Explaining, convincing and proving

Draw some isosceles triangles with an area of $9cm^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Can you find triangles on a 9-point circle? Can you work out their angles?

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

Are these games fair? How can you tell?

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Can you work out which drink has the stronger flavour?

Invent a scoring system for a 'guess the weight' competition.