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" |
| 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. |
| Adding Potions with Unlike Fractions Part 1: | Explore how to add fractions less than one with unlike denominators in this magical, interactive tutorial. |
| 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. |
| Name |
Description |
| 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. |
| Let's Have a Fraction Party!: | In this lesson, students will use addition and subtraction of fractions with unlike denominators to solve word problems involving situations that arise with the children who were invited to a party. They will use fraction strips as number models and connect the algorithm with these real-life word problems. |
| Fractions make the real WORLD problems go round: | In this lesson students will use a graphic organizer to to solve addition and subtraction word problems. Students will create their own word problems in PowerPoint, by using pen and paper, or dry erase boards to help them to connect to and understand the structure of word problems. |
| Aaron and Anya's Discovery: Adding Fractions with Unlike Denominators: | In this situational story, Aaron and Anya find several pieces of ribbon/cord of varying fractional lengths. They decide to choose 3 pieces and make a belt. All of the fractions have different denominators; students have to determine common denominators in order to add the fractional pieces. After students successfully add three fractional pieces, they make a belt and label it with their fractional pieces. |
| 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. |
| Using Models to Add Fractions with Unlike Denominators: | This lesson is specific to adding fractions with unlike denominators. It requires students to already have a working knowledge of adding fractions with common denominators, and equivalent fractions. Subtracting fractions with unlike denominators will follow in a subsequent lesson. |
| 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. |
| 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. |
| Using Models to Subtract Fractions with Unlike Denominators: | This lesson is specific to subtracting fractions with unlike denominators. It requires students to already have a working knowledge of subtracting fractions with common denominators and equivalent fractions. |
| Modeling Fraction Multiplication: | This lesson involves students modeling fraction multiplication with rectangular arrays in order to discover the rule for multiplication of fractions. |
| Adding and Subtracting Mixed Numbers with Unlike Denominators: | This lesson helps fifth graders combine their understanding of adding and subtracting fractions with unlike denominators, finding equivalent fractions, and adding and subtracting mixed numbers with like denominators to move on to adding and subtracting mixed numbers with unlike denominators. |
| Discovering Common Denominators: | Students use pattern blocks to represent fractions with unlike denominators. Students discover that they need to convert the pattern blocks to the same size in order to add them. Therefore, they find and use common denominators for the addition 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. |
| Name |
Description |
| Comparing Sums of Unit Fractions: | The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size. |
| 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. |
| Mixed Numbers with Unlike Denominators: | The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting. The two primary ways one can expect students to add are converting the mixed numbers to fractions greater than 1 or adding the whole numbers and fractional parts separately. It is good for students to develop a sense of which approach would be better in a particular context. |
| Making S'Mores: | The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context. |
| 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. |
| Jog-A-Thon: | The purpose of this task is to present students with a situation where it is natural to add fractions with unlike denominators; it can be used for either assessment or instructional purposes. Teachers should anticipate two types of solutions: one where students calculate the distance Alex ran to determine an answer, and one where students compare the two parts of his run to benchmark fractions. |
| 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. |
| Finding Common Denominators to Subtract: | Part (a) of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. Part (b) does not ask students to do it in more than one way; the purpose is to give them an opportunity to choose a denominator and possibly compare with another student who chose a different denominator. The purpose of part (c) is to help students move away from a reliance on drawing pictures. Students can draw a picture if they want, but this subtraction problem is easier to do symbolically, which helps students appreciate the power of symbolic notation. |
| Finding Common Denominators to Add: | Part (a) of this task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator. Part (b) does not ask students to solve the given addition problem in more than one way. Instead, the purpose of this question is to give students an opportunity to choose a denominator and possibly to compare their solution method with another student who chose a different denominator. The purpose of part (c) is to give students who are ready to work symbolically a chance to work more efficiently. |
| 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. |
| Egyptian Fractions: | One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions. |
| 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. |
| Do These Add Up?: | This task addresses common errors that students make when interpreting adding fractions word problems. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions. |
| 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. |
| 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. |
| Name |
Description |
| Arithmetic Operations with Fractions: | 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 q b. In general, (a/b) x (c/d) = ac/bd. |
| Creating Common Denominators: | This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd). The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion. |
| Least Common Denominators: | In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases. Elementary teachers should note this is not a requirement for elementary standards and consider whether this video will further student knowledge or create confusion. This chapter explains how to find the smallest possible common denominator. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. |
| Adding and Subtracting Fractions: | This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving. |
| How Do You Divide Fractions?: | 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. |
| Multiplying Fractions: | The video describes how to multiply fractions and state the answer in lowest terms. |
| 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. |
| Subtracting Fractions: | In this web-based tutorial, students learn procedures for subtracting fractions. The tutorial includes visual representations of the problems using pizzas, animations of the algorithm, and links to related lessons, worksheets, and practice problems. |
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" |
| 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. |
| Adding Potions with Unlike Fractions Part 1: | Explore how to add fractions less than one with unlike denominators in this magical, interactive tutorial. |
| 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. |
| Title |
Description |
| Comparing Sums of Unit Fractions: | The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size. |
| 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. |
| Mixed Numbers with Unlike Denominators: | The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting. The two primary ways one can expect students to add are converting the mixed numbers to fractions greater than 1 or adding the whole numbers and fractional parts separately. It is good for students to develop a sense of which approach would be better in a particular context. |
| Making S'Mores: | The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context. |
| 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. |
| Jog-A-Thon: | The purpose of this task is to present students with a situation where it is natural to add fractions with unlike denominators; it can be used for either assessment or instructional purposes. Teachers should anticipate two types of solutions: one where students calculate the distance Alex ran to determine an answer, and one where students compare the two parts of his run to benchmark fractions. |
| 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. |
| Finding Common Denominators to Subtract: | Part (a) of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. Part (b) does not ask students to do it in more than one way; the purpose is to give them an opportunity to choose a denominator and possibly compare with another student who chose a different denominator. The purpose of part (c) is to help students move away from a reliance on drawing pictures. Students can draw a picture if they want, but this subtraction problem is easier to do symbolically, which helps students appreciate the power of symbolic notation. |
| Finding Common Denominators to Add: | Part (a) of this task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator. Part (b) does not ask students to solve the given addition problem in more than one way. Instead, the purpose of this question is to give students an opportunity to choose a denominator and possibly to compare their solution method with another student who chose a different denominator. The purpose of part (c) is to give students who are ready to work symbolically a chance to work more efficiently. |
| 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. |
| Egyptian Fractions: | One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions. |
| 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. |
| Do These Add Up?: | This task addresses common errors that students make when interpreting adding fractions word problems. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions. |
| 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. |
| 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. |
| Title |
Description |
| Arithmetic Operations with Fractions: | 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. |
| Creating Common Denominators: | This tutorial explores the addition and subtraction of fractions with unlike denominators. Using the number line, this mathematical process can be easily visualized and connected to the final strategy of multiplying the denominators (a/b + c/d = ad +bc/bd). The video number line does show negative numbers which goes beyond elementary standards so an elementary teacher would need to reflect on whether this video will enrich student knowledge or cause confusion. |
| Least Common Denominators: | In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases. Elementary teachers should note this is not a requirement for elementary standards and consider whether this video will further student knowledge or create confusion. This chapter explains how to find the smallest possible common denominator. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. |
| Adding and Subtracting Fractions: | This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting fractions. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving. |
| Multiplying Fractions: | The video describes how to multiply fractions and state the answer in lowest terms. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
| Title |
Description |
| Comparing Sums of Unit Fractions: | The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task. Notice that students are not asked to find the sum so this may be given to students who are limited to computing sums of fractions with the same denominator. Rather, they need to apply a firm understanding of unit fractions (fractions with one in the numerator) and reason about their relative size. |
| 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. |
| Mixed Numbers with Unlike Denominators: | The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting. The two primary ways one can expect students to add are converting the mixed numbers to fractions greater than 1 or adding the whole numbers and fractional parts separately. It is good for students to develop a sense of which approach would be better in a particular context. |
| Making S'Mores: | The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have students moving back and forth between the abstract representation of the fractions and the meaning of the fractions in the context. |
| 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. |
| Jog-A-Thon: | The purpose of this task is to present students with a situation where it is natural to add fractions with unlike denominators; it can be used for either assessment or instructional purposes. Teachers should anticipate two types of solutions: one where students calculate the distance Alex ran to determine an answer, and one where students compare the two parts of his run to benchmark fractions. |
| 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. |
| Finding Common Denominators to Subtract: | Part (a) of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. Part (b) does not ask students to do it in more than one way; the purpose is to give them an opportunity to choose a denominator and possibly compare with another student who chose a different denominator. The purpose of part (c) is to help students move away from a reliance on drawing pictures. Students can draw a picture if they want, but this subtraction problem is easier to do symbolically, which helps students appreciate the power of symbolic notation. |
| Finding Common Denominators to Add: | Part (a) of this task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator. Part (b) does not ask students to solve the given addition problem in more than one way. Instead, the purpose of this question is to give students an opportunity to choose a denominator and possibly to compare their solution method with another student who chose a different denominator. The purpose of part (c) is to give students who are ready to work symbolically a chance to work more efficiently. |
| 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. |
| Egyptian Fractions: | One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions. |
| 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. |
| Do These Add Up?: | This task addresses common errors that students make when interpreting adding fractions word problems. It is very important for students to recognize that they only add fractions when the fractions refer to the same whole, and also when the fractions of the whole being added do not overlap. This set of questions is designed to enhance a student's understanding of when it is and is not appropriate to add fractions. |
| 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. |
| 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. |
