Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

See if you can anticipate successive 'generations' of the two animals shown here.

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?

Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?

A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

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

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

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 Little Ming?

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

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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

This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.

Can you work out what is wrong with the cogs on a UK 2 pound coin?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Can you fit the tangram pieces into the outlines of these clocks?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Can you fit the tangram pieces into the outlines of these people?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Exchange the positions of the two sets of counters in the least possible number of moves

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

How many different triangles can you make on a circular pegboard that has nine pegs?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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 this telephone?

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Can you fit the tangram pieces into the outline of Granma T?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

Can you fit the tangram pieces into the outline of this sports car?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?