Did that in the US in the mid 2000s, though spent hardly a week on either IIRC. Something like base 20 Mayans, base 60 Sumerians, and base 2 computers. Do math in each and convert them to/from base 10.
I think that's been dropped from most US elementary school curricula now, bit of a shame.
Richard Feynman was pretty harshly critical of this in his stories of working as a textbook reviewer. I really appreciated that my elementary school did it, but I had a sense that most students didn't quite understand the significance (or remember it afterward if they weren't into computer programming). I think it has a lot of potential value in terms of understanding what place value is and where a place value system comes from.
When I've tried to teach programming, I've found that most people who aren't already programming enthusiasts don't remember the binary system or say they never learned it at all.
Edit: the Wikipedia article I linked to also has several examples of people making fun of non-base-10 arithmetic and kids being taught it in the New Math, including a song by Tom Lehrer!
