Reasoning, convincing and proving

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

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Simple additions can lead to intriguing results...

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

This problem looks at how one example of your choice can show something about the general structure of multiplication.

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.