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'Arrow Arithmetic 3' printed from http://nrich.maths.org/
One good way to realise a twizzle as a manipulative is with a piece
of elastic. You need to mark 3 spots on the elastic - say a black
spot for the origin, a blue spot for the end of the unit arrow, and
a red spot for the end of the number arrow.
Make up a few of these elastic twizzles, and see if you can use
them to do simple calculations.
You might want to worry a little about the implicit enlargement
that happens in this solution. Can you convince yourself that this
can be achieved by completely geometrical means?