In this article Chris Gregory, Senior Lecturer in Mathematics at Bradford and Ilkley Community College, looks at the way that the programming of basic shapes can be built upon.
Some children have, in fact, invented similar procedures themselves.
Otherwise, it can be productive to give them this procedure and invite them to find out how it works and modify it to suit their own tastes. They could vary the polygon on which it is based and also the number of 'steps' in the pattern.
Time spent constructing and investigating tessellations can be very worthwhile. This is an excellent medium for exploring the properties of shapes, and the ubiquity of such patterns in the natural and man-made worlds ensures that this is a very useful stimulus for a variety of cross-curricular activities.
A more modest project is to produce a limited pattern such as:
When all the necessary moves have been determined, try to put them all together into a superprocedure with a name such as HEXPAT.
It will help greatly if children have first hand experience of building up tessellations by physically fitting shapes together. The Mathematical Activity Tiles - MATS - are a cheap and attractive material for this purpose.
Some further activities:
Write a procedure which will draw it with the least possible number of
Do the same with this pattern of equilateral triangles.
Note: MATs are available from the Association of Teachers of Mathematics, Shaftesbury St., Derby.
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