2D shapes and their properties

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

Can you find the squares hidden on these coordinate grids?

We started drawing some quadrilaterals - can you complete them?

How many questions do you need to identify my quadrilateral?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.