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.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
If you are a teacher click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on ...
Nine squares with side lengths $1, 4, 7, 8, 9, 10, 14, 15$ and $18$ cm can be fitted together with no gaps and no overlaps, to form a rectangle.
What are the dimensions of the rectangle?
Once you've had a chance to think about it, click below to see how three different pupils began working on the task.
This is how Anna started:
Here is what Brendan tried:
Here is Chandra's initial approach to the problem:
Can you take each of these starting ideas and develop them into a solution?