Conjecturing and generalising

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

How well can you estimate 10 seconds? Investigate with our timing tool.

Can you minimise the amount of wood needed to build the roof of my garden shed?

Play around with sets of five numbers and see what you can discover about different types of average...

Play around with the Fibonacci sequence and discover some surprising results!

Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?