There are some interesting ideas in this post. I teach binary numeral notation, and then arithmetic with that notation, to third graders each year as part of the math classes I teach in my town. One of my favorite resources is the book Algebra by Gelfand and Shen,

http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773

which includes problems in representing numbers in binary notation and doing arithmetic with binary notation that are very approachable to young learners. (The problems are also very good review for undergraduate math majors

http://www.ocf.berkeley.edu/~abhishek/chicmath.htm

and help adults think more deeply about mathematics, which is why I like teaching with this book as a source of lesson topics.)

Edit after seeing other comment: I also mention to the children in my classes the Babylonian numerals,

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babyl...

in which the implicit base is base sixty. The link shown here mentions speculation from ancient Greece that that base was chosen because it has many different prime factors. That Babylonian system of numerals, whatever its origin, appears to be related to historical relics such as counting sixty minutes in an hour or 360 degrees of arc in a circle.

A slight variation that I read years ago using only the socratic method (the teacher only asked probing questions) to teach third graders binary arithmetic. Interesting how he weaved aliens into it.

http://www.garlikov.com/Soc_Meth.html

Edit: If I'd read to the bottom - I would have seen the author also references the above post.

Maybe overly pedantic, but I don't like http://www.exploringbinary.com/wp-content/uploads/27.decimal...

For the tens you're counting lines of blocks, and for the ones you're counting blocks, so it doesn't match up. Maybe if the ones were lined horizontally so you're still counting vertical lines, they just happen to be 1 block tall instead of 10 blocks tall.

There was a cool computer game called the Zoombinis that we used to play at home. One of the puzzles taught binary arithmetic using strange characters that had two expressions. There's a picture here:

http://www.computingwithkids.com/column/20011026.asp

The addition went up to 15 I think. You had to aim the pinballs at the group that would 'overflow' and jump in the river.

There were some very challenging puzzles in the Zoombinis titles - but they were teaching the conceptual foundations and encouraging intuition, not focussing on the terminology and modern applications.

Edit: a more useful link, with educational context and a larger picture, is this, although it's in French:

http://la-rochelle-ecole-barthelemy-profit.pagesperso-orange...

I love how you showed them three different ways. Brilliant. Research shows that kind of patterning repetition in learning is key.

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I think such engaging and visual teaching methods are far more etching on the mind. Great post.

He could have also mentioned the old babylonians and their base 12 system. We still have an extra word for 12 (a dozen) and it explains our strange counting of time (212 hours in a day, 512 in an hour or minute).

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Great idea for a site, so simple and yet so deep.