CPALMS Logo Generated on 9/17/2025 at 10:31 PM
The webpage this document was printed/exported from can be found at the following URL:
https://www.cpalms.org//PreviewStandard/Preview/15874
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.
Standard #: MA.6.AR.3.5
Standard Information
Standard Clarifications
Clarification 1: Instruction includes the use of tables, tape diagrams and number lines.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Algebraic Reasoning
Standard: Understand ratio and unit rate concepts and use them to solve problems.
Date Adopted or Revised: 08/20
Status: State Board Approved
Standard Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Customary units
  • Metric units
  • Rate
  • Unit Rate

 

Vertical Alignment

Previous Benchmarks

Next Benchmarks

 

Purpose and Instructional Strategies

In elementary grades, students developed an understanding of fraction concepts and operations, often in the context of the relationship that relates parts to wholes. Students also learned how to convert measurements within the same measurement system. In grade 6, students solve problems involving ratio relationships. In grade 7, students will solve problems involving proportional relationships. This benchmark is the culmination of the MA.6.AR.3 standard. It combines all of the concepts developed in the previous four benchmarks and applies them to a variety of mathematical and real-world contexts, including conversions of units within a measurement system. In grade 7, students are expected to convert units across different measurement systems.
  • Instruction includes a variety of problem types including comparison, mixtures, lengths and conversions. Students should work within the same measurement system, for example, standard measurement to standard measurement or metric system to metric system.
  • It is not the expectation of this benchmark to solve problems using proportions; however, problem types will naturally start to build the foundation of proportions and proportional relationships. 
  • Instruction includes the use of bar models, tables and number lines to help students see relationships and relevance to real-world application (MTR.2.1).
    • For example, 3 toy cars cost Mikela $5 at the local superstore. Mikela needs 18 toy cars. How much will it cost Mikela to buy the cars?
      • Bar Models
        Toy cars vs dollars on a bar model
      • Number Lines
        Toy cars vs dollars on a number line.
      • Tables
        Toy cars vs dollars on a table.
  • Discussion about why students used certain methods to solve specific problems can help students see the patterns for determining their own processes in the future (MTR.2.1, MTR.5.1, MTR.7.1).
  • Instruction includes many opportunities for converting between units in the same measurement system.

 

Common Misconceptions or Errors

  • Some students may struggle to determine a process for solving problems in a real-world context. Instruction highlights strategies for students to build perseverance by modifying methods as needed and analyzing the problem in a way that makes sense (MTR.1.1).

 

Strategies to Support Tiered Instruction

  • Teacher provides opportunities for students to comprehend the context or situation by engaging in questions (writing questions on flash cards to reuse will be useful) such as:
    • What do you know from the problem?
    • What is the problem asking you to find?
    • Can you create a visual model to help you understand or see patterns in your problem?
  • Instruction includes using colored pencils to identify the units in each corresponding portion of a ratio and identifying the units before writing the numerical values.
  • Instruction includes the use of a three-read strategy. Students read the problem three different times, each with a different purpose.
    • First, read the problem with the purpose of answering the question: What is the problem, context, or story about?
    • Second, read the problem with the purpose of answering the question: What are we trying to find out?
    • Third, read the problem with the purpose of answering the question: What information is important in the problem?
  • Instruction highlights strategies for students to build perseverance by modifying methods as needed and analyzing the problem in a way that makes sense.

 

Instructional Tasks

Instructional Task 1 (MTR.7.1)
On the first day of camp, Sara hiked 20 miles in 5 hours.
  • Part A. At this rate, how long would it take Sara to hike 12 miles? Show and explain how you determined this.
  • Part B. At this same rate, how many miles could Sara hike in 2 hours? Show and explain how you determined this.

Instructional Task 2 (MTR.7.1)
Chris and Jenny are comparing two similar punch recipes. Each recipe calls for cranberry juice and ginger ale but in different amounts. The tables below show the amounts of cranberry juice and ginger ale for four different quantities of punch.
Chris's Punch and Jenny's Punch
  • Part A. Is the ratio of the punch that is cranberry juice the same in each of Chris’s recipes given in his table? Explain how you determined your answer.
  • Part B. Is the ratio of the punch that is cranberry juice the same in each of Jenny’s recipes given in her table? Explain how you determined your answer.
  • Part C. Is the ratio of the punch that is cranberry juice the same in Chris’s recipes as it is in Jenny’s recipes? If not, whose punch has a greater concentration of cranberry juice? Explain how you determined your answer.

 

Instructional Items

Instructional Item 1
A recent study found that parking lots for offices should have a ratio of 6 spaces for every 1000 square feet of floor space. If a new office building has 19,000 square feet of floor space, how many spaces should there be in the parking lot?

Instructional Item 2
Jessica made 8 out of 24 free throws. Bob made 5 out of 20 free throws. Who has the highest free throw ratio?

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
  • MA.6.AR.3.AP.5a # Use tools, models or manipulatives to solve problems involving ratio relationships including mixtures and ratios of length.
  • MA.6.AR.3.AP.5b # Use tools, models or manipulatives to solve ratio, rate or unit rate problems involving conversions within the same measurement system.
Related Resources
Formative Assessments
Lesson Plans
  • 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.
  • 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
  • "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.
  • 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.
  • 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.
  • 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.
  • 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
  • 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
  • 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.
  • 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.
  • 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.
Perspectives Video: Expert
Perspectives Video: Professional/Enthusiasts
Perspectives Video: Teaching Idea
Problem-Solving Tasks
  • 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.
  • 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.
Teaching Idea
  • Bad Date (A Real World Application of Ratios) # In this video from Math Snacks, a women goes on three dates, after which she analyzes the ratio of how many words she speaks compared to the number of words her date speaks. By attaining a 1:1 ratio of words, she attains her "Happily Ever After." A learner's guide, teachers guide, and transcript of the video is included.
Tutorials
STEM Lessons - Model Eliciting Activity
  • 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.
  • 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.
  • 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
  • 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
  • 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
  • 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.
  • 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
MFAS Formative Assessments
Print Page | Close this window