Slithering Snake
How it works
We're trying to help a snake move around a 3 x 3 grid. The snake can move left, right, up, or down, but it can't move diagonally and it can't revisit squares or cross over itself. Can you find a path for the snake that covers every square in the grid without getting trapped? Does it matter where you start? What about on a 4 x 4 grid? A 3 x 4 grid? Other grids?
In this activity, students start by classifying the squares of a 3 x 3 grid as "winning" squares (where it's possible to find a path starting in that square that covers all the squares of the grid) or "losing" squares (where it's not possible). They then do the same for other grids, developing strategies to efficiently figure out which squares are winning squares and which are losing squares.
Winning and Losing Squares handout
Starting & Ending Squares handout
Why we like this activity
- It’s fun! Students enjoy finding paths for the snake and figuring out which squares are winning squares and which are losing squares.
- 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 find paths for the snake that cover all the squares
Using logic / making and testing predictions / understanding and explaining when trying to figure out which squares are winning squares and which squares are losing squares without drawing paths
Looking for patterns / making and testing predictions / understanding and explaining when trying to predict the distribution of winning and losing squares on different grids
- It has a low floor and a high ceiling: It's easy for students to start figuring out which squares are winning squares and losing squares by trial and error, but doing this efficiently requires more advanced strategies.
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.