Stars – An Introduction

Every now and again you come across an idea that’s immensely rich in all the good things you want a topic to offer – accessibility, scope for exploration, coverage of a wide range of mathematical ideas, available to a wide range of ages and abilities, ….  – but which is totally ignored in syllabuses and schemes of work.

Just what was wanted, in fact, when I was asked to do a series of sessions to be televised to a selection of schools in England and Pakistan. There was no chance of finding what each different group had covered, so I needed to use topics which were visual, accessible, exploratory – and which I could be pretty sure were not covered in their schemes of work.

I was working with secondary schools, but in different circumstances I’ve used most of the ideas equally well with primary children.

(There will be a short pause while you think of the topics you might have chosen in similar circumstances.)

Very high up on my list was the theme of Stars, and here’s where I got my starting point from.

 

Service was rather slow in Pizza Express and we discovered my wife and I were both doodling stars.  Jill was drawing six-pointed stars, and all mine had five points.  Jill drew hers by drawing an equilateral triangle and then another on top of it, turned through 180°.

Unlike hers, my pencil never left the paper.  I drew one continuous line which turned at four points and eventually got back where it started.

Our sketches looked something like this:STARS 5 6

A couple of questions immediately arose. Could our methods be interchanged? Could we produce a five-pointed star by overlapping two shapes, and could we draw a six-pointed star from one continuous line?

Now that gave us a lot of fun, and you may like to think about it for a while and try a few sketches.

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Probably before long you’ve convinced yourself that the two methods are not interchangeable.  But that only generates further questions, and the very first is to wonder what happens if you try stars with a different number of points.

So how are you going to draw a seven-pointed star?  Overlap?  Or zig-zag?   And eight?  And are any hypotheses developing?

I’ll post a second part soon.

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