General Information
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Test Item Specifications
Items using the comparison of a ratio will use whole numbers. Rates can be expressed as fractions, with “:” or with words. Items may involve mixed units within each system (e.g. convert hours/min to seconds). Context itself does not determine the order. Name the amount of either quantity in terms of the other as long as one of the values is one unit.
No
Required
Sample Test Items (2)
Test Item # | Question | Difficulty | Type |
Sample Item 1 | Which statement describes a unit rate?
|
N/A | MC: Multiple Choice |
Sample Item 2 | Dominic is buying candy by the pound for a party. For every 10 pounds of
candy he buys, he pays $12. What is the cost, per pound, for the candy? |
N/A | EE: Equation Editor |
Related Courses
Course Number1111 | Course Title222 |
1205010: | M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
1205020: | M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 - 2024, 2024 and beyond (current)) |
1204000: | M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) |
7812015: | Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current)) |
7912110: | Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated)) |
Related Resources
Formative Assessments
Name | Description |
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. |
Book Rates | Students write and explain the meaning of a ratio and corresponding unit rate in the context of a word problem. |
Lesson Plans
Name | Description |
Build Me a Beach House | This is a multi-day activity that reinforces science, math, and technology skills by taking the students through the design process. Students will be tasked with designing and building a structure that could withstand high winds and water as would be found close to the seashore. |
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 |
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. |
Recognizing Proportional Relationships to Develop Sense of Scale | This 90-minute lesson (15-minute pre-lesson, 60-minute lesson and 15-minute follow up lesson or homework) asks students to analyze proportional relationships to solve real world and mathematical problems. The examples use recipes, paint, and buildings. Students begin by working individually, then in pairs or threes, and then as a whole class. Student will need calculators, large sheets of paper to make a poster and the lesson materials. |
Catapult a Rate | This lesson uses student created data to find the unit rate of distance per time. Students catapult three different coins, measure time and distance to find the rate of flight for each coin. |
"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. |
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 |
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. |
What Does a Ratio Look Like? | The class will use a PowerPoint presentation to take a stroll down the beach for some ice cream. The students must investigate how to write the number of ice cream cones in relation to the cost of ice cream. |
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. |
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. |
Pancakes over a Campfire! | In this activity, students will learn how to set up ratios and calculate unit rates using a recipe. |
Original Student Tutorial
Name | Description |
Farmers Market: Ratios, Rates and Unit Rates | Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial. |
Perspectives Video: Expert
Name | Description |
Statistical Sampling Results in setting Legal Catch Rate | Fish Ecologist, Dean Grubbs, discusses how using statistical sampling can help determine legal catch rates for fish that may be endangered. Download the CPALMS Perspectives video student note taking guide. |
Perspectives Video: Professional/Enthusiasts
Name | Description |
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. |
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. |
Problem-Solving Tasks
Name | Description |
The Escalator, Assessment Variation | Students are provided seven choices and are asked to determine the ratios that are correct for the given context. |
Mangos for Sale | Students are asked to determine if two different ratios are both appropriate for the same context. |
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 - Make Some Chocolate Crispies | In this activity students calculate the ratio of chocolate to cereal when making a cake. Students then use that ratio to calculate to amount of chocolate and cereal necessary to make 21 cakes. |
Tutorials
Name | Description |
Solving Unit Rate Problem | This video demonstrates solving a unit rate problem using equivalent ratios. |
Solving Unit Price Problem | This video demonstrates solving a unit price problem using equivalent ratios. |
Student Resources
Original Student Tutorial
Name | Description |
Farmers Market: Ratios, Rates and Unit Rates: | Learn how to identify and calculate unit rates by helping Milo find prices per item at a farmer's market in this interactive tutorial. |
Problem-Solving Tasks
Name | Description |
Mangos for Sale: | Students are asked to determine if two different ratios are both appropriate for the same context. |
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. |
Tutorial
Name | Description |
Solving Unit Price Problem: | This video demonstrates solving a unit price problem using equivalent ratios. |
Parent Resources
Problem-Solving Tasks
Name | Description |
Mangos for Sale: | Students are asked to determine if two different ratios are both appropriate for the same context. |
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 - Make Some Chocolate Crispies: | In this activity students calculate the ratio of chocolate to cereal when making a cake. Students then use that ratio to calculate to amount of chocolate and cereal necessary to make 21 cakes. |