Vector Racer
Printable sheets: Instructions, race track 1, race track 2 (avoid the pits)
To play this game, you will need to print off a copy of the race track, and you will need someone to play with.
Rules:
Each player moves in turn, and uses vector notation to describe their moves around the race track.
Each player starts off from rest.
Each horizontal and vertical component cannot differ by more than two from the previous move.
For example, after a move of $\pmatrix{0\cr 2}$ the following moves are possible:
| $\pmatrix{-2\cr 0}$ | $\pmatrix{-1\cr 0}$ | $\pmatrix{0\cr 0}$ | $\pmatrix{1\cr 0}$ | $\pmatrix{2\cr 0}$ |
| $\pmatrix{-2\cr 1}$ | $\pmatrix{-1\cr 1}$ | $\pmatrix{0\cr 1}$ | $\pmatrix{1\cr 1}$ | $\pmatrix{2\cr 1}$ |
| $\pmatrix{-2\cr 2}$ | $\pmatrix{-1\cr 2}$ | $\pmatrix{0\cr 2}$ | $\pmatrix{1\cr 2}$ | $\pmatrix{2\cr 2}$ |
| $\pmatrix{-2\cr 3}$ | $\pmatrix{-1\cr 3}$ | $\pmatrix{0\cr 3}$ | $\pmatrix{1\cr 3}$ | $\pmatrix{2\cr 3}$ |
| $\pmatrix{-2\cr 4}$ | $\pmatrix{-1\cr 4}$ | $\pmatrix{0\cr 4}$ | $\pmatrix{1\cr 4}$ | $\pmatrix{2\cr 4}$ |
Challenge a friend to a race.
Choose your starting positions and agree what the penalty will be for going off the track.
Who can get round in the fewest moves?
”‹Here is an alternative version you might like to try.
The challenge is to avoid the pits.
Extension:
Who can get round in the shortest distance?
This could be introduced as a competitive game, but you could then invite your students to work together to find the most efficient route.
To start off with, some students may find it easier to change the vector's components by at most 1.