Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

Move just three of the circles so that the triangle faces in the opposite direction.

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?

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

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

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 Little Ming and Little Fung dancing?

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

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 the telescope and microscope?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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 Little Ming playing the board game?

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 outline of this telephone?

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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 goat and giraffe?

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

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?

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Can you fit the tangram pieces into the outline of these convex shapes?

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

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

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 plaque design?

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?

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

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

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

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 chairs?

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

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

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

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

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