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I'm partial to vihart's perspective on this at http://www.youtube.com/watch?v=a-e8fzqv3CE It's moderately interesting, but ultimately just a way of doing the exact same thing. Multiplication can be reduced entirely or partially to counting, that's worth understanding. And, if explained correctly, this can give insight into multiplying polynomials. Also, showing that counting the intersections of 8 lines crossing 9 lines is tedious may present times tables as convenient time savers rather than teacher inflicted torture.

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