Why on earth didn't anyone teach me about this when I was in school! I've been covering the whiteboard in these ever since I saw this going past on Facebook (I haven't yet found definitive proof that it's of Japanese origin).

After a couple of fascinated scribbles (please excuse the mouse handwriting), I realized that by counting the intersections, you're doing exactly the same thing as the normal long multiplication method of multiplying each position by each other position, just laying it out visually... but it's so satisfying to see it fall out of a tartan picnic rug like that. Besides, it's prettier than a column of numbers.

I will have to remember this for when I next have paper to hand but not a calculator, which in today's environment will be round about never.