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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. Click on two of the dots to create a line between them.
If you prefer to work on paper, you might find this sheet of nine-peg boards
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').