Tiles in a Public Building
1 out of 3
What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?
Problem
In a public building in England, I found this wonderful tiled floor:
Really interesting I thought, because so much that looked the same at first glance was in fact different.
Look at the three images of the patterns I found along the centre of the tiling (below).
What is the same about them and what is different?
Now look again at the picture of the whole of the main tiled area. It was made from nine complete patterns each like one of the three above.
At the ends there were partial patterns, both like the one in the foreground. The pattern was surrounded by a rectangle of black tiles with some further tiling beyond.
Describe the pattern.
How many of each type of tile are included in the pattern?
How could you check?
Can you reproduce parts of the pattern?
Can you extend it sideways?
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
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.
Possible approach
Key questions
Possible extension
Extend the idea to tessellating a set of different tiles. You might like to use ATM MATs .
Possible support
Have a set of about a dozen of each of the basic tiles for learners to recreate each pattern to start with.