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

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

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?

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

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

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

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

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

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 outlines of the candle and sundial?

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 Mai Ling and Chi Wing?

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?

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

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

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

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

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

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

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 people?

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?

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

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 outline of the child walking home from school?

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

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?

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 fit the tangram pieces into the outlines of these clocks?

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

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.

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

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

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

This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

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

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

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

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

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

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

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

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

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?

Square It game for an adult and child. Can you come up with a way of always winning this game?