Cultivating Teamwork in Math Class

Establishing community in the classroom can be a challenge. Here's an activity my students participated in on the first day of school. I learned about this activity while participating in the Advanced Educator International Space Camp in Huntsville, Alabama. The objective is for two crews of astronauts to exchange positions in cramped quarters when a new crew shows up to relieve the old crew at the International Space Station.

How the Game is Played


Players must follow these rules:

  1. Only one person can move at a time.
  2. Only movement forward (in the direction a person faces) is allowed. In the above diagram, orange players can only move right, while blue players can only move left.
  3. A person can move to an empty space in front of them.
  4. A person can jump an opposing team member in front of them.

What Does It Mean to Win the Game?

The teams win the challenge when they have exchanged their original positions. See the ending position diagram for an example of what this looks like.



What If...?

A teacher could use an agility (speed) ladder for this activitTapeOnFloory. Or if a ladder isn't handy, use tape. This is a shot of my classroom the first day. It's pretty unlikely a teacher would have only eight students. I put down three tape ladders in my classroom on the floor. If the number of students is not a multiple of eight (like my class was), the teacher could place the extra students on the side as coaches. To up the responsibility of the coach, add the rule that no one inside the ladder can talk to anyone else.

Teacher Moves

While this activity was going on, I floated between the groups and listened very carefully. I wanted to learn about which of my students would step up and take initiative; which would be a leader; which would be concerned about the frustration of others and take action to minimize other students' discomfort/anxiety. This activity helped me better understand how to assign groups for course work in a meaningful way.

Examples of Student Moves

Below is an example of what some students might do.



If the third blue player from the right jumps the lone orange player, the blue team has a problem. With two blue players in adjacent cells, the game is gridlocked and ends.


Computational Thinking

Once the students came up with the solution, I gave them the sequence "1-2-3-4-4-3-2-1" and asked them how it relates to this situation. Think of this sequence as the answer key.

1: Orange moves first
2: Blue moves next - twice
3: Orange moves three times
4: Blue moves four times
4: Orange moves four times
3: Blue moves three times
2: Orange moves two times
1: Blue moves one time

Low Entry, High Ceiling (Extending the Task)

  • Ask the students to come up with some pseudo-code to describe how they would build this game on a computer using programming applications.
  • Ask the students whether the strategy remains the same if there are teams of five? Or if there are two empty middle squares? Three empty middle squares?
  • Ask the students to write a program that allows the user to watch the game. Then ask the students to write a program that allows the user to play the game.ExampleOfMoves
  • Example from my classroom I had two students come up with different lines of thinking for coding this game on a computer. One student thought of a number line to label each cell, using the values -4, -3, -2, -1, 0, 1, 2, 3, 4. Another student thought of simply have numbers represent each student. The starting configuration would be
    1 2 3 4 _ 5 6 7 8. Then, each move would be a shuffling of the sequence. The second row would be 1 2 3 _ 4 5 6 7 8. The third row would be 1 2 3 5 4 _ 6 7 8. The fourth row would be 1 2 3 5 _ 4 6 7 8. We had a really spirited discussion of the issues that could arise from each organizational coding strategy.


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