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

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

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?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

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?

What is the greatest number of squares you can make by overlapping three squares?

Exchange the positions of the two sets of counters in the least possible number of moves

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

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 sports car?

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

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

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 fit the tangram pieces into the outline of this junk?

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

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?

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

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 watering can and man in a boat?

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

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!

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

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

Which of these dice are right-handed and which are left-handed?

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.

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Here are shadows of some 3D shapes. What shapes could have made them?

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.

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 workmen?

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

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 Fung at the table?

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

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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

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?

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

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

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

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

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