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Clarifications
Clarification 1: Instruction includes the use of tables, tape diagrams and number lines.Benchmark 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 understanding of fraction concepts and operations, often in the context of the relationship that relates parts to wholes. 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
- Number Lines
- Tables
- Bar Models
- 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?
- 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, including conversions of areas and volumes and conversions that are commonly used in the science classroom.
Common Misconceptions or Errors
- Some students may struggle to determine a process for solving in real-world context problems. Instruction highlights strategies for students to build perseverance by modifying methods as needed and analyze 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.
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.
- 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 1A 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
Related Resources
Formative Assessments
Lesson Plans
Perspectives Video: Expert
Perspectives Video: Professional/Enthusiasts
Perspectives Video: Teaching Idea
Tutorials
STEM Lessons - Model Eliciting Activity
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.
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.
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.
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
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.
MFAS Formative Assessments
Students are given the prices of three different quantities of cereal and are asked to determine which is the best buy.
Students are asked to solve rate problems given the time it takes each of two animals to run different distances.
Student Resources
Perspectives Video: Professional/Enthusiast
An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.
Type: Perspectives Video: Professional/Enthusiast
Tutorials
In this video, watch as we solve this word problem using what we know about equivalent ratios.
Type: Tutorial
In this video, a ratio is given and then applied to solve a problem.
Type: Tutorial
In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.
Type: Tutorial
Parent Resources
Perspectives Video: Professional/Enthusiast
An archaeologist describes how mathematics can help prove a theory about mysterious prehistoric structures called shell rings.
Type: Perspectives Video: Professional/Enthusiast
