less than one by relating the standard algorithm to visual models as he runs his bakery in this interactive tutorial.
This is part 2 of a 4-part series. Click below to open other tutorials in the series.
Type: Original Student Tutorial
Help Buffy the Baker use visual models to multiply fractions less than one as he runs his bakery in this interactive tutorial.
This is part 1 of a 4-part series. Click below to open other tutorials in the series.
- Part 2: Multiplying Fractions
- Part 3 Using Models to Multiply a Fraction by a Whole Number
- Part 4: Multiplying a Fraction by a Whole Number - Standard Algorithm
Type: Original Student Tutorial
Try to escape from this room using multiplication as scaling in this interactive tutorial.
Note: this tutorial is an introductory lesson on multiplying a given number without calculating before working with fractions.
Type: Original Student Tutorial
Learn how to define, declare and initialize variables as you start the journey to "bee" a coder in this interactive tutorial. Variables are structures used by computer programs to store information. You'll use your math skills to represent a fraction as a decimal to be stored in a variable.
This is part 1 of a 4-part series on coding. Click below to open the other tutorials in the series.
- Bee A Coder Part 2: Condition Statements
- Bee A Coder Part 3: If Statements
- Bee A Coder Part 4: Repeat Loops
Type: Original Student Tutorial
Learn to identify a fraction as division of the numerator by the denominator using fraction models in this interactive tutorial.
Type: Original Student Tutorial
Educational Games
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
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
Problem-Solving Tasks
Students are asked to find the volume of water in a tank that is 3/4 of the way full.
Type: Problem-Solving Task
Students are asked to find the height of a rectangular prism when given the length, width and volume.
Type: Problem-Solving Task
The purpose of this task is to help students see the connection between a÷b and a/b in a particular concrete example. This task is probably best suited for instruction or formative assessment.
Type: Problem-Solving Task
This task provides a context for performing division of a whole number by a unit fraction. This problem is a "How many groups?'' example of division: the "groups'' in this case are the servings of oatmeal and the question is asking how many servings (or groups) there are in the package.
Type: Problem-Solving Task
The purpose of this task is to provide students with a situation in which it is natural for them to divide a unit fraction by a non-zero whole number. Determining the amount of paint that Kulani needs for each wall illustrates an understanding of the meaning of dividing a unit fraction by a non-zero whole number.
Type: Problem-Solving Task
The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.
Type: Problem-Solving Task
The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution. Calculating the number of origami stars that Avery and Megan can make illustrates student understanding of the process of dividing a whole number by a unit fraction.
Type: Problem-Solving Task
This tasks lends itself very well to multiple solution methods. Students may learn a lot by comparing different methods. Students who are already comfortable with fraction multiplication can go straight to the numeric solutions given below. Students who are still unsure of the meanings of these operations can draw pictures or diagrams.
Type: Problem-Solving Task
The purpose of this task is to familiarize students with multiplying fractions with real-world questions.
Type: Problem-Solving Task
The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.
Type: Problem-Solving Task
The task could be one of the first activities for introducing the multiplication of fractions. The task has fractions which are easy to draw and provides a linear situation. Students benefit from reasoning through the solution to such word problems before they are told that they can be solved by multiplying the fractions; this helps them develop meaning for fraction multiplication.
Type: Problem-Solving Task
The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.
Type: Problem-Solving Task
This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.
Type: Problem-Solving Task
This is the third problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. The first, Running to school, does not require that the unit fractions that comprise 3/4 be subdivided in order to find 1/3 of 3/4. The second task, Drinking Juice, does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2. This task also requires subdivision and involves multiplying a fraction and a mixed number.
Type: Problem-Solving Task
The purpose of this task is to gain a better understanding of multiplying with fractions. Students should use the diagram provided to support their findings.
Type: Problem-Solving Task
This problem helps students gain a better understanding of multiplying with fractions.
Type: Problem-Solving Task
The purpose of this task is to provide students with a concrete experience they can relate to fraction multiplication. Perhaps more importantly, the task also purposefully relates length and locations of points on a number line, a common trouble spot for students. This task is meant for instruction and would be a useful as part of an introductory unit on fraction multiplication.
Type: Problem-Solving Task
The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.
Type: Problem-Solving Task
This task is intended to complement "How many servings of oatmeal?" and "Molly's run.'' All three tasks address the division problem 4÷1/3 but from different points of view. This task provides a how many in each group version of 4÷1/3. This task should be done together with the "How many servings of oatmeal" task with specific attention paid to the very different pictures representing the two situations.
Type: Problem-Solving Task
This is the second problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. This task does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2.
Type: Problem-Solving Task
This task requires students to recognize both "number of groups unknown" (part (a)) and "group size unknown" (part (d)) division problems in the context of a whole number divided by a unit fraction. It also addresses a common misconception that students have where they confuse dividing by 2 or multiplying by 1/2 with dividing by 1/2.
Type: Problem-Solving Task
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
The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.
Type: Problem-Solving Task
This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.
Type: Problem-Solving Task
The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction. For students who are just beginning to think about the meaning of division by a unit fraction (or students who have never cooked), the teacher can bring in a 1/4 cup measuring cup so that students can act it out. If students can reason through parts (a) and (b) successfully, they will be well-situated to think about part (c) which could yield different solution methods.
Type: Problem-Solving Task
Tutorials
In this tutorial, the four operations are applied to fractions with the visualization of the number line. This tutorial starts by adding fractions with the same denominators and explains the logic behind multiplication of fractions. This tutorial also highlights the application and extension of previous understandings of mulitplication to multiply a fraction or whole number by a fraction.
a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x qb. In general, (a/b) x (c/d) = ac/bd.
Type: Tutorial
The video describes how to multiply fractions and state the answer in lowest terms.
Type: Tutorial
Parent Resources
Problem-Solving Tasks
Students are asked to find the volume of water in a tank that is 3/4 of the way full.
Type: Problem-Solving Task
Students are asked to find the height of a rectangular prism when given the length, width and volume.
Type: Problem-Solving Task
The purpose of this task is to help students see the connection between a÷b and a/b in a particular concrete example. This task is probably best suited for instruction or formative assessment.
Type: Problem-Solving Task
This task provides a context for performing division of a whole number by a unit fraction. This problem is a "How many groups?'' example of division: the "groups'' in this case are the servings of oatmeal and the question is asking how many servings (or groups) there are in the package.
Type: Problem-Solving Task
The purpose of this task is to provide students with a situation in which it is natural for them to divide a unit fraction by a non-zero whole number. Determining the amount of paint that Kulani needs for each wall illustrates an understanding of the meaning of dividing a unit fraction by a non-zero whole number.
Type: Problem-Solving Task
The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where students are in their understanding of fraction multiplication.
Type: Problem-Solving Task
The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution. Calculating the number of origami stars that Avery and Megan can make illustrates student understanding of the process of dividing a whole number by a unit fraction.
Type: Problem-Solving Task
This tasks lends itself very well to multiple solution methods. Students may learn a lot by comparing different methods. Students who are already comfortable with fraction multiplication can go straight to the numeric solutions given below. Students who are still unsure of the meanings of these operations can draw pictures or diagrams.
Type: Problem-Solving Task
The purpose of this task is to familiarize students with multiplying fractions with real-world questions.
Type: Problem-Solving Task
The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of addition as joining two separate quantities.
Type: Problem-Solving Task
The task could be one of the first activities for introducing the multiplication of fractions. The task has fractions which are easy to draw and provides a linear situation. Students benefit from reasoning through the solution to such word problems before they are told that they can be solved by multiplying the fractions; this helps them develop meaning for fraction multiplication.
Type: Problem-Solving Task
The solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The students need to explain why that is so.
Type: Problem-Solving Task
This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and the magnitude of the product.
Type: Problem-Solving Task
This is the third problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. The first, Running to school, does not require that the unit fractions that comprise 3/4 be subdivided in order to find 1/3 of 3/4. The second task, Drinking Juice, does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2. This task also requires subdivision and involves multiplying a fraction and a mixed number.
Type: Problem-Solving Task
The purpose of this task is to gain a better understanding of multiplying with fractions. Students should use the diagram provided to support their findings.
Type: Problem-Solving Task
This problem helps students gain a better understanding of multiplying with fractions.
Type: Problem-Solving Task
The purpose of this task is to provide students with a concrete experience they can relate to fraction multiplication. Perhaps more importantly, the task also purposefully relates length and locations of points on a number line, a common trouble spot for students. This task is meant for instruction and would be a useful as part of an introductory unit on fraction multiplication.
Type: Problem-Solving Task
The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units.
Type: Problem-Solving Task
This task is intended to complement "How many servings of oatmeal?" and "Molly's run.'' All three tasks address the division problem 4÷1/3 but from different points of view. This task provides a how many in each group version of 4÷1/3. This task should be done together with the "How many servings of oatmeal" task with specific attention paid to the very different pictures representing the two situations.
Type: Problem-Solving Task
This is the second problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. This task does require students to subdivide the unit fractions that comprise 1/2 in order to find 3/4 of 1/2.
Type: Problem-Solving Task
This task requires students to recognize both "number of groups unknown" (part (a)) and "group size unknown" (part (d)) division problems in the context of a whole number divided by a unit fraction. It also addresses a common misconception that students have where they confuse dividing by 2 or multiplying by 1/2 with dividing by 1/2.
Type: Problem-Solving Task
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
The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. As written, this task could be used in a summative assessment context, but it might be more useful in an instructional setting where students are asked to explain their answers either to a partner or in a whole class discussion.
Type: Problem-Solving Task
This particular problem deals with multiplication. Even though students can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number.
Type: Problem-Solving Task
The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction. For students who are just beginning to think about the meaning of division by a unit fraction (or students who have never cooked), the teacher can bring in a 1/4 cup measuring cup so that students can act it out. If students can reason through parts (a) and (b) successfully, they will be well-situated to think about part (c) which could yield different solution methods.
Type: Problem-Solving Task
Tutorials
This five-minute video answers the question "Must one always invert and multiply?" when dividing fractions. An alternative algorithm is presented which works well in certain cases. The video focuses on sense-making in using either method, and on judging the reasonableness of answers.
Type: Tutorial
The video describes how to multiply fractions and state the answer in lowest terms.
Type: Tutorial