Solve mathematical and real-world problems involving ratios, rates and unit rates, including comparisons, mixtures, ratios of lengths and conversions within the same measurement system.
Instruction includes the use of tables, tape diagrams and number lines.
| 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 |
| 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. |
| 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. |
| 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. |
| 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. |
| 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 |
| 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. |
| 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. |
| 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. |
| Name |
Description |
| 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. |
| 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. |
| 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. |
| 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. |
| Name |
Description |
| 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. |
| 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. |
| 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. |
| Name |
Description |
| 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. |
| 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. |
| 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. |
| 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. |
