Maths Investigation 1

Today we worked on a couple of maths investigations that gave us a bit of brain drain.

Firstly, the Corner to Corner counter game... on a 3x3 grid, how many moves does it take to get the red counter from the top right corner to the (empty) bottom left?

We found that the shortest number of moves is 13, and then tried out the game with a 2x2, 4x4 and 5x5 grid. We charted our progress and a pattern emerged. We found that every time a new grid was used the number of moves increased by 8.
We worked toward finding a rule for the pattern.

Lastly we investigated Ninety degree Spirolaterals. This is the pattern for drawing a 3- spirolateral: 1 + 2 + 3 + 1 + 2 + 3 etc. You draw for one square, then turn ninety degrees, draw two squares, turn ninety, draw three squares, turn ninety, and start again at one. We found that some spirolaterals come round to the start, and others (like the four) do not. They continue on indefinitely.