Splitt

"Thirty-four is just thirty and four," Splitt said, pulling the number into two parts. "So seven times thirty-four is seven times thirty, plus seven times four. Seven times thirty — that's seven times three, twenty-one, with a zero, two hundred ten. Seven times four is twenty-eight. Now add the pieces back: two hundred ten plus twenty-eight — two hundred thirty-eight." Splitt pushed the blocks back together. "Seven times thirty-four is two thirty-eight. I never multiplied by thirty-four. I multiplied by thirty, then by four, then glued the answers together."

"This is the one trick under all the others," Splitt said. "Any number you're scared of, you can split into friendly place-value pieces — tens and ones, hundreds and tens and ones — multiply each piece by itself, and add. It works because multiplying is fair to pieces: a whole times a sum is the same as the whole times each part, added up. So I get to trade one hard multiplication I don't know for two or three easy ones I do know. Twelve times fifteen? Twelve times ten is a hundred twenty, twelve times five is sixty, together a hundred eighty. I'm never stuck, because I can always break the lump smaller until every piece is a fact I own."

The student tried 6 × 23. "Twenty-three is twenty and three. Six times twenty is a hundred twenty. Six times three is eighteen. Add them — a hundred thirty-eight." They looked up, a little stunned. "Six times twenty-three is a hundred thirty-eight, and I only ever did six-times-twenty and six-times-three. I knew both of those." Splitt grinned. "That's the secret. You already know more than enough small facts to build every big one. You just break the big one down until it's made of the small ones you own."