Make or Break
How it works
Here's a 2-player game:
Player 1 breaks a stick into 4 pieces.
Player 2 chooses 3 of the 4 pieces.
Player 2 wins if it's possible to make a triangle with the 3 pieces they've chosen, and Player 1 wins if not.
Can Player 1 win? If so, what is the smallest stick where Player 1 can win? What if Player 1 has to break the stick into 5 pieces instead of 4? What about 6 pieces? 7 pieces? 10 pieces? What if Player 2 has to choose 4 pieces to use to make a quadrilateral?
Why we like this activity
- It’s fun! Students enjoy playing the game and trying to figure out how to win.
- It helps students to develop spatial reasoning.
- It helps students to develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
Finding and using strategies to figure out how to choose 3 pieces that can make a triangle.
Finding and using strategies to figure out how to break the stick into 4 pieces so it's not possible to choose 3 that can make a triangle.
Making observations / comparing and contrasting / looking for patterns / making and testing predictions / understanding and explaining when trying to figure out the smallest stick where Player 1 can win when they break the stick into 4 pieces / 5 pieces / 6 pieces / etc.
- It has a low floor and a high ceiling: It's easy for students to start playing the game by trial and error, but finding the smallest possible stick where Player 1 can win requires more careful strategizing.
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.