A long time ago, when I was in the second year of secondary school, our maths teacher introduced us to a little bit of history and a man called Jakow Trachtenberg. After a brief history of his life, including time in a Nazi concentration camp, he went on to explain some of the Trachtenberg system of arithmetic, which he devised during his imprisonment.
I still remember some of the arithmetic checks and was asked recently where I learnt them as they were not familiar with such trickery. I had a quick search, based on memories and lo and behold his book is now in pdf form, free on the internet.
https://drtayeb.files.wordpress.com/...erg-system.pdf
Fascinating stuff if anyone is interested. It changed many a schoolboy's attitude to maths when I was a kid.