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

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

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

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

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

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

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

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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.

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

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?

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

Can you make the birds from the egg tangram?

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

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

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

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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

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

Make some celtic knot patterns using tiling techniques

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

Make a mobius band and investigate its properties.

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

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

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. . . .

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

Did you know mazes tell stories? Find out more about mazes and make one 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?

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

Make a cube out of straws and have a go at this practical challenge.

Surprise your friends with this magic square trick.

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

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

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 this telephone?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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

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

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

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

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 lobster, yacht and cyclist?

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

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?