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

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. . . .

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. . . .

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?

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.

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

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?

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?

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