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.

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

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

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 sports car?

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 ...

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

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

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.

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 watering can and man in a boat?

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

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 Wai Ping, Wah Ming and Chi Wing?

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

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

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?

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?

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

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?

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

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

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

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

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

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

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

What is the best way to shunt these carriages so that each train can continue its journey?

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?

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

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?

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 outline of this telephone?

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

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 this shape. How would you describe it?

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

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

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

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?

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

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

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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

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 Granma T?