I do pretty much the same thing. I was taught traditional long multiplication in school, but its a technique that is designed to be worked out with a pen and p

I do pretty much the same thing. I was taught traditional long multiplication in school, but its a technique that is designed to be worked out with a pen and paper, and doesn't tell you a lot about why the technique works. The grid system seems more geared toward mental arithmetic and understanding, and allows one to easily approximate an answer, rather than working it out exactly. This is pretty much exactly what's required in the modern world, and that's probably why lots of people have discovered this technique independently.