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

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

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

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?

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

Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

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

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?

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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.

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

Use the clues about the symmetrical properties of these letters to place them on the grid.

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

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

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

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

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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. . . .

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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