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

Can you place the blocks so that you see the relection in the picture?

This problem explores the shapes and symmetries in some national flags.

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

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

What is the missing symbol? Can you decode this in a similar way?

This article describes the scope for practical exploration of tessellations both in and out of the classroom. It seems a golden opportunity to link art with maths, allowing the creative side of your. . . .

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

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?

Some local pupils lost a geometric opportunity recently as they surveyed the cars in the car park. Did you know that car tyres, and the wheels that they on, are a rich source of geometry?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?

This article describes a practical approach to enhance the teaching and learning of coordinates.

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

Numbers arranged in a square but some exceptional spatial awareness probably needed.

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

A challenging activity focusing on finding all possible ways of stacking rods.

Explore the effect of reflecting in two intersecting mirror lines.

Explore the effect of reflecting in two parallel mirror lines.

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.

These clocks have been reflected in a mirror. What times do they say?

Why not challenge a friend to play this transformation game?

How many different symmetrical shapes can you make by shading triangles or squares?

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

In how many ways can you fit all three pieces together to make shapes with line symmetry?

In how many ways can you stack these rods, following the rules?

Plex lets you specify a mapping between points and their images. Then you can draw and see the transformed image.

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

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

Can you explain why it is impossible to construct this triangle?

This article for teachers suggests ideas for activities built around 10 and 2010.

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!