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.

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 outline of Little Ming and Little Fung dancing?

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 workmen?

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?

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

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!

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

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

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

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

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

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?

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?

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.

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

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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.

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

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

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

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

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?

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 this plaque design?

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 Little Ming playing the board game?

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?

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

An activity centred around observations of dots and how we visualise number arrangement patterns.

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?