A game in which players take it in turns to choose a number. Can you block your opponent?

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

A game to make and play based on the number line.

Use the tangram pieces to make our pictures, or to design some of your own!

Factors and Multiples game for an adult and child. How can you make sure you win this game?

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Can you fit the tangram pieces into the outline of Little Ming?

Make a clinometer and use it to help you estimate the heights of tall objects.

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Make an equilateral triangle by folding paper and use it to make patterns of your own.

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Can you make the birds from the egg tangram?

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outlines of the workmen?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of Little Fung at the table?

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Here's a simple way to make a Tangram without any measuring or ruling lines.

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Here is a chance to create some Celtic knots and explore the mathematics behind them.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

How can you make a curve from straight strips of paper?

Can you fit the tangram pieces into the outline of this junk?

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

Can you fit the tangram pieces into the outline of the child walking home from school?