I actually use a similar system for squaring two digit numbers (I use a base ten system) so I can actually compute it without a calculator or even paper.

eg.

what is 22 squared?

10x20 plus 10x20 plus 22 x2

22x10=220 plus 220= 440 plus 44= 484.

No one ever taught me the above. I learned it on my own when bored in history class. But it goes to show just how naturally our minds adopt a base ten system.