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'Nine-pin Triangles' printed from http://nrich.maths.org/
How many different triangles can you make on a circular pegboard that has nine pegs?
You may like to use the interactivity to try out your ideas. If you prefer to work on paper, you might find this sheet of nine-peg boards
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Once you've done this, have a look here
for some extension questions!
Many thanks to Geoff Faux who introduced us to the merits of the nine-pin circular geoboard.
For further ideas about using geoboards in the classroom, please see Geoff's publications available through the Association of Teachers of Mathematics (search for 'geoboards').