This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| 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. |
| Making Art Part 2: Solving Addition and Subtraction Fraction Word Problems: | Learn to solve addition and subtraction word problems involving fractions with unlike denominators. As you complete this art-themed, interactive tutorial, you'll use visual models, write and solve equations, and check the reasonableness of results based on estimates.
This is part 2 of a two-part series. Click below to open part 1.
|
| Making Art Part 1: Estimating Adding and Subtracting Fractions Using Benchmarks: | Read word problems and use number lines with benchmarks to solve multi-step problems involving addition and subtraction of fractions with unlike denominators. In this tutorial, you will help Daisy and Angie paint pictures using fractions. |
| Samantha’s Shell-Collecting Adventure: | Learn to interpret data presented on a line plot and use operations on fractions to solve problems involving information presented in line plots as you complete this beach-themed, interactive tutorial. |
| Name |
Description |
| Solving Multi-Step Word Problems With "Undecided" Colonists: | Students will be divided into groups and given a set of multi-step real-world problems to solve. The word problems will be specific to topics important to the neutral colonists during the American Revolution. The lesson will conclude with a class discussion of the word problems tying the math and civics together in this integrated lesson plan. |
| Solving Multi-Step Word Problems with Loyalists and Patriots: | Students will be divided into groups and given a set of multi-step real-world problems to solve. The word problems will be specific to topics important to the Loyalists during the American Revolution. The lesson will conclude with a class discussion of the word problems tying the math and civics together in this integrated lesson plan. |
| Solving Real-World Problems P-3: | This integrated lesson includes students practicing multistep problem-solving while analyzing the mathematical thinking of others and justifying their results by explaining methods and processes. Students will work in groups to solve a real-world problem, involving a citizenship context, by using a strategy of their choice. As a class, the students will analyze the different ways the remainder can be interpreted based on different questions involving the same context.
|
| Solving Multi-Step Word Problems With Patriots and Loyalists: | Students will be divided into groups and given a set of multi-step real-world problems to solve. The word problems will be specific to topics important to the Patriots during the American Revolution. The lesson will conclude with a class discussion of the word problems tying the math and civics together in this integrated lesson plan. |
| Solving Real-World Problems P-2: | This integrated lesson includes students solving multi-step real-world word problems using the four operations. Students will solve word problems involving citizen’s duties and responsibilities by using a strategy of their choice and analyzing the context to interpret remainders. |
| Solving Real World Problems P-1: | Students will be exposed to several word problems involving citizens' duties and responsibilities, guiding them to reflect on what could happen if citizens do not fulfill their responsibilities. As the lesson progresses, the students will learn to combine addition, subtraction, multiplication, and division to solve multistep word problems in this integrated lesson plan. |
| 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.
|
| 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. |
| Gimme Two Steps!: | In this lesson, students will create representations for different multi-step word problems. One of these representations will be an expression with a variable. |
| 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. |
| Blessings in a Bag!!: | In this MEA, the students will help a charitable organization select 5 snack items from a list to provide nutritious snacks for children in low-income communities. Students will practice using the four operations to solve real-world problems and use decimal notation to make calculations involving money. Additionally, they will be asked to compare multi-digit numbers to the thousandths. |
| Getting the Top Mini-Fridge not a Small Deal: | In this MEA, students will create a procedure to rank five mini-refrigerators to determine which one should be purchased for the school by the PTA based on size, type, features, energy usage, and cost. In the process, students will solve real-world problems involving the multiplication of multi-digit numbers with decimals to the hundredths, including using money. Students will also determine the volume of a rectangular prism using a formula. |
| Museum Dilemma: | In this MEA, students evaluate the contributions of various explorers to help a museum select the subject who provided the most impact on Western development for a new exhibit. Students will need to convert units to have the necessary information to help come up with a solution to the problem. |
| 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. |
| One Step at a Time: Word Problems: | In this lesson, students will use the four operations to solve multi-step word problems composed of whole numbers. Students will be asked to estimate, write equations, decide if their answers are reasonable, and explain their decision. Several problems include explaining the meaning of the remainder in a division problem. |
| 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. |
| Are You Ready for a Hurricane?: | This activity allows students to determine the types of items that should be in a hurricane survival kit, use a budget and calculations to determine the items to include in the kit and gain an understanding of hurricanes and the need to prepare for them. 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. |
| Estimating Fractions Using Benchmark Fractions 0, 1/2, or 1: | In this lesson, students use models (fractions tiles or number lines) to round fractions using benchmark fractions of 0, 1/2, or 1. |
| Diving deeper into division: | This lesson introduces students to dividing with 2 digit divisors. Students are asked to apply strategies that they learned in dividing with 1 digit divisors such as partial quotients or breaking numbers apart using the distributive property. |
| 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. |
| 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. |
| Wallpaper Woes Money Math: Lessons for Life: | Students hear a story about a middle-school student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs. |
| 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. |
| Rockin' Remainders: | This is a lesson designed to teach interpreting remainders in division based on the context of the word problem. Included with the lesson plan is a PowerPoint for direct instruction and word problems for small group or individual practice. |
| 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. |
| Carnival Tickets: | The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases. |
| What is 23 ÷ 5?: | When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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 |
| 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. |
| Making Art Part 2: Solving Addition and Subtraction Fraction Word Problems: | Learn to solve addition and subtraction word problems involving fractions with unlike denominators. As you complete this art-themed, interactive tutorial, you'll use visual models, write and solve equations, and check the reasonableness of results based on estimates.
This is part 2 of a two-part series. Click below to open part 1.
|
| Making Art Part 1: Estimating Adding and Subtracting Fractions Using Benchmarks: | Read word problems and use number lines with benchmarks to solve multi-step problems involving addition and subtraction of fractions with unlike denominators. In this tutorial, you will help Daisy and Angie paint pictures using fractions. |
| Samantha’s Shell-Collecting Adventure: | Learn to interpret data presented on a line plot and use operations on fractions to solve problems involving information presented in line plots as you complete this beach-themed, 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. |
| Carnival Tickets: | The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases. |
| What is 23 ÷ 5?: | When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| Carnival Tickets: | The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases. |
| What is 23 ÷ 5?: | When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
