Collaborative Problem Solving Project
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 on solving 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 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.
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. Show students how to access the rubric. 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.
Create and provide an enhanced version of the rubric with embedded text structures (labels, highlights, words in bold) to cue students to pay closer attention to particular terms.
SWD: Make sure all students have access to and can comprehend the information in the rubric. Students with disabilities will benefit from explicit explanation of expectations. Use multiple means of representing the information in the rubric (visual presentation of text, TTS, visual supports, etc.).
ELL: It is difficult to hear and decode the meaning of something that is being read out aloud in a foreign language. Provide students access to a written version of the information you are discussing about the project. Give students time to read the rubric first so that they can re-read it themselves while you read aloud.
Introduction to the Project
Today you will choose a topic and a group for a project. This project can relate to anything you have learned this year.
You will work on this project 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 through the project rubric, and discuss it with your classmates.
HANDOUT: Beginning a Project
Discuss the Math Mission. Students will choose a project group and project topic, and they will write a proposal for their project.
Choose a project group and project topic, and write a proposal for your project.
Choose a 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.
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 work and 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: Struggling students have difficulty articulating their thinking and constructing viable project ideas. Pull a small group of struggling students to provide guided modeling and more support. If pulling a small group is not feasible, forming strategic partnerships with students who can articulate their thinking and are able to peer mentor will be beneficial to struggling students.
ELL: Encourage students to work cooperatively. For this exercise, you may want to group students who are fluent in English with students who are not fluent so that they can assist each other with how to explain their project ideas.
Choose a Project
One way to get ideas for your project topic is to look through the Gallery problems you worked on during the year to see if there is a topic that you would like to explore further.
To develop any of these topics into project ideas, use a wide variety of sources and formats (such as social media, video, art, the Internet, books, TV, magazines, teachers, and parents.)
- Choose one of the suggested project topics, or propose a topic of your own.
About the Project
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.
About the Project
Each project must contain:
- A written explanation of the mathematics in your project.
- Accurate representations (such as equations, graphs, tables, and diagrams) of the mathematics in your project.
- Look at the rubric. Your teacher will use this rubric to judge your project. Refer back to it periodically as you work on your project so you can make sure you are covering all the key points of the rubric.
Spend a few minutes having students share their project ideas with the class.
ELL: Make sure ELLs participate in this type of activity and don't shy away from speaking.
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 what students like about their project idea.
Write a reflection about your work today. Use the sentence starter below if you find it to be helpful:
What I like about my project topic is …