Here are some short problems for you to try. Talk to your friends about how you work them out.

An activity centred around observations of dots and how we visualise number arrangement patterns.

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

A simple visual exploration into halving and doubling.

Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?

Can you find different ways of showing the same fraction? Try this matching game and see.

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

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

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

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

This challenge produced some thoughtful ideas and reasons that would lead to a proof - very good for primary school children!

This article looks at how images, concrete apparatus and representations can help students develop deeper understandings of abstract mathematical ideas.

This article looks at how models support mathematical thinking about numbers and the number system