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How many triangles can you make on the 3 by 3 pegboard?

Cutting Corners

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?


Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Nine-pin Triangles

Age 7 to 11
Challenge Level
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 useful.

Once you've had a go at this, why not investigate the number of different triangles you can create on circular pegboards with more or fewer pegs?
You might also like to have a look at this task 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').