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

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. . . .

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

These images are taken from the Topkapi Palace in Istanbul, Turkey. Can you work out the basic unit that makes up each pattern? Can you continue the pattern? Can you see any similarities and. . . .

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?

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?

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

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.

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

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

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

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

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

Explore the effect of reflecting in two parallel mirror lines.

Why not challenge a friend to play this transformation game?

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

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

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

Explore the effect of combining enlargements.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?