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Arrow Arithmetic 1

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.

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Arrow Arithmetic 2

Introduces the idea of a twizzle to represent number and asks how one can use this representation to add and subtract geometrically.

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Twizzle Arithmetic

Arrow arithmetic, but with a twist.

Arrow Arithmetic 3

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?