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

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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

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 this sports car?

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

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 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.

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

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?

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

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

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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

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 work out what is wrong with the cogs on a UK 2 pound coin?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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

Can you fit the tangram pieces into the outline of these rabbits?

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

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

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

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 Little Ming playing the board game?

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

This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.

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

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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!

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

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

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 fit the tangram pieces into the outline of this junk?

Can you visualise what shape this piece of paper will make when it is folded?

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

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?

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

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

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