Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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

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

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!

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

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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

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?

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

Can you fit the tangram pieces into the outlines of the convex shapes?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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?

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?

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

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

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

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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

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

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

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?

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

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?

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

Can you logically construct these silhouettes using the tangram pieces?

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

Can you fit the tangram pieces into the silhouette of the junk?

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

Can you fit the tangram pieces into the outline of the playing piece?

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

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

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

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

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

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.

Can you fit the tangram pieces into the outlines of the camel and giraffe?

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

Join pentagons together edge to edge. Will they form a ring?

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

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

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