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Say that multiplication by -1 is a 180 degree rotation of the number line. Then -1 * -1 is a 360 degree rotation -- which is the same as a 0 degree rotation.

Note that saying it like this is non-intuitive, but the point is that it's actually a geometric interpretation, so you draw a picture. This also helps students with the idea that there's actually some connection between algebra and geometry --- even though this is really fundamental, it's often omitted from mathematics education.

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