Can you make five differently sized squares from the tangram
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
This activity investigates how you might make squares and pentominoes from Polydron.
One aspect of developing a winning strategy that could be considered is the number of distinctly different starting points ($6$ on a $5 \times 5$ board) and the number of different squares that can be drawn that include each of those points. That is, "Is there a good place to start and why?". This is a great investigation, with the capacity to expand by changing the sizes of the starting grid,
and which leads back into the game itself.
Working on the properties of a square offers an opportunity to look at gradients to establish whether a square is a square.