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. . . .
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.
Sort the frieze patterns into seven pairs according to the way in
which the motif is repeated.
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?
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
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?
What is the relationship between these first two shapes? Which
shape relates to the third one in the same way? Can you explain
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?
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?
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?
Explore the effect of reflecting in two parallel mirror lines.
Plex lets you specify a mapping between points and their images.
Then you can draw and see the transformed image.
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
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?
Investigate what happens to the equation of different lines when
you translate them. Try to predict what will happen. Explain your
Explore the effect of combining enlargements.