Revisiting James Tanton’s base 3/2 exercise

Several years ago we played around with James Tanton’s base 3/2 idea:

Fun with James Tanton’s base 1.5

A tweet from Tanton reminded me about his project earlier this week. I was excited to revisit it and got a double surprise when my older son told me that he actually did it in his 7th grade math class last week! It is nice – actually amazing – to see Tanton’s work showing up in my son’s math class!

An unfortunate common theme with some of our recent projects is that they aren’t going as well as I hoped they would. Still, though, this was fun and I’ll have to spend a bit more time thinking about the last bit – how to write 1/3 using base 3/2.

We started by reviewing base 2 and, in particular, how you can play around with binary using blocks.

Next we looked at base 3/2. I’m sorry that this video runs 10 min – I definitely should have broken it into 2 pieces.

Finally we accidentally walked into a black hole. I assumed that writing 1/3 in base 3/2 wouldn’t be that difficult and that an easy pattern would emerge quickly. Whoops.

Turns out that no pattern emerges quickly, and even playing around on Mathematica for a bit after we turned off the camera we couldn’t find the pattern. The discussion facilitated by the work on Mathematica was great – at least my kids learned that (i) there are multiple ways to write a number in base 3/2, and (ii) there are easy sounding project that I can’t figure out!

I hope to revisit this part after I understand it better myself. Any help in the comments would be appreciated.

I really like this project and am sad that a little bit of stumbling around by us might have obscured the beauty of Tanton’s idea. Hope we’ll be able to revisit it soon.

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