The Clumsy Tiler G
Recognise and invent patterns with reflection symmetry.
Devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment).
This problem is one of three parallel problems. Each one takes up the basic theme of Fred and his difficulty with tiles. But this one has a geometric flavour while the other two have statistical and numerical aspects (see The Clumsy Tiler S and The Clumsy Tiler N, respectively). All of the problems are at Level 4.
One of the points of these lessons is to show that by changing a problem by just a little, it ends up in another strand of the curriculum.
The current lesson deals with the different ways that tiles can be laid and have reflection symmetry and the Extension takes in rotational symmetry. Symmetry plays an important role in mathematics. Because symmetric things are clearly related, an argument that applies to one will apply to another. For instance, suppose we were thinking about all the ways that there are of playing Noughts and Crosses. If we start with a cross, then there are only essentially three places that we need to worry about putting it. This is because the all the corner squares are the same and all the middle squares on a side are the same too.
On the other hand in a more geometrical setting, if two things are symmetric and we know the dimensions of one of them, then we know the dimensions of the other. This type of argument is at the root of trigonometry. Not only does trigonometry allow us to find heights of mountains, a geometric application, but it also allows us to predict all manner of things that behave in a periodic way that may have nothing to do with geometry at all.
| Attachment | Size |
|---|---|
| ClumsyTilerG.pdf | 40.55 KB |
| ClumsyTilerGMaori.pdf | 44.61 KB |
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