Students choose a project idea and a partner or group. They write a proposal for the project.
Projects engage students in the applications of mathematics. It is important for students to apply mathematical ways of thinking to solve rich problems. Students are more motivated to understand mathematical concepts if they are engaged in solving a problem of their own choosing. In this lesson, students are challenged to identify an interesting mathematical problem and to choose a partner or a group to work with collaboratively in order to solve that problem. Students gain valuable skills in problem solving, reasoning, and communicating mathematical ideas with others.
Goals and Learning Objectives
- Identify a project idea
- Identify a partner or group to work with collaboratively on a math project
Introduction to the Project
Introduce the project and have pairs review the project rubric together for a few minutes. Then discuss the rubric with the class.
SWD: Grouping students by skill level will allow for more efficient provision of teacher support, while grouping students heterogeneously will promote cooperative teaching and learning opportunities for students with varying mathematical skills. Monitor groups to ensure all students’ progress. It is often best practice to pair students with disabilities with typically developing peers.
ELL: If ELLs don’t know what a rubric is, show one and explain how it is used. Allow ELLs to use a dictionary if they wish.
Tell students that problem solving gives them opportunities to generate and answer real-world mathematical questions. Students may choose questions that use any of the mathematics they have learned so far in class.
Give students the big picture of the project:
- Explain the purpose and importance of projects.
- Encourage students to think about questions that might lend themselves to a project idea: mathematical questions that puzzle students, amuse them, or pique their curiosity.
- Discuss the amount of class time that students will devote to projects:
- One day to choose the project and their work partner or group
- One day to work on the project in class
- Two days to present and learn from the projects
- Detail your expectations for time spent on the project outside of class.
- Outline how the project will fit into the grading scheme.
Tell students that they will be using a rubric to evaluate their projects. Tell them the rubric will be used to score their project. Let students know that they will have a chance to customize the rubric so that it fits their problem-solving projects as closely as possible. Have students look through the rubric and talk about how they will be using it to evaluate their own and each other’s projects.
Introduction to the Project
Today you will choose a topic for a ratio project. The topic you choose must incorporate working with ratios in some way.
You will work on this project with your group over the course of the unit. You will be given some class time to work on your project, but you will also work on it at home.
At the end of the unit, your group will present your project to the class. Your teacher will use a project rubric to evaluate all of the projects. Look at the rubric and discuss it with your classmates.
HANDOUT: Project Rubric: Ratio
Discuss the Math Mission. Students will choose a project topic and a partner or group. They will write a proposal for the project.
Choose a project topic and work with your group to write a proposal for your project.
Choose a Project
Begin by letting students know that at the end of the period, everyone will know their project idea and their project partner or group. Explain the structure of the day:
- Generate and practice talking about project ideas: Students use a list of project ideas and their own ideas to talk in pairs about which topics interest them. Each student pair talks for a short time and then students switch partners. The goal is for students to exchange ideas with as many students as possible.
- Hear more ideas and think about possible work partners or groups: Ask students to share any interesting project ideas they heard.
- Prepare for partner or group selection: If students have a project idea, have them write it on a slip of paper.
- Form project groups: Have students stand and circulate to find a partner or group. Remind students that they need partners or group members who will share the work equally. Have students identify their partner or group and their project idea.
- Finalize project ideas and begin work: For the last part of class, have pairs or groups work as follows:
- Pairs or groups who have a project idea meet to write a project proposal and begin project planning.
- Pairs or groups who do not have a project idea work to select a project from a list of suggested project ideas.
Tell students that they will have one day to work on the project in class. Give them that calendar date and the dates for the presentations. Emphasize that a well-done project typically requires more work time than a single class session, so students are expected to work outside of class.
SWD: Post the project requirements, important due dates, timeline for completed steps, and the rubric in the classroom for students to use as a resource as they work.
Choose a Project
Did you know that when you fly on an airplane, ride your bicycle, or bake a cake, ratios are “helping you out”? It’s true! Airplanes fly based on glide ratios, bicycles shift gears based on gear ratios, and using the right ratio of ingredients in a cake recipe is what makes the cake turn out to be so yummy.
Ratios are all around us, which means you can have some fun deciding on a project topic about ratios. Your ratio project could be about building model airplanes with the best glide ratios, finding the best formulas to use to create a volcanic eruption, or exploring gears in various contexts.
Look at the list of possible project topics, as well as resources that will help you get started.
You can choose one of these topics or propose a topic of your own.
HANDOUT: Project Ideas
About Your Project
Not all students will pose good project ideas independently. Though some may do so, you will probably need to help others word their ideas carefully. Try to provide most of this help by asking clarifying questions.
Some students may want to change projects midstream. Use your judgment, but consider the value of having students stick with their choices. The experience may help them learn to be more careful when choosing their next project.
About Your Project
Look at the project rubric again. Your teacher will use this rubric to judge your project. Refer to it periodically as you work on your project so that you can make sure you are covering all the key points of the rubric.
Each project must contain the following:
- 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
Spend a few minutes having students share their project ideas with the class.
Students may ask to see examples of projects, especially if they have not done projects before. This is a good idea, with two caveats:
- Make sample projects available for students’ inspection without spending class time reviewing them. Students must choose to invest their time and decide whether it is a worthwhile endeavor.
- Provide sample projects that are not projects that can be done for this unit. The projects can be from an adjacent grade level or from a different unit you have taught. This will help ensure that you do not get imitative projects.
Ways of Thinking: Make Connections
Listen as your classmates share their project ideas with the class.
As your classmates present, ask questions such as:
- Why did you choose this project?
- What will you have to do to make the project successful?
- Have you thought about how you will present your project?
Reflect On Your Work
Have each student write a brief reflection before the end of class. Review the reflections to learn why students chose their ratio project.
ELL: When writing the reflection, allow some additional time for ELLs to discuss with a partner before writing to help them organize their thoughts. Allow ELLs who share the same native language to discuss in their preferred language and to use a dictionary.
Write a reflection about the project ideas discussed in class today. Use the sentence starter below if you find it to be helpful.
I chose my ratio project because …