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Clarifications
Clarification 1: Instruction includes using one or more operations to solve problems.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Rational Number
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
Students solve real-world problems involving any of the four operations with positive multi-digit decimals or positive fractions, including mixed numbers in grade 6, with all rational numbers in grade 7, and with rational numbers including exponents and radicals in grade 8.- This benchmark applies the procedural fluency skills of the previous benchmark to real-world problems (MTR.3.1).
- Students should develop fluency with and without the use of a calculator when performing operations with rational numbers.
- Instruction includes the use of technology to help emphasize the proper use of grouping symbols for order of operations.
- With the completion of operations with rational numbers in grade 7, students should have experience using technology with decimals and fractions as they occur in the real world. This experience will help to prepare students working with irrational numbers in grade 8.
- Open-ended tasks with real-world contexts (MTR.7.1) will allow students to practice multiple pathways for solutions as well as to make comparisons with their peers (MTR.4.1) to refine their problem-solving methods.
- Instruction includes support in vocabulary development as related to the context of the real-world problems when necessary.
Common Misconceptions or Errors
- Students may incorrectly perform operations with the numbers in the problem based on what has recently been taught, rather than what is most appropriate for a solution. To overcome this misconception, have students estimate or predict solutions prior to solving and then compare those predictions to their actual solution to see if it is reasonable (MTR.6.1).
- Students may incorrectly oversimplify a problem by circling the numbers, underlining the question, boxing in key words, and eliminating context information that is needed for the solution. This process can cause students to not be able to comprehend the context or the situation (MTR.2.1, MTR.4.1, MTR.5.1, MTR.7.1).
Strategies to Support Tiered Instruction
- Instruction includes the use of visual representations and manipulatives to represent the given situation and use the chosen representation to help find the solution.
- The teacher provides opportunities for students to comprehend the context or situation by engaging in questions like the ones below.
- 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?
- Teacher co-creates a graphic organizer with students to review operations with positive fractions and operations with integers to assist when applying operations with rational numbers.
- Instruction includes the use of a three-read strategy. Students read the problem three different times, each with a different purpose. Laminating these questions on a printed card for students to utilize as a resource in and out of the classroom would be helpful.
- 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 includes having students estimate or predict solutions prior to solving and then compare those predictions to their actual solution to see if it is reasonable.
Instructional Tasks
Instructional Task 1 (MTR.7.1)All of the 7th grade homeroom classes collected recycling, with the top three classes splitting the grand prize of $800 toward building their own gardens. Mr. Brogle’s class turned in 237 pounds of recycling, Mrs. Abiola’s class turned in 192 pounds and Mr. Wheeler’s class turned in 179 pounds. How should these top three divide the money so that each class gets the same fraction of the prize money as the fraction of recycling they collected?
Instructional Task 2 (MTR.7.1)
Kari and Natalia went to the Fun Warehouse with $20 each to spend. There is a $3 entry fee each and the menu of activities is shown below. What are some possible combinations of activities Kari and Natalia can enjoy before they each run out of money?
Instructional Task 3 (MTR.4.1, MTR.7.1)
Anjeanette is making cupcakes for her sister’s birthday. Among other ingredients, her recipe calls for 2 cups of flour, cup of butter and cup sugar in one batch. In the kitchen, she has 8 cups of flour, 2 cups of butter and 2 cups of sugar.
- Part A. How many batches of cupcakes can Anjeanette make?
- Part B. What should Anjeanette ask for if she wants to borrow from her neighbor to make one more batch?
Instructional Items
Instructional Item 1Kari and Natalia went to the Fun Warehouse with $20 each to spend. They paid the $3 entry fee each and then decided they would both play laser tag and mini-bowling. If they finished the day with playing 4 video games each, how much money will be left?
*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: Teaching Idea
Problem-Solving Tasks
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will help analyze, compare, and select fencing options for a college’s pool and recreation area. Students will use unit conversions, calculate total costs, and justify their recommendations to develop problem solving and critical thinking skills within a purchasing context.
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
In this Model Eliciting Activity, MEA, students will use the order of operations to develop and apply a scoring system to evaluate different lawn tractors for a company. Students will justify their rankings using their analysis, calculations, and scoring system.
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
In this MEA, the students will compare data to decide which franchise would be best for a person wanting to open their own fried chicken franchise.
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.
In this Model Eliciting Activity, MEA, students will evaluate and compare daycare centers near a neighborhood. They will develop a scoring system to assess various characteristics of each center and justify their ranking using averages, ratios, and other mathematical calculations.
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
In this Model Eliciting Activities, MEA, students will calculate unit rate & circumference, compare & order decimals, convert metric units, and round decimals. Bubble Burst Corporation has developed some chewing gum prototypes and has requested the students to assist in the selection of which gum prototypes will be mass produced by using both quantitative and qualitative data to rank the prototypes for Bubble Burst Corporation.
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
In this Model Eliciting Activity, MEA, students will analyze and interpret data to recommend the best vehicle purchases for a school district. Students will work collaboratively to perform calculations that can be used to make comparisons and create composite scores for each vehicle.
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
In this Model Eliciting Activity, MEA, students are asked to rank fabrics designated for a new women's volleyball team. Students will use proportional reasoning, percentages, and conversions to analyze and compare fabrics to support their rankings.
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
In this Model Eliciting Activity, MEA, students will use unit rates and scoring systems to analyze and interpret data to recommend the best store from which a family restaurant should purchase its weekly non-frozen food items.
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
In this Model Eliciting Activity, MEA, students will analyze various costs and develop a procedure to recommend the best shipping methods for machine parts. They will use mathematical skills such as calculating total costs, comparing rates, and applying percentage discounts and surcharges to determine the most cost-effective shipping options.
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
In this Model Eliciting Activity (MEA), students will analyze data related to tiling rooms in a house. Students will calculate the square footage of various rooms, convert measurements to determine the amount of tile needed, and compute both the cost of the tiles and the cost of installation. They will evaluate and compare different flooring options based on cost, quality, and installation factors, and develop a procedure to recommend the best choices.
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
In this 7th grade MEA, students will form teams to rank the best vacation package for the Johansson family vacation. They will have to calculate the total cost of the vacation package making sure they don't go over budget. Teams will suggest what the family should do with any excess money. They will also suggest any deletion of activities if the package is over budget. Teams will make a presentation of the first choice recommendation.
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 7th grade MEA Laura Banks requests a consulting firm, JJ Consulting, to help her make a decision on an employer. Students are to use the data table to calculate unit rates (nightly rate and hourly rate) and then rank her choices and write a recommendation with the procedure used to come up with the ranking.
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.
This is a NASA-themed, MEA (Model Eliciting Activity) lesson that challenges students to solve a real world open ended problem, while promoting collaboration through teamwork. This lesson asks each group of students to choose five positions and assign salaries to the positions with a given budget of $500,000. The students' original decision (and "twist") will be based on information from the client's letter(s) and data set(s). Groups are to write a detailed letter to the client of the procedure used.
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 must use their knowledge of radioactive dating and geologic time to select an effective elemental isotope to be used to date three rare specimens. This decision requires an understanding of the concept of a half-life and the benefits and limitations of radiometric dating. Students must complete mathematical calculations involving equations and operations with fractions and percentages. Students completing this MEA must develop two essays that respond in a professional manner to a client in the scientific industry.
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, students will apply their knowledge of rational numbers and order of operations to analyze and compare data to provide recommendations on the best camera to use in an introductory photography class.
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
In this Model Eliciting Activity, MEA, "Sticks and Stones May Break My Bones", teams of students work as forensic anthropologists and use equations to determine the height and gender of persons to whom a series of newly discovered bones may belong.
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, students will act as travel agents to plan a vacation package for a family of 5. Students will apply proportional reasoning and multi-step problem-solving skills to design vacation packages that meet specific criteria and stay within a given budget.
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
This resource provides a Model-Eliciting Activity where students will analyze a real-world scenario to solve a client's problem and provide the best possible solution based on a logically justified process. The students will consider a request from Always On Time Delivery Service to evaluate several GPS units and help them decide which unit they should purchase.
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
The Whirl Wind Corporation would like to install Wind Turbines in the Mojave Desert. The company produces various models of these turbines and is looking for help in selecting the best one for the job.
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, students will analyze and compare data for various products sold in a joke shop to make recommendations on the best, and worst, products. Students will apply weighted averages, ratios, percentages, and proportions to perform calculations that support their recommendations as well as create graphical representations to help make sense of and compare the 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. 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
Students are asked to assess the reasonableness of an answer using mental computation and estimation strategies.
Students are asked to solve a word problem that involves finding the average of positive and negative decimal numbers.
Students are asked to assess the reasonableness of answers using estimation strategies.
Student Resources
Problem-Solving Tasks
In this task, students answer a question about the difference between two temperatures that are negative numbers.
Type: Problem-Solving Task
Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.
Type: Problem-Solving Task
Parent Resources
Perspectives Video: Teaching Idea
Why did the math teacher KROS the ocean? Because it made for a wonderful way to engage students and do something unique.
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.
Type: Perspectives Video: Teaching Idea
Problem-Solving Tasks
In this task, students answer a question about the difference between two temperatures that are negative numbers.
Type: Problem-Solving Task
Students are asked to determine how to distribute prize money among three classes based on the contribution of each class.
Type: Problem-Solving Task
