Slithering Snake
How it works
Imagine that you'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 of the grid? Can you always do it, no matter where the snake starts? What about on a 3 x 4 grid? A 4 x 4 grid? A 3 x 5 grid?
In this activity, students start by classifying each square on a 3 x 3 grid as "possible" (that is, it is possible to find a path for the snake that starts in that square and covers every square) or "impossible". Then they do the same for a variety of other grids of different sizes, trying to use logic and patterns to predict which squares will be possible or impossible.
Possible and Impossible Squares handout
Starting and Ending Squares handout
Why we like this activity
It’s fun! Students enjoy finding paths for the snake and figuring out which squares are possible squares and which are impossible 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 possible squares and which squares are impossible squares without actually testing each square one by one
Looking for patterns / making and testing predictions / understanding and explaining when trying to predict the distribution of possible and impossible squares on different grids
It has a low floor and a high ceiling: Students can start identifying possible and impossible squares by trial and error, but finding ways to do this more efficiently than checking each square one by one requires more advanced reasoning and strategy.
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.