This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Unit Rate Length: | Students are asked to write ratios and unit rates from fractional values. |
| Unit Rate Area: | Students are asked to convert a ratio of mixed numbers to a unit rate and explain its contextual meaning. |
| Finding the Whole: | Students are asked to find the whole given a part and a percent. |
| Comparing Unit Rates: | Students are asked to compute unit rates from values that include fractions. |
| Measurement Conversion: | Students are asked to make unit conversions. |
| Comparing Rates: | Students are asked to solve rate problems given the time it takes each of two animals to run different distances. |
| Homework Time: | Students are asked to convert a given rate to an equivalent rate out of 100. |
| Making Coffee: | Students are asked to write ratios equivalent to a given ratio. |
| Computing Unit Rates: | Students are asked to compute and interpret unit rates in two different ways from values that include fractions and mixed numbers. |
| Sara’s Hike: | Students are asked to solve a problem involving ratios. |
| Party Punch - Compare Ratios: | Students are asked to compare ratios given in two different tables. |
| Writing Unit Rates: | Students are given verbal descriptions of rates and asked to write them as unit rates. |
| Identifying Unit Rates: | Students are asked to decide if given statements express unit rates. |
| Explaining Rates: | Students are asked to explain the meaning of given rates and identify any that are unit rates. |
| Writing Ratios: | Students are asked to write part-to-part and part-to-whole ratios using values given in a table. |
| Interpreting Ratios: | Students are asked to explain the meaning of ratios in the context of problems. |
| Comparing Time: | Students are given a scenario involving an additive comparison of two quantities, asked to write a ratio, and explain its meaning. |
| Comparing Rectangles: | Students are asked to determine which of three given comparisons contains a correctly computed ratio in a context involving rectangles. |
| Book Rates: | Students write and explain the meaning of a ratio and corresponding unit rate in the context of a word problem. |
| Bargain Breakfast: | Students are given the prices of three different quantities of cereal and are asked to determine which is the best buy. |
| Name |
Description |
| Bottymals @ RobottoysTM: | In this Model Eliciting Activity (MEA), students will learn how to use very different pieces of information and data to select the best "Bottymals" for a company that wants to manufacture them and place them on the market. The MEA includes information about animal/insect anatomy (locomotion), manufacturing materials used in robotics, and physical science of the 6th grade level. Extensive information is provided to students, thus pre-requisites are minimal.
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 |
| Cool Special Effects: | In this MEA, students will apply the concepts of heat transfer, especially convection. Students will analyze factors such as temperature that affect the behavior of fluids as they form convection currents.
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. |
| Rate Your Local Produce Market: | The students will rank the local produce markets by using qualitative and quantitative data. The students will have to calculate unit rates and compare and order 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. |
| Champion Volleyball Team: | Students will help create a championship volleyball team by selecting 4 volleyball players to be added to open positions on the team. The students will use quantitative (ratios and decimals) and qualitative data to make their decisions. 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. |
| Cosmic Nose Cones: | Students will design specific nose cones for a water bottle rocket. They will test them to find out and rate which one is most effective in terms of accuracy, speed, distance, and cost effectiveness. This information will be used as criteria for a company that designs nose cones for orbitary missions.
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. |
| Ares Habitation Corporation and the Search for Lunarcrete: | In this Model Eliciting Activity, MEA, students will create a working model that can determine the best regolith to binder solution for a settlement on Mars. The students are contacted by a company that requests their services. Students will read about, study and create their own lunarcrete (moon concrete). Students will work as a team to evaluate the provided data and determine which solution is most effective. Students will find the unit rate of the lunacrete mixes. Finally, students will write a letter to the company defending their process giving reasons and data. 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. |
| All “Tired” Up: | In this lesson students will utilize mathematical computation skills involving percentages and critical thinking skills to select the best tire deals advertised. |
| Real Estate Rental Agency: | In this Model Eliciting Activity, MEA, students will choose the best location for a family relocating and will find the monthly costs per month to make the best decision. 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. |
| Fast Food Frenzy: | In this activity, students will engage critically with nutritional information and macronutrient content of several fast food meals. This is an MEA that requires students to build on prior knowledge of nutrition and working with percentages. 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. |
| Smooth Smoothie: | In this Model Eliciting Activity, MEA, students will analyze data to decide what blender to use, the number of times the recipes are used and the total ingredients needed. 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. |
| Selecting a Car for Display/Ratio: | Teacher will use students’ responses to their selection of the most efficient car to create and introduce ratio concepts and reasoning. The activities can be completed as a whole group, a few groups, or individually. The teacher may also alternate so that certain parts of the activities can be whole group, few groups, or individually according to the classrooms functional, behavioral, and academic levels. 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. |
| Best Day Care Center for William: | This MEA requires students to formulate a comparison-based solution to a problem involving choosing the BEST daycare based upon safety, playground equipment, meals, teacher to student ratio, cost, holiday availability and toilet training availability. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client. Students will receive practice on calculating a discount, finding the sum of the discounts, working with ratios and ranking day cares based on the data given. 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. |
| The Best Domestic Car: | In this MEA students will use problem-solving strategies to determine which car to recommend to Americans living in India. 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. |
| Lily's Cola TV Commercial: | In this Model Eliciting Activity, MEA, given a tight budget, students need to find the number of people that can be hired to film a soda commercial. Students will make the selection using a table that contains information about two types of extras. Experienced extras earn more money per hour than novice extras; however, novice extras need more time to shoot the commercial than experienced extras. In addition, students will select the design that would be used for the commercial taking into account the area that needs to be covered and the aesthetic factor. 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. |
| Can you say that another way?: | Students will model how to express an addition problem using the distributive property. |
| Scuba Diving Mask Search: | This MEA asks the students to decide which company would be the “best and the worst” to use to purchase scuba diving masks for Tino’s Scuba Diving School to provide to their diving certification students. Furthermore, the students are asked to suggest which type of scuba diving masks should be purchased in term of multiple panes – single pane mask, double pane mask, full face mask, skirt color, fit, durability, and price. Students must provide a "top choice" scuba diving mask to the company owner and explain how they arrived at their solution. 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. |
| Paper Route Logic: | Students will be helping Lily Rae find the most efficient delivery route by using speed and distance values to calculate the shortest time to make it to all of her customers.
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 |
| Better Buy: 75 fl oz or 150 fl oz?: | The students will clip out advertisements or use the attached PowerPoint to determine the better buy between small quantities and large quantities. The students will answer the question, "Which item costs less per unit?" and demonstrate fluency in dividing with decimals. |
| Orange Juice Conversion: | In this MEA, the students will be able to convert measurements within systems and between systems. They will be able to use problem solving skills to create a process for ranking orange juices for a Bed and Breakfast. 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. |
| Name |
Description |
| Mathematical Thinking for Ceramic 3D Printing: | In this video, Matthew Lawrence describes how mathematical thinking is important for 3D printing with ceramic materials.
Download the CPALMS Perspectives video student note taking guide. |
| Unit Rates in Swimming: | In this video, David Fermin demonstrates real-time estimates for monitoring swimming performance and physiology.
Download the CPALMS Perspectives video student note taking guide. |
| Unit Rate: Spring Water Bottling: | Nestle Waters discusses the importance of unit rate in the manufacturing process of bottling spring water.
Download the CPALMS Perspectives video student note taking guide. |
| Unit Rate and Florida Cave Formation: | How long does it take to form speleothems in the caves at Florida Caverns State Parks?
Download the CPALMS Perspectives video student note taking guide. |
| Pizza Pi: Area, Circumference & Unit Rate: | How many times larger is the area of a large pizza compared to a small pizza? Which pizza is the better deal? Michael McKinnon of Gaines Street Pies talks about how the area, circumference and price per square inch is different depending on the size of the pizza.
Download the CPALMS Perspectives video student note taking guide. |
| Amping Up Violin Tuning with Math: | Kyle Dunn, a Tallahassee-based luthier and owner of Stringfest, discusses how math is related to music.
Download the CPALMS Perspectives video student note taking guide. |
| Building Scale Models to Solve an Archaeological Mystery: | An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings. |
| Coffee Mathematics: Ratios and Total Dissolvable Solids: | Math - the secret ingredient for an excellent cup of coffee!
Download the CPALMS Perspectives video student note taking guide. |
| Bicycle Mathematics: Selecting Gear Ratios for Performance: | Don't let math derail you. Learn how bicycle gears use ratios to help you ride comfortably on all kinds of terrain.
Download the CPALMS Perspectives video student note taking guide. |
| Motorcycle Mathematics: Tuning Compression Ratios for Performance: | Get revved up about math when this motorcycle mechanic explains compression ratios.
Download the CPALMS Perspectives video student note taking guide. |
| KROS Pacific Ocean Kayak Journey: Calories, Distance, and Rowing Rates: | Food is fuel, especially important when your body is powering a boat across the ocean.
Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]
Download the CPALMS Perspectives video student note taking guide. |
| KROS Pacific Ocean Kayak Journey: Calories, Exercise, and Metabolism Rates: | How much food do you need to cross the Pacific in a kayak? Get a calculator and a bag of almonds before you watch this.
Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]
Download the CPALMS Perspectives video student note taking guide. |
| KROS Pacific Ocean Kayak Journey: Kites, Wind, and Speed: | Lofty ideas about kites helped power a kayak from California to Hawaii.
Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]
Download the CPALMS Perspectives video student note taking guide. |
| Isotopes and Paleoclimates: | Let this researcher explain how studying fossils and isotopes can help us understand ancient climate conditions!
Download the CPALMS Perspectives video student note taking guide. |
| Ratios of Horse Feed: | An equestrian describes, nay, explains mathematics principles applied to feeding a horse!
Download the CPALMS Perspectives video student note taking guide. |
| Name |
Description |
| Kendall's Vase - Tax: | This problem asks the student to find a 3% sales tax on a vase valued at $450. |
| Converting Square Units: | The purpose of this task is converting square units. Use the information provided to answer the questions posed. This task asks students to critique Jada's reasoning. |
| Jim and Jesse's Money: | Students are asked to use a ratio to determine how much money Jim and Jesse had at the start of their trip. |
| Security Camera: | Students are asked to determine the percent of the area of a store covered by a security camera. Then, students are asked to determine the "best" place to position the camera and support their answer. |
| Shirt Sale: | Use the information provided to find out the original price of Selina's shirt. There are several different ways to reason through this problem; two approaches are shown. |
| Voting for Three, Variation 1: | This problem is the fifth in a series of seven about ratios. Even though there are three quantities (the number of each candidates' votes), they are only considered two at a time. |
| Voting for Three, Variation 2: | This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex. In this problem, the students are asked to determine the difference in votes received by two of the three candidates. |
| Voting for Three, Variation 3: | This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions. |
| Voting for Two, Variation 3: | This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory. |
| Voting for Two, Variation 1: | This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate. |
| Voting for Two, Variation 2: | This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes. |
| Voting for Two, Variation 4: | This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required. |
| Cooking with the Whole Cup: | Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe. |
| Currency Exchange: | The purpose of this task is to have students convert multiple currencies to answer the problem. Students may find the CDN abbreviation for Canada confusing. Teachers may need to explain the fact that money in Canada is also called dollars, so to distinguish them, we call them Canadian dollars. |
| Dana's House: | Use the information provided to find out what percentage of Dana's lot won't be covered by the house. |
| Data Transfer: | This task asks the students to solve a real-world problem involving unit rates (data per unit time) using units that many teens and pre-teens have heard of but may not know the definition for. While the computations involved are not particularly complex, the units will be abstract for many students. The first solution relies more on reasoning about the meaning of multiplication and division, while the second solution uses units to help keep track of the steps in the solution process. |
| Friends Meeting on Bicycles: | Students are asked to use knowledge of rates and ratios to answer a series of questions involving time, distance, and speed. |
| Games at Recess: | Students are asked to write complete sentences to describe ratios for the context. |
| Buying Gas: | There are two aspects to fluency with division of multi-digit numbers: knowing when it should be applied, and knowing how to compute it. While this task is very straightforward, it represents the kind of problem that sixth graders should be able to recognize and solve relatively quickly. Easily recognizing contexts that require division is a necessary conceptual prerequisite to more complex modeling problems that students will be asked to solve later in middle and high school.
This task also has a natural carryover to work with ratios and rates, so students should also be building connections between these kinds of division problems and finding unit rates. |
| Mixing Concrete: | Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete. |
| Overlapping Squares: | This problem provides an interesting geometric context to work on the notion of percent. Two different methods for analyzing the geometry are provided: the first places the two squares next to one another and then moves one so that they overlap. The second solution sets up an equation to find the overlap in terms of given information which reflects the mathematical ideas reason about and solve one-variable equations and inequalities. |
| Price Per Pound and Pounds Per Dollar: | Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context. |
| Ratio of Boys to Girls: | Use the information provided to find the ratio of boys to girls. Tasks like these help build appropriate connections between ratios and fractions. Students often write ratios as fractions, but in fact we reserve fractions to represent numbers or quantities rather than relationships between quantities. In some textbooks, a distinction is made between a ratio, which is assumed to have a common unit for both quantities, and a rate, which is defined to be a quotient of two quantities with different units (e.g. a ratio of the number of miles to the number of hours). |
| Running at a Constant Speed: | Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Kendall's Vase - Tax: | This problem asks the student to find a 3% sales tax on a vase valued at $450. |
| Converting Square Units: | The purpose of this task is converting square units. Use the information provided to answer the questions posed. This task asks students to critique Jada's reasoning. |
| Jim and Jesse's Money: | Students are asked to use a ratio to determine how much money Jim and Jesse had at the start of their trip. |
| Security Camera: | Students are asked to determine the percent of the area of a store covered by a security camera. Then, students are asked to determine the "best" place to position the camera and support their answer. |
| Shirt Sale: | Use the information provided to find out the original price of Selina's shirt. There are several different ways to reason through this problem; two approaches are shown. |
| Voting for Three, Variation 1: | This problem is the fifth in a series of seven about ratios. Even though there are three quantities (the number of each candidates' votes), they are only considered two at a time. |
| Voting for Three, Variation 2: | This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex. In this problem, the students are asked to determine the difference in votes received by two of the three candidates. |
| Voting for Three, Variation 3: | This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions. |
| Voting for Two, Variation 3: | This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory. |
| Voting for Two, Variation 1: | This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate. |
| Voting for Two, Variation 2: | This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes. |
| Voting for Two, Variation 4: | This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required. |
| Cooking with the Whole Cup: | Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe. |
| Currency Exchange: | The purpose of this task is to have students convert multiple currencies to answer the problem. Students may find the CDN abbreviation for Canada confusing. Teachers may need to explain the fact that money in Canada is also called dollars, so to distinguish them, we call them Canadian dollars. |
| Dana's House: | Use the information provided to find out what percentage of Dana's lot won't be covered by the house. |
| Data Transfer: | This task asks the students to solve a real-world problem involving unit rates (data per unit time) using units that many teens and pre-teens have heard of but may not know the definition for. While the computations involved are not particularly complex, the units will be abstract for many students. The first solution relies more on reasoning about the meaning of multiplication and division, while the second solution uses units to help keep track of the steps in the solution process. |
| Friends Meeting on Bicycles: | Students are asked to use knowledge of rates and ratios to answer a series of questions involving time, distance, and speed. |
| Games at Recess: | Students are asked to write complete sentences to describe ratios for the context. |
| Mixing Concrete: | Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete. |
| Overlapping Squares: | This problem provides an interesting geometric context to work on the notion of percent. Two different methods for analyzing the geometry are provided: the first places the two squares next to one another and then moves one so that they overlap. The second solution sets up an equation to find the overlap in terms of given information which reflects the mathematical ideas reason about and solve one-variable equations and inequalities. |
| Price Per Pound and Pounds Per Dollar: | Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context. |
| Running at a Constant Speed: | Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
| Title |
Description |
| Kendall's Vase - Tax: | This problem asks the student to find a 3% sales tax on a vase valued at $450. |
| Converting Square Units: | The purpose of this task is converting square units. Use the information provided to answer the questions posed. This task asks students to critique Jada's reasoning. |
| Jim and Jesse's Money: | Students are asked to use a ratio to determine how much money Jim and Jesse had at the start of their trip. |
| Security Camera: | Students are asked to determine the percent of the area of a store covered by a security camera. Then, students are asked to determine the "best" place to position the camera and support their answer. |
| Shirt Sale: | Use the information provided to find out the original price of Selina's shirt. There are several different ways to reason through this problem; two approaches are shown. |
| Voting for Three, Variation 1: | This problem is the fifth in a series of seven about ratios. Even though there are three quantities (the number of each candidates' votes), they are only considered two at a time. |
| Voting for Three, Variation 2: | This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex. In this problem, the students are asked to determine the difference in votes received by two of the three candidates. |
| Voting for Three, Variation 3: | This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions. |
| Voting for Two, Variation 3: | This problem is the third in a series of tasks set in the context of a class election. Students are given a ratio and total number of voters and are asked to determine the difference between the winning number of votes received and the number of votes needed for victory. |
| Voting for Two, Variation 1: | This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Students are given a ratio and total number of voters and are asked to determine the number of votes received by each candidate. |
| Voting for Two, Variation 2: | This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes. |
| Voting for Two, Variation 4: | This is the fourth in a series of tasks about ratios set in the context of a classroom election. Given only a ratio, students are asked to determine the fractional difference between votes received and votes required. |
| Cooking with the Whole Cup: | Students are asked to use proportional reasoning to answer a series of questions in the context of a recipe. |
| Currency Exchange: | The purpose of this task is to have students convert multiple currencies to answer the problem. Students may find the CDN abbreviation for Canada confusing. Teachers may need to explain the fact that money in Canada is also called dollars, so to distinguish them, we call them Canadian dollars. |
| Dana's House: | Use the information provided to find out what percentage of Dana's lot won't be covered by the house. |
| Data Transfer: | This task asks the students to solve a real-world problem involving unit rates (data per unit time) using units that many teens and pre-teens have heard of but may not know the definition for. While the computations involved are not particularly complex, the units will be abstract for many students. The first solution relies more on reasoning about the meaning of multiplication and division, while the second solution uses units to help keep track of the steps in the solution process. |
| Friends Meeting on Bicycles: | Students are asked to use knowledge of rates and ratios to answer a series of questions involving time, distance, and speed. |
| Games at Recess: | Students are asked to write complete sentences to describe ratios for the context. |
| Buying Gas: | There are two aspects to fluency with division of multi-digit numbers: knowing when it should be applied, and knowing how to compute it. While this task is very straightforward, it represents the kind of problem that sixth graders should be able to recognize and solve relatively quickly. Easily recognizing contexts that require division is a necessary conceptual prerequisite to more complex modeling problems that students will be asked to solve later in middle and high school.
This task also has a natural carryover to work with ratios and rates, so students should also be building connections between these kinds of division problems and finding unit rates. |
| Mixing Concrete: | Given a ratio, students are asked to determine how much of each ingredient is needed to make concrete. |
| Overlapping Squares: | This problem provides an interesting geometric context to work on the notion of percent. Two different methods for analyzing the geometry are provided: the first places the two squares next to one another and then moves one so that they overlap. The second solution sets up an equation to find the overlap in terms of given information which reflects the mathematical ideas reason about and solve one-variable equations and inequalities. |
| Price Per Pound and Pounds Per Dollar: | Students are asked to use a given ratio to determine if two different interpretations of the ratio are correct and to determine the maximum quantity that could be purchased within a given context. |
| Running at a Constant Speed: | Students are asked apply knowledge of ratios to answer several questions regarding speed, distance and time. |
, a to b, or a:b where b ≠ 0.