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.

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Exploring and predicting folding, cutting and punching holes and making spirals.

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

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 work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

Can you cut up a square in the way shown and make the pieces into a triangle?

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

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

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

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Can you fit the tangram pieces into the outline of Mai Ling?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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?

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

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

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

Can you fit the tangram pieces into the outline of the rocket?

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

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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

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

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?

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 outlines of Mai Ling and Chi Wing?

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 ...

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 outline of this telephone?

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

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 the child walking home from school?

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

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

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

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

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 outlines of the watering can and man in a boat?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?