The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.

Introduces the idea of a twizzle to represent number and asks how one can use this representation to add and subtract geometrically.

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. . . .

Points off a rolling wheel make traces. What makes those traces have symmetry?

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

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

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?

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?

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

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. . . .

Why not challenge a friend to play this transformation game?

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

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

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

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

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

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

Explore the effect of reflecting in two parallel mirror lines.

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

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?

Explore the effect of combining enlargements.

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.

Explore the two quadratic functions and find out how their graphs are related.