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

Explore the effect of combining enlargements.

Explore the effect of reflecting in two intersecting mirror lines.

Explore the effect of reflecting in two parallel mirror lines.

Why not challenge a friend to play this transformation game?

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

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.

Can you construct a cubic equation with a certain distance between its turning points?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?

Does changing the order of transformations always/sometimes/never produce the same transformation?

See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.

Scientist Bryan Rickett has a vision of the future - and it is one in which self-parking cars prowl the tarmac plains, hunting down suitable parking spots and manoeuvring elegantly into them.

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be. . . .

This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping. . . .

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

These grids are filled according to some rules - can you complete them?

This problem is based on the idea of building patterns using transformations.

Can you logically construct these silhouettes using the tangram pieces?

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

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 Little Fung at the table?

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 these clocks?

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 the lobster, yacht and cyclist?

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

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 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?

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

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 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?

Can you use the interactive to complete the tangrams in the shape of butterflies?