Conjecturing and generalising

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Explore the effect of reflecting in two intersecting mirror lines.

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

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

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

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