When I was working through basic arithmetic with my kids a few years ago I thought it would be fun to teach them about different bases. One of the first different bases that we studied was binary, and the way we looked at it was to make a “binary adding machine” out of duplo blocks.

These are two example videos with my younger son:

The kids were amazed that you could use duplo blocks to do simple arithmetic.

While I was in London last week, I saw a really neat post on twitter from James Tanton. The title alone made me want to see it: “Exploding Dots: On base One-and-a-Half”:

In this video he introduces the concept of base 1.5 and talks about a few fun open problems. It is always such a thrill to see a new idea that is relatively easy to understand. I couldn’t wait to get back to the US and go through it with the boys.

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As an extra bonus, the “exploding dots” method of arithmetic that Tanton talks through is almost exactly how my kids taught themselves to do arithmetic. Those videos will be fun to go through with the boys, too.