Material Type:
Lesson Plan
Middle School
  • 6th Grade Mathematics
  • Double Number Lines
  • Graphs
  • Problem-Solving
  • Tape Diagrams
    Creative Commons Attribution Non-Commercial
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    Apply Your Knowledge about Ratios

    Apply Your Knowledge about Ratios


    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 apply their knowledge about ratios to solve a problem. They represent ratios using models such as tables, tape diagrams, double number lines, or graphs.

    Goals and Learning Objectives

    • Use and interpret ratios to solve a problem.
    • Model ratios—including tables, tape diagrams, double number lines, graphs—to represent a problem situation.
    • Articulate strategies, thought processes, and approaches to solving a problem and defend why the solution is reasonable.

    Project Rubric

    Lesson Guide

    Have students review the project rubric on the What Is in the Rubric? handout. Give students 2 minutes to study the rubric. Then have students follow the directions for talking about the rubric. 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.


    Project Rubric

    Work with a partner to review the project rubric in the What Is in the Rubric? handout.

    Take 2 minutes to study the rubric by yourself.

    Then have one partner (without looking at the rubric) take 1 minute to describe the rubric as completely as possible to the other partner (who can see it). This partner should listen carefully to the description.

    Briefly look at the rubric again together. The partner who was previously the listener should now take 30 seconds to add to the description—without looking at the rubric and without repeating any of what the other partner said.

    HANDOUT: What Is in the Rubric?

    Math Mission

    Lesson Guide

    Discuss the Math Mission. Students will design and work on their ratio project.

    ELL: Consider providing your expectations and grading scheme in writing to be sure ELLs have clarity around these topics.


    Design and work on your ratio project.

    Project Work

    Lesson Guide

    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).

    Provide useful feedback by circulating 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?

    Remind students to look at the list of what their presentation should include.

    ELL: Project these questions so that all students (especially ELLs) can view them as they are asked to respond.

    Work Time

    Project Work

    Work on your project with your project group.

    Part of your work today may involve planning, making calculations, and finding needed information.

    When your presentation is finished, it must contain the following items:

    • A written explanation that describes how you used ratios in your project
    • At least one diagram or graph that shows how you used ratios in your project
    • Accurate mathematical representations

    Use the project rubric to evaluate your project in its current state to make sure you are on the right track.

    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 (bee the last 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; after the class discussion, adopt whichever criteria have the support of the class.

    (Note: 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.)

    SWD: Students with disabilities may demonstrate difficulty assessing how to improve their projects. To promote success, consider how you will support students as they reflect. Provide possible responses from which students can choose. Model how to observe and reflect on parts of a project, so students are clear on how to best improve their work.

    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?

    Look at the bottom row, which is blank. Is there any scoring criterion for the ratio project that you think should be added here?

    Take a few minutes to discuss these questions with your 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, decide as a group whether to adopt any of the suggestions.

    Reflect On Your Work

    Lesson Guide

    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.

    SWD: Students with disabilities may have a more challenging time identifying next steps for completing their projects. Model explicitly for students (using an example project or student sample) how to review a project by using the rubric to assess and plan for revisions based on that assessment.

    Work Time


    Write a reflection about today's project work. Use the sentence starters below if you find them to be helpful.

    Today my group accomplished …

    Our next steps are …