What happens when you try and fit the triomino pieces into these two grids?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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?

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

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

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

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?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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

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?

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

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 outlines of the workmen?

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 telescope and microscope?

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 these convex shapes?

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

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

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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 fit the tangram pieces into the outline of this junk?

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

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

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

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

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

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

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

Can you split each of the shapes below in half so that the two parts are exactly the same?

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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 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 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 describe a piece of paper clearly enough for your partner to know which piece it is?

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

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?