What is the Trachtenberg system?

A set of mental-calculation rules devised by Jakow Trachtenberg (while imprisoned in a Nazi concentration camp) that give a specific procedure for each multiplier.

Instead of general algorithms, it offers a tailored rule per number — for ×11, ×12, ×6, and so on — plus systematic methods for larger multiplications, all doable digit-by-digit without memorising times tables. It's a real, self-contained system built for speed and for teaching arithmetic to children; its ×11 rule is a clean example (next card).