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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?