Schemes like this multiplication technique are fascinating, the patterns one can see are beautiful. The fact they are not taught in schools is scandalous. Their use is actively discouraged.
My Dad bought me a book about the Trachtenberg System of Basic Mathematics[1] when I was a kid, it had all sorts of funky new ways to solve maths problems just like this. My primary school hated it, they marked me down for not showing my working and doing it the wrong way. I was brilliant at maths mainly because of this book, but didn't get the extra marks for doing it the "right" way.