A few years ago I had an in-depth conversation with a (then) sixth-grader of my acquaintance, and came away impressed with the "Common Core" way of teaching maths. His parents were frustrated with it, because it didn't match the paper-based methods of calculation they (and you and I) had been taught, but he'd learned a bunch of these sorts of tricks, and from them had derived a good (probably, if I'm honest, better than mine) intuition for arithmetic relationships.