Reasoning, convincing and proving

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Here are two games you can play. Which offers the better chance of winning?

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Are these games fair? How can you tell?

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...