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

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

Can all unit fractions be written as the sum of two unit fractions?

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Can you deduce which Olympic athletics events are represented by the graphs?

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

These Olympic quantities have been jumbled up! Can you put them back together again?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

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 describe this route to infinity? Where will the arrows take you next?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Which countries have the most naturally athletic populations?

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?