math problem solving rubric

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• Resource Library
• 7th Grade Mathematics
• Problem-Solving

Education Standards

Maryland college and career ready math standards.

Learning Domain: Statistics and Probability

Standard: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Standard: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Standard: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"ť), identify the outcomes in the sample space which compose the event.

Standard: Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Common Core State Standards Math

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Project Rubric: Making Connections

Project rubric: putting math to work, project rubric & criteria.

Students design and work on their projects in class. They review the project rubric and, as a class, add criteria relevant to their specific projects.

Key Concepts

Students are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills.

Students will:

• Try a variety of strategies to approaching different types of problems.
• Devise a problem-solving plan and implement their plan systematically.
• Become aware that problems can be solved in more than one way.
• See the value of approaching problems in a systematic manner.
• Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.
• Make connections between previous learning and real-world problems.
• Create efficacy and confidence in solving challenging problems in a real-world setting.

Goals and Learning Objectives

• Create and implement a problem-solving plan.
• Organize and interpret data presented in a problem situation.
• Use multiple representations—including tables, graphs, and equations—to organize and communicate data.
• Articulate strategies, thought processes, and approaches to solving a problem and defend why the solution is reasonable.

Project Rubric

Lesson guide.

Have students view the project rubric. Give students a minute to study the rubric. Then have students take turns saying one thing about the rubric without looking at it.

When students are finished, tell them that today they will add any specifics to the rubric that they think are needed for evaluating their projects.

SWD: Students with disabilities may have a more challenging time identifying areas of improvement to target in their projects. Teach your students how to review a project using the rubric and a sample project. Model for students how to evaluate their project to ensure they are completing all components needed and identifying any areas that need to be addressed that are not in the rubric.

Work with a partner to review the project rubric.

• Take a few minutes to study the rubric by yourself.
• Without looking at the rubric, take 1 minute to describe the rubric as completely as possible to your partner (who can look at the rubric). Your partner should listen carefully to your description.
• Briefly look at the rubric again. Your partner should now take 30 seconds to add to your description of the rubric—without repeating any of your description and without looking at the rubric.

Math Mission

Discuss the Math Mission. Students will work on their projects and evaluate their progress using the project rubric.

Work on your project, and evaluate your progress using the project rubric.

Organize and Analyze Project Data

Make sure students understand that the best use of this in-class project work day is to accomplish what they can't easily do later outside of class. Big, beautiful displays are a last step; now is the time for groups to decide how they will go about completing their project. Today's work is messy and preliminary; some of it may be devoted to finding resources (Internet-based and elsewhere).

Circulate among the working pairs and groups—listening to what they say and watching what they do. Ask clarifying questions:

• What mathematical concepts can you use to investigate your question?
• What materials are necessary?
• How will you investigate your question?
• How can you use units to clarify your results?
• How will you communicate your results to your audience?

SWD: Some students with disabilities may struggle with time management, create a timeline and “to do list” for students so they know where their progress should be regarding project completion. Hang this information in a prominent location in your classroom.

Today you will:

• Conduct research to gather information or collect data.
• Organize your information or data.
• Analyze your information or data in order to answer your question.

As you work on your project, consider these questions:

• What mathematical concepts do you need to use in order to investigate your question?

Examples: Numerical reasoning, probability, statistics, geometry, ratios and proportional relationships, expressions, and equations

• How will you communicate your conclusions to the class?

Examples: Diagrams and graphs, equations, verbal explanations, and models

As you work, use the project rubric to evaluate your progress and make sure you are on the right track.

Your Completed Project

Go over the list of what the presentations should include.

Your completed project should include:

• The information or data you researched.
• Graphs or diagrams that communicate your findings.
• Expressions, equations, or formulas that you used to make your conclusions.
• A summary of your findings.
• Your conclusions regarding your specific question.

Make Connections

Have students return to the project rubric. Tell them that, as a class, they can agree to add to—but not subtract from—the general rubric to improve the fit with their problem-solving projects.

There are two main ways to add to the rubric:

• Add detail to one or more of the descriptions of score 4.
• See the column “Specific to This Project.”
• Add a new criterion for scoring, and then describe the score 4 for that criterion. See the blank, last row.

Give students a couple of minutes to talk with their partner or group. Then let individuals propose any specific additions. You or a student may record these additions, and after the class discussion, adopt whichever criteria have the support of the class.

Note that this is a brief, focused opportunity for students to take ownership of the rubric. They may make several additions or none. The objective is their buy-in.

Performance Task

Ways of thinking: make connections.

Look at the rubric again.

• Notice the blank column with the heading “Specific to This Project.” Is there anything that you think should be added to this column?
• Next, look at the bottom row that is blank. Is there any scoring criterion for the project that you think should be added here?

Take a few minutes to discuss these questions with a partner.

• Write down any ideas you have.
• Discuss your ideas as a class. As you propose an idea make sure to explain why you think it is important. After all ideas are discussed the class will decide as a group whether to adopt any of the suggestions.

Reflect on Your Work

Give students a few minutes to respond individually to two simple prompts, focused on what they accomplished today and what their next steps are. These reflections can be quite skeletal—very short lists are fine.

Then give partners and groups a few more minutes to share their individual reflections.

Make sure students realize that their reflections now serve as their starter for the work they will do outside of class to complete their problem-solving project.

ELL: The “Reflect on Your Work” section provides opportunities for ELLs to develop literacy in English and proficiency in mathematics. Make sure students use both academic and specialized mathematical language when reflecting on their project. Give students time to discuss the summary before they write, and make sure students create a task list for completing their project based upon the rubric.

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful. After you have finished, share your reflections with your group.

Today my group accomplished…

Our next steps are…

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