Students choose a project idea and a partner or group. They write a proposal for their 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 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.
ELL: Give ELLs a chance to preview the project rubric ahead of time. Also, allow ELLs to discuss in their language of origin if needed.
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 this year.
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 they will be using a rubric to evaluate their projects. 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 others' projects.
Explain that problem solving provides many opportunities to generate and answer significant mathematical questions regarding the world surrounding them. Students may choose questions that employ any of the mathematics they have learned throughout this year. For students who are not secure in generating questions to pursue, this unit provides support in the form of suggested projects.
Give a few examples of possible projects.
- Create surveys and conduct random sampling to draw inferences about a population.
- Create carnival games.
- Create scale drawings or scale models.
- Use art as inspiration to discuss geometry and patterns.
- Make a game using mathematical concepts.
- Write a song or poem about math concepts.
- Create a piece of art using ratios or lines and describing the piece mathematically.
- Explore any mathematical concept students would like to know more about.
- Pose an interesting question and use mathematics and problem solving to answer the question.
Introduction to the Project
In this unit you will work with a group to complete a project.
For your project, you will answer a mathematical question of your choice that requires you to apply one or more of the mathematical concepts you explored 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 outside of class.
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 the projects.
- Look through the rubric and briefly discuss it with your classmates.
Discuss the Math Mission. Students will choose a project idea and a partner or group. They will write a proposal for the project.
ELL: After providing students with possible project options, give students time to discuss which project is the most interesting to them. Monitor students' project selection. Make sure that all students have a firm understanding about which project they will work on, and who their partner(s) will be.
Choose a project group and project topic, and write a proposal for your project.
Choose a Project Topic
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: Partner Work is designed to help students consolidate their learning by justifying their solutions to their peers. Students will have an opportunity to collaborate with peers as they summarize, analyze, problem solve, explain, and apply new knowledge. Monitor all pairs/groups to make sure they have chosen their partners wisely.
ELL: Choosing a presentation topic can be difficult when students are creating their own topics. Provide sentence starters that will support ELLs in writing their presentation proposal.
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.
Choose a Project Topic
Here are some question ideas for your problem-solving project. You can choose one of these questions, or come up with a question of your own.
- How can you use sampling, graphs, and statistical measures to make conclusions about what is typical for a population?
- How is numerical reasoning incorporated in the creation of magic squares?
- How is product pricing related to the weight or volume of the product?
- What patterns and relationships do you see in Pascal’s triangle?
If you want to come up with your own project question, choose an area that interests you and think about questions that relate to the mathematical concepts you studied in this unit. Remember that you can use the Internet to collect any data or information you need. Here are some ideas:
- Art: How do artists use geometrical concepts in their artwork?
- Science: How do hours of sunlight and average daily temperature relate to distance from the equator?
- Games: Choose or create a carnival game. What is the probability of winning the game? If you included the game in your next school fair, what kind of profit could you expect?
Share Your Project Topic
Spend a few minutes having students share their project ideas with the class.
SWD: Document all of your students' presentation topics, and post on a learning chart. This will make your students' ideas visible, and will allow you to better monitor their progress.
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: Share Your Project Topic
Listen as classmates share their project topics with the class.
As students present, ask questions such as:
- Why did you choose this project topic?
- What to you expect the results to be?
- How are you going to collect your data?
- 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 think will be challenging about their project idea.
Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.
What I think will be challenging about this project is…