Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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?

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

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 Little Ming and Little Fung dancing?

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

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.

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 outlines of the workmen?

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 Mai Ling?

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

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 shape. How would you describe it?

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

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

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 outlines of Mai Ling and Chi Wing?

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.

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

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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?

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

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 outline of this brazier for roasting chestnuts?

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

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 outlines of these clocks?

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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

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

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Can you make a 3x3 cube with these shapes made from small cubes?

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 cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

Reasoning about the number of matches needed to build squares that share their sides.

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.