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

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Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

Nine-pin Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 useful.

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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').