When our kids were little, I bought them a large abacus to play with, and while they napped had great fun figuring out how to multiply and divide on the darn thing. Later, when my dad gave me his old slide rule, I loved sliding the center bar to calculate numbers. Both these tools use some brain power and attention in order to work, whereas a calculator is often too easy and thus the answer is often wrong if you're just punching buttons.
My 13 year old son has recently become interested in learning mental math, using a book by Arthur Benjamin that I had in the basement. We have races now to see who can square a two-digit number faster -- I'm still winning, but like chess where he's edged me out over the past year, suspect I won't be reigning champion for long. This stuff is so fun, in a geeky sort of way.
Just so you can see how amazing a true human calculator can be, here is a fun video of Arthur Benjamin doing his numbers "magic" show. This guy is incredible!
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