| Code |
Description |
| MAFS.5.NF.2.3: | Interpret a fraction as division of the numerator by the denominator
(a/b = a ÷ b). Solve word problems involving division of whole
numbers leading to answers in the form of fractions or mixed numbers,
e.g., by using visual fraction models or equations to represent the
problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting
that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared
equally among 4 people each person has a share of size 3/4. If 9 people
want to share a 50-pound sack of rice equally by weight, how many
pounds of rice should each person get? Between what two whole numbers
does your answer lie? |
| MAFS.5.NF.2.4: | Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
- Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
|
| MAFS.5.NF.2.5: | Interpret multiplication as scaling (resizing), by:
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
|
| MAFS.5.NF.2.6: | Solve real world problems involving multiplication of fractions and
mixed numbers, e.g., by using visual fraction models or equations to
represent the problem. |
| MAFS.5.NF.2.7: | Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
- Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
- Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
- Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
|
This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Carnival Craziness!: | 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. |
| Chocolate Shop Challenge Part 2: Dividing Unit Fractions and Whole Numbers Using Number Lines: | 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" |
| Chocolate Shop Challenge Part 1: Dividing Unit Fractions and Whole Numbers Using Fraction Bar Models: | 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" |
| David Divides Desserts: Divide a Unit Fraction by a Whole Number: | 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. |
| Share and Share Alike: | Learn how to divide a unit fraction by a whole number to share yummy picnic goodies equally in this interactive tutorial. |
| 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.
|
| Buffy's Bakery Part 2: Multiplying Fractions: |
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.
|
| Buffy’s Bakery Part 1: Visual Models and Multiplying Fractions: | 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.
|
| Scaling Up to Escape: | 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. |
| Bee A Coder Part 1: Declare Variables: | 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.
|
| #InterpretAFractionAsDivision: | Learn to identify a fraction as division of the numerator by the denominator using fraction models in this interactive tutorial. |
| Name |
Description |
| Multiplying by a Fraction Greater Than One: | Students are asked to describe the size of a product of a fraction greater than one and a whole number without multiplying. |
| Multiplying by a Fraction Less than One: | Students are asked to describe the size of a product of a fraction less than one and a whole number without multiplying. |
| More Than or Less Than Two Miles: | Students are asked to reason about the size of the product of fractions and whole numbers presented in context. |
| Estimating Products: | Students are given three products, each involving a whole number and a fraction, and are asked to estimate the size of the product and explain their reasoning. |
| Fractions Divided by Whole Numbers: | Students are given a division expression and asked to write a story context to match the expression and use a visual fraction model to solve the problem. |
| Bags of Fudge: | Students are asked to solve a word problem involving division of a whole number by a fraction. |
| Relay Race: | Students are asked to solve a word problem involving division of a fraction by a whole number. |
| Whole Numbers Divided by Fractions: | Students are given a division expression and asked to write a story context to match the expression and use a visual fraction model to solve the problem. |
| Two Thirds: | Students are asked to interpret a fraction and write a word problem to match the context of the fraction. |
| Pizza Party: | Students are asked to solve a word problem by finding the product of two fractions. |
| Half of a Recipe: | Students are asked to solve a word problem by finding the product of a fraction and a mixed number. |
| Five Thirds: | Students are asked to interpret an improper fraction and then write a word problem to match the context of the fraction. |
| Candy at the Party: | Students are asked to solve a word problem by finding the product of two mixed numbers. |
| Box Factory: | Students are asked to solve a word problem by finding the product of two fractions. |
| Using Visual Fraction Models: | Students interpret a visual fraction model showing multiplication of two fractions less than one. |
| Sharing Brownies: | Students are asked to draw a visual fraction model to solve a division word problem. |
| The Rectangle: | Students determine the area of a rectangle with given fractional dimensions by multiplying. Students are then asked to draw a model to find the area of the same rectangle. |
| Multiplying Fractions by Fractions: | Students are asked to consider an equation involving multiplication of fractions, then create a visual fraction model, and write a story context to match. |
| 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. |
| Sharing Pizzas: | Students are asked to draw a visual fraction model to solve a division word problem. |
| Name |
Description |
| Voter Task Force: | Students will help the Supervisor of Elections determine which voter registration locations could be improved to help more citizens get registered to vote. Students will learn about the number of citizens who registered to vote in a general election year compared to the total population of those eligible to vote. They will discuss which voter registration locations will provide the most access to citizens and allocate funds to help address the issue in this modeling eliciting activity.
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.
|
| Natural Disaster Dividing Fractions: | In this lesson, students will extend learning of dividing unit fractions and whole numbers within the context of governmental response to an emergency situation. |
| Coding Geometry Challenge 8, 9 & 17: | This set of geometry challenges focuses on using area/perimeter as students problem solve and think as they learn to code using block coding software. Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor. |
| Coding Geometry Challenge #10 & 11: | This set of geometry challenges focuses on scaled drawings and area as students problem solve and think as they learn to code using block coding software. Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor. |
| Fraction Frenzy! (Division/Fractional Word Problems): | Students will draw models to solve real-life word problems and show the relationship between division and fractions. This is not an introductory lesson to this standard. By the end of this lesson, they should be able to create their own word problems and explain if the answer will be a mixed number or a fraction less than one. |
| Real-World Fractions: | This lesson focuses on providing students with real-world experiences where they will be required to multiply fractions. Students will be required to use visual fraction models or equations to represent the problem. This is a practice and application lesson, not an introductory lesson. |
| Bill of Rights Billboard: | This MEA will deepen students' knowledge of the Bill of Rights through collaborative problem solving. Students are required to analyze data in order to recommend three Amendments to celebrate during a community festival. They will perform operations with fractions and mixed numbers to recommend advertising options for the festival within a budget. |
| Sharing Fairly: | The students will connect fractions with division. They will solve word problems involving the division of whole numbers by using the strategy of drawing a model and/or equations with a fraction or mixed number for the answer. Next they will write word problems with a story context that represent problems involving division of whole numbers that lead to a fraction or mixed number answer. |
| Wildlife Refuge MEA- Feeding the Animals: | Students use mathematical practices to recommend food packages for the Wildlife Refuge of North America to order.
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. |
| Birds Now: | The Birds Now Pet Store is increasing the size of its bird department. By increasing the number and types of birds, they need to purchase more bird food and the type of food needs to be one that different types of birds can eat. The students need to rank the companies that sell bird food base on the basic requirements out lined in the client's letter.
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 process. 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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx |
| Multiplying Fractions With GeoGebra Using An Area Model: | In this lesson, students will derive an algorithm for multiplying fractions by using area models. They will use a GeoGebra applet to visualize fraction multiplication. They will also translate between pictorial and symbolic representations of fraction multiplication. |
| Multiplying a Fraction by a Fraction: | In this lesson, students will solve problems related to training for a marathon to apply and make sense of multiplying fractions. The student will complete a function table to help illustrate patterns in the numerator/denominator relationships. This lesson utilizes the linear model as a concrete representation and moves towards the standard algorithm (a/b) x (c/d) = ac/bd. |
| Wazzup Charter Schools Playground Dilemma MEA: | This Model Eliciting Activity (MEA) is written at a 5th grade level. The Wazzup Charter School MEA provides students with an engineering problem in which they must work as a team to design a procedure to select the best type of surface for a playground at a charter school. 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. |
| Area Models: Multiplying Fractions: | In this lesson students will investigate the relationship between area models and the concept of multiplying fractions. Students will use area models to develop understanding of the concept of multiplying fractions as well as to find the product of two common fractions. The teacher will use the free application GeoGebra (see download link under Suggested Technology) to provide students with a visual representation of how area models can be used at the time of multiplying fractions. |
| Multiplying a Fraction by a Fraction: | Students will multiply a fraction times a fraction. The students will section off a square through rows and columns that will represent the strategy of multiplying numerators and then denominators.
|
| Garden Variety Fractions: | Students explore the multiplication of a fraction times a fraction through story problems about a garden using models on Geoboards and pictorial representations on grid paper. Students make a connection between their models and the numerical representation of the equation. |
| Modeling Fraction Multiplication: | This lesson involves students modeling fraction multiplication with rectangular arrays in order to discover the rule for multiplication of fractions. |
| Looking for Patterns in a Sequence of Fractions: | Students generate and describe a numerical pattern using the multiplication and subtraction of fractions. |
| It's My Party and I'll Make Dividing by Fractions Easier if I Want to!: | During this lesson students will relate their understanding of whole number division situations to help them interpret situations involving dividing by unit fractions. They will then develop models and strategies for representing the division of a whole number by a unit fraction. |
| Picture This! Fractions as Division: | In this lesson the student will apply and extend previous understandings of division to represent division as a fraction. This includes representations and word problems where the answer is a fraction. |
| Sunshine Beach Restaurant: | This Model Eliciting Activity (MEA) asks students to develop a procedure to select a hurricane shutter company based on several data points.
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 process. 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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx |
| Those Pesky Remainders: | This is a lesson to help students understand how to interpret the remainder in a division problem. Real world problems are presented in a PowerPoint so students may visualize situations and discover the four treatments of a remainder. |
| Name |
Description |
| Computing Volume Progression 2: | Students are asked to find the volume of water in a tank that is 3/4 of the way full. |
| Computing Volume Progression 3: | Students are asked to find the height of a rectangular prism when given the length, width and volume. |
| How Much Pie?: | 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. |
| How many servings of oatmeal?: | 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. |
| Painting a room: | 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. |
| Painting a Wall: | 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. |
| Origami Stars: | 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. |
| Making Cookies: | 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. |
| To Multiply or not to multiply?: | The purpose of this task is to familiarize students with multiplying fractions with real-world questions. |
| Salad Dressing: | 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. |
| Running to School: | 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. |
| Running a Mile: | 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. |
| Reasoning about Multiplication: | 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. |
| Half of a Recipe: | 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. |
| Grass Seedlings: | 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. |
| Fundraising: | This problem helps students gain a better understanding of multiplying with fractions. |
| Folding Strips of Paper: | 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. |
| Converting Fractions of a Unit into a Smaller Unit: | The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units. |
| How many marbles?: | 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. |
| Drinking Juice: | 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. |
| Dividing by One-Half: | 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. |
| 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. |
| Comparing a Number and a Product: | 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. |
| Calculator Trouble: | 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. |
| Banana Pudding: | 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. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Carnival Craziness!: | 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. |
| Chocolate Shop Challenge Part 2: Dividing Unit Fractions and Whole Numbers Using Number Lines: | 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" |
| Chocolate Shop Challenge Part 1: Dividing Unit Fractions and Whole Numbers Using Fraction Bar Models: | 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" |
| David Divides Desserts: Divide a Unit Fraction by a Whole Number: | 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. |
| Share and Share Alike: | Learn how to divide a unit fraction by a whole number to share yummy picnic goodies equally in this interactive tutorial. |
| 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.
|
| Buffy's Bakery Part 2: Multiplying Fractions: |
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.
|
| Buffy’s Bakery Part 1: Visual Models and Multiplying Fractions: | 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.
|
| Scaling Up to Escape: | 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. |
| Bee A Coder Part 1: Declare Variables: | 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.
|
| #InterpretAFractionAsDivision: | Learn to identify a fraction as division of the numerator by the denominator using fraction models in this interactive tutorial. |
| Title |
Description |
| Computing Volume Progression 2: | Students are asked to find the volume of water in a tank that is 3/4 of the way full. |
| Computing Volume Progression 3: | Students are asked to find the height of a rectangular prism when given the length, width and volume. |
| How Much Pie?: | 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. |
| How many servings of oatmeal?: | 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. |
| Painting a room: | 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. |
| Painting a Wall: | 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. |
| Origami Stars: | 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. |
| Making Cookies: | 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. |
| To Multiply or not to multiply?: | The purpose of this task is to familiarize students with multiplying fractions with real-world questions. |
| Salad Dressing: | 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. |
| Running to School: | 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. |
| Running a Mile: | 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. |
| Reasoning about Multiplication: | 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. |
| Half of a Recipe: | 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. |
| Grass Seedlings: | 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. |
| Fundraising: | This problem helps students gain a better understanding of multiplying with fractions. |
| Folding Strips of Paper: | 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. |
| Converting Fractions of a Unit into a Smaller Unit: | The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units. |
| How many marbles?: | 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. |
| Drinking Juice: | 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. |
| Dividing by One-Half: | 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. |
| 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. |
| Comparing a Number and a Product: | 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. |
| Calculator Trouble: | 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. |
| Banana Pudding: | 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. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
| Title |
Description |
| Computing Volume Progression 2: | Students are asked to find the volume of water in a tank that is 3/4 of the way full. |
| Computing Volume Progression 3: | Students are asked to find the height of a rectangular prism when given the length, width and volume. |
| How Much Pie?: | 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. |
| How many servings of oatmeal?: | 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. |
| Painting a room: | 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. |
| Painting a Wall: | 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. |
| Origami Stars: | 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. |
| Making Cookies: | 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. |
| To Multiply or not to multiply?: | The purpose of this task is to familiarize students with multiplying fractions with real-world questions. |
| Salad Dressing: | 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. |
| Running to School: | 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. |
| Running a Mile: | 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. |
| Reasoning about Multiplication: | 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. |
| Half of a Recipe: | 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. |
| Grass Seedlings: | 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. |
| Fundraising: | This problem helps students gain a better understanding of multiplying with fractions. |
| Folding Strips of Paper: | 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. |
| Converting Fractions of a Unit into a Smaller Unit: | The purpose of this task is to help students gain a better understanding of fractions and the conversion of fractions into smaller units. |
| How many marbles?: | 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. |
| Drinking Juice: | 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. |
| Dividing by One-Half: | 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. |
| 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. |
| Comparing a Number and a Product: | 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. |
| Calculator Trouble: | 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. |
| Banana Pudding: | 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. |
b. In general, (a/b) x (c/d) = ac/bd.