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I like your reflexive, symmetric, transitive lesson.

No good for geometry, but for algebra, is our commutative, associative, closure lesson. Plus and Times are not very useful. But a max b (returns the bigger), a average b (returns the average), a right b (returns b), these sorts of operations catch their attention. Not as colorful as "is the sibling of" or "kisses on the mouth," but when I was a kid I remember thinking that this sort of stuff was a waste of time. I like that we force our kids to think. Your stuff certainly does the trick!

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