We always use this activity before students work on math together, as it helps improve group interactions. Teachers who have tried this activity have been pleased by students’ thoughtful responses and found the students’ thoughts and words helpful in creating a positive and supportive environment. The first thing to do is to ask students, in groups, to reflect on things they don’t like people to say or do in a group when they are working on math together. Students come up with quite a few important ideas, such as not liking people to give away the answer, to rush through the work, or to ignore other people’s ideas. When students have had enough time in groups brainstorming, collect the ideas. We usually do this by making a What We Don’t Like list or poster and asking each group to contribute one idea, moving around the room until a few good ideas have been shared (usually about 10). Then we do the same for the What We Do Like list or poster. It can be good to present the final posters to the class as the agreed‐on classroom norms that you and they can reflect back on over the year. If any student shares a negative comment, such as “I don’t like waiting for slow people,” do not put it on the poster; instead use it as a chance to discuss the issue. This rarely happens, and students are usually very thoughtful and respectful in the ideas they share.
| Activity | Time | Description/Prompt | Materials |
| Launch | 5 min | Explain to students that working in groups is an important part of what mathematicians do. Mathematicians discuss their ideas and work together to solve challenging problems. It’s important to work together, and we need to discuss what helps us work well together. | |
| Explore | 10 min | Assign a group facilitator to make sure that all students get to share their thoughts on points 1 and 2. Groups should record every group member’s ideas and then decide which they will share during the whole‐class discussion. In your groups . . .
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| Discuss | 10 min | Ask each group to share their findings. Condense their responses and make a poster so that the student ideas are visible and you can refer to them during the class. |
Two to four pieces of large poster paper to collect the students’ ideas |
One of the most important topics in mathematics is reasoning. Whereas scientists prove or disprove ideas by finding cases, mathematicians prove their ideas by reasoning—making logical connections between ideas. This activity gives students an opportunity to learn to reason well by having to convince others who are being skeptical.
Before beginning the activity, explain to students that their role is to be convincing. The easiest person to convince is yourself. A higher level of being convincing is to convince a friend, and the highest level of all is to convince a skeptic. In this activity, the students learn to reason to the extent that they can convince a skeptic. Students should work in pairs and take turns to be the one convincing and the one being a skeptic.
Give each student a square piece of paper. If you already have 8.5 × 11 paper, you can ask them to make the square first.
The first challenge is for one of the students to fold the paper to make a right triangle that does not include any of the edges of the paper. They should convince their partner that it is a right triangle, using what she knows about right triangle to be convincing. The skeptic partner should ask lots of skeptical questions, such as “How do you know that this angle is 90 degress?” and not accept that they are because it looks like they are.
The partners should then switch roles, and the other student folds the paper into an equilateral triangle that does not include any of the edges of the paper. Their partner should be skeptical and push for high levels of reasoning.
The partners should then switch again, and the challenge is to fold the paper to make an isosceles triangle, again not using the edges of the paper.
The fourth challenge is to make a scalene triangle triangle. For each challenge, partners must reason and be skeptical.
When the task is complete, facilitate a whole‐class discussion in which students discuss the following questions:
| Activity | Time | Description/Prompt | Materials |
| Launch | 5 min | Tell students that their role for the day is to be convincing and to be a skeptic. Ask students to fold a piece of paper into a rectangle that is not a square. Choose a student and model being a skeptic. | |
| Explore | 10 min | Show students the task and explain that in each round, they are to solve the folding problem. In pairs, students alternate folding and reasoning and being the skeptic. After students convince themselves they have solved each problem, they switch roles and fold the next challenge. Give students square paper or ask them to start by making a square. The convincing challenges are as follows:
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| Discuss | 10 min | Discuss the activity as a class. Make sure to discuss the roles of convincer and skeptic. |
Reflection:
Switch roles
Reflection:
Switch roles
Reflection:
Switch roles
Reflection: