Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

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

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

What do you see as you watch this video? Can you create a similar video for the number 12?

Are these statements always true, sometimes true or never true?

Can you find ways of joining cubes together so that 28 faces are visible?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.

Can you find any perfect numbers? Read this article to find out more...

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Marion Bond recommends that children should be allowed to use 'apparatus', so that they can physically handle the numbers involved in their calculations, for longer, or across a wider ability band,. . . .

Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.

What would you do if your teacher asked you add all the numbers from 1 to 100? Find out how Carl Gauss responded when he was asked to do just that.

A case is found with a combination lock. There is one clue about the number needed to open the case. Can you find the number and open the case?

Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.