Tag Team
How it works
Imagine that you're playing a game of tag. This version of tag is a little different than usual, though: In this version, everyone stands in a square grid pattern and no one chases anyone. There are multiple "it"s, and each round, all the "it"s tag all of their neighbors (not including diagonals). If a person gets tagged by at least two "it"s, then they become "it" (but not if they only get tagged by one "it"). If a person becomes "it", they stay "it" until the end of the game. The game ends when everyone is "it" or when it isn't possible for anyone else to become "it". What is the smallest number of people who need to start out as "it"s in order for it to be possible for everyone to become "it"? Where should these "it"s be located to make sure that everyone becomes "it"?
In this activity, students start by exploring how to place "it"s on small square grids. After finding the minimum number of "it"s they need for everyone to become "it", they explore trying to do this with additional constraints (for example, if they're not allowed to have an "it" in every row and column). Then they move on to larger square grids, as well as rectangular, hexagonal, and triangular grids.
Why we like this activity
- It’s fun! Students enjoy placing the "it"s and watching how the team of "it"s grows.
- It helps students to develop spatial reasoning.
It requires students to engage in mathematical habits of mind:
Finding and using strategies to find ways to place the "it"s so that everyone eventually becomes "it".
Making observations / comparing and contrasting / looking for patterns / making and testing predictions / finding and using strategies / understanding and explaining when exploring the game on different grid sizes and shapes.
- It has a low floor and a high ceiling: It's easy for students to start trying to find solutions by trial and error, but when there are additional constraints, students need to strategize more carefully.
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.