How many different triangles can you make on a circular pegboard that has nine pegs?

Can you fit the tangram pieces into the outline of the telescope and microscope?

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 these rabbits?

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 this plaque design?

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

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

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

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

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

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

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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 workmen?

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 candle and sundial?

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

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

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 goat and giraffe?

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

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 telephone?

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

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 these convex shapes?

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 this shape. How would you describe it?

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 outlines of the chairs?

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

What is the shape of wrapping paper that you would need to completely wrap this model?

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?

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

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

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

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.

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

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

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

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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?

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