If you're curious about why something works, it can really help to find different ways of showing (or representing) your thinking. For example, you might draw a picture or use some equipment. The problems below will give you chance to think carefully about different representations, whether they are created by you or by someone else.

It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?

How would you find out how many football cards Catrina has collected?

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Play this game and see if you can figure out the computer's chosen number.

Can you find examples of magic crosses? Can you find all the possibilities?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?