Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

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

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

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.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

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

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 outline of Granma T?

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

Can you visualise what shape this piece of paper will make when it is folded?

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?

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?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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!

What shape is made when you fold using this crease pattern? Can you make a ring design?

Make a flower design using the same shape made out of different sizes of paper.

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?

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

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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?

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

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

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?

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

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

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

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

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

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

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

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

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

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?

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 these clocks?

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?

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

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

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

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

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.