This cluster includes the following access points.
Vetted resources educators can use to teach the concepts and skills in this topic.
| 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 |
| Real Life Tax, Tip, and Discount!: | Students calculate the tax, tip, and discount in real-world situations. |
| Robots Get a Job: | In this MEA, students will select the robots that are more efficient at doing a certain type of job. They will have to analyze data tables that include force, force units, mass, mass units, and friction.
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 processes. 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 MEAs 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: | In this Model Eliciting Activity, MEA, the students will rank the local produce markets by using qualitative and quantitative data. The students will have to calculate unit rates of produce prices and then 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. 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 |
| 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. |
| Lightyear Rockets: | Students are asked to evaluate and test several rocket fin designs to determine the most effective design. After launch, the students are asked to test an additional design and also design their own rocket fin. Additionally, students will record and graph their results.
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 Model Eliciting Activity, MEA, students will utilize mathematical computation skills involving percentages and critical thinking skills to select the best tire deals advertised.
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 |
| 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. |
| Basketball All Star Team: | In this Model Eliciting Activity, MEA, students will create a procedure for ranking high school basketball players. Students are given statistics for each player and are asked to recommend the best player to play for an all-star team after determining the free throw, three-point, and field goal percentages. Students write about the procedure used to make their decisions. In a twist, students are given additional data to determine the mean points per game.
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 |
| 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. 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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx |
| "Ad" it Up: | Students will learn how to calculate markup, markdown, percent increase, and percent decrease. Using sales "ad" inserts from the internet, newspapers, and store flyers, students will understand how these concepts apply to real-world situations. |
| Running and Rising: | In this lesson students will graph and compare two proportional relationships from different representations in contextual problems and be introduced to the constant of proportionality as the unit rate. |
| Pricing Twelve Days of Celebration: | Students will discover how much items would cost if they were to give gifts for 12 days. They will learn how to calculate and add sales tax to find a total. |
| For Students by Students: | Students are presented with the task of evaluating several types of fabric based on each of its characteristics. They need to analyze their current uniform needs and decide by choosing which type of fabric will best fit their uniform needs. Then they have to write a report explaining the procedure they used to analyze their choices, reasoning for their ranking and make the requested recommendations.
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. |
| Shopping the Ads: | Have you ever heard students ask the question, "Why do I have to learn this?" This lesson answers that question because it requires the students to apply their knowledge in real world scenarios but does not teach a basic conceptual understanding of percentages. The teacher may use the whole lesson or select specific problems. |
| The Dazzling Painting Co.: | Students will read a letter from a painting company from New York who are planning to expand to Florida. They need help deciding on which paint sprayers to purchase. Students will use their understanding of rate and percentages to analyze data and make suggestions.
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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx |
| Travel Troubles: | This activity engages the students into time scheduling, budgeting, and decision making to maximize time efficiency.
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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx. |
| "Analyzing Wordless Stories" An Introduction to Solving Unit Rates: | In this lesson, students will apply their understanding of ratios and prior knowledge of division to determine the unit rate for a given ratio. After some initial instruction on unit rates, students will determine unit rates from diagrams with teacher guidance, and they will determine unit rates from narrative descriptions independently. |
| Makeover, Home Edition Final Part IV: | This is the final part of the lesson "Makeover, Home Edition." This lesson is designed to teach students the applicability of finding the area of composite figures as well as understanding the importance of ratios in the real world. Part I (#48705) dealt with determining backyard dimensions for fence installation. Part II (#48967) concentrated on inserting a pool and patio into this backyard. Part III (#49025) dealt with creating a scale drawing of the backyard. |
| 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. 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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx |
| 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. |
| Makeover, Home Edition Part II: | This is the second part of the lesson, "Makeover, Home Edition." This lesson will continue focusing on unit prices, but also incorporates area and volume. Part I (Makeover, Home Edition #48705) is based on creating backyard dimensions for fencing. Part III (Makeover, Home Edition #49025) will deal with creating a scale drawing of this backyard. Part IV (Makeover, Home Edition Final #49090) will focus on inserting a window and painting walls inside the house. |
| Savvy Shopper: | This unit rate culminating activity has students apply knowledge to purchasing groceries. Specifically, knowledge of how unit rates can help save money over time. |
| Equivalent Fractions and Percents: | This lesson is designed to give students their very first experience with the concept and representation of percents. The activities seeks to lay a conceptual foundation for later problem solving with percents by building on students' prior knowledge of fractions with denominators of 10 or 100 and finding equivalent ratios. Throughout the lesson they use art to show the visual connection between fractions and percents. Students develop the knowledge that a percent is a part/whole ratio where the whole is measured in hundredths. The lesson gives students the opportunity to visually represent fractions and percents on a 10 x 10 grid, along with an enrichment activity if the teacher wants in expand to include decimal conversions and finding. |
| Can you say that another way?: | Students will model how to express an addition problem using the distributive property. |
| The Concept of Ratios: | This lesson introduces students to the term ratio, its meaning and use, and the various ways in which a ratio can be presented. |
| But Mom, I Really Want an iPad!!!!!! Part 2: | This is the 2nd Lesson where students are asked to solve a problem concerning the purchase of an iPad. Please see But Mom, I Really Want an iPad !! Part 1 (Resource 47500) for Lesson 1. Students are encouraged to use strategies to find equivalent ratios in their solutions. |
| 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 |
| Makeover, Home Edition Part I: | This is the first part of the lesson, "Makeover Home Edition." This lesson is designed to increase student engagement. Students must think critically about fencing in their new "dream" backyard by calculating the total fencing needed. They will choose the most cost-effective method of purchasing their fencing by comparing unit rates mathematically and graphically. CPALMS Lesson Part II (#48967) will concentrate on inserting a pool and patio into this backyard. Part III (#49025) will include the creation of a scale drawing of this backyard. Part IV (#49090) focuses on inserting a window and painting walls inside the house. |
| Fancy Fractions Catering Company Project: | Fancy Fractions Catering Company will be hosting a party and need your help to make it happen! Your help is needed to determine which recipe would be best for them to use in their pasta dish taking into account ingredient cost and customer preference.
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 processes. 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 MEAs 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. |
| But Mom, I Really Want an iPad!!!!! Part 1: | In this lesson, students are asked to find how long it will take for a girl to raise the money needed to buy an iPad. Students explore various solution strategies, including making tables of equivalent ratios and writing an equation to find equivalent ratios. A situational story is used to capture the students' interest and to help students create a visual for the relationship between quantities in a ratio. |
| Rank Our Pressure Cleaners: | In this Model Eliciting Activity, MEA, students are to decide on a pressure cleaning machine that will provide the Sidewalks and Roof Cleaning Services Incorporated with the best value for their money. Students are asked to provide a "Best Value" pressure cleaner to the company owner and explain how they arrived at their solution.
Model Eliciting Activities 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 |
| Is It Fair?: | In this lesson students will use their understanding of ratios and unit rate to solve problems where they must decide whether various situations are fair. |
| Here's a tip!: | Students will solve problems involving sales tax and tips; students will apply the properties of operations with numbers in decimal, percent, and fraction form. Students will convert between numbers in any form as appropriate. |
| Happy Lawns: Lawn Care Service MEA: | This Model Eliciting Activity (MEA) is written at a 6th grade level.
This MEA asks the students to decide on a lawn mower that will provide the Happy Lawns: Lawn Care Service with the best value for their money. Students are asked to rank order the lawn mowers in term of gas tank capacity, customer rating, speed, amount of time the mower takes to cut an acre of grass, shipping, and cost of the lawn mower. Students must provide a "Best Value" lawn mower 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. 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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx |
| Summer Road Trip: | Students will go on a virtual "road trip" with a partner. Using the scale on a map, students will calculate the distance traveled, the amount of gas used, and the cost of the gas. |
| 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. |
| sandundertheswingset2024: | The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set? |
| 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. |
| sandundertheswingset2024: | The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set? |
| 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. |
| sandundertheswingset2024: | The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started. The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set? |
| 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.