Reasoning, convincing and proving

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Who said that adding couldn't be fun?

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

Can you find the hidden factors which multiply together to produce each quadratic expression?

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?