Why do this problem?
demonstrates a practical application of symmetry and tessellations. It offers opportunities not only to investigate and analyse the images but to create similar patterns using the same basic ideas.
contains the four images which can be copied onto cards for use by groups of learners. First spend some time investigating the basic units for the floor tiling and how they are combined (for example, six different square tiles all linked into cross patterns using the brown and black spacers).
Start by looking at images 2 and 3. What is the same and what is different about them?
Now compare these with image 1. How does this image differ and how is it the same?
Now pose the main problem and ask learners to calculate the numbers of each tile they would need to create the pattern.
At this point learners could create their own tile patterns (groups produce one pattern each), which are copied onto coloured paper. The class could then work collaboratively, using combinations of these tiles to produce a display for a "tiled floor".
How is the symmetry of each basic pattern the same and how are they different?
How could you extend the pattern to the sides? Is anything implied by the edges that are visible?
Extend the idea to tessellating a set of different tiles. You might like to use ATM MATs
Have a set of about a dozen of each of the basic tiles
for learners to recreate each pattern to start with.