Rounda

"Thirty-nine is about forty," Rounda said. "Twenty-one is about twenty. Forty times twenty is eight hundred. So the answer should live somewhere around eight hundred — a little less, since I rounded up. That's my estimate, done in one breath, before any careful work." Rounda pointed at the student's 179. "But you wrote a hundred seventy-nine. That's not in the neighbourhood at all — it's five streets away. So without checking a single digit of your exact work, I already know something went wrong. You probably multiplied thirty-nine by one instead of twenty-one, or dropped a place."

"That's the whole reason I estimate first," Rounda said. "Not to replace the exact answer — I still want the real one — but to know what neighbourhood it belongs in before I calculate. Then when the exact answer arrives, I glance at it and ask: does it live where I expected? If it does, I relax. If it's wildly off, I catch it instantly, because a right answer can't be in the wrong neighbourhood. It's the difference between an answer that could be anything and an answer I've already fenced in. A calculator can hand you a crazy number with total confidence. An estimate is how you stay the boss of it."

The student redid 39 × 21 carefully — forty times twenty-one is eight forty, minus twenty-one, eight hundred nineteen — and then checked it against the estimate. "Eight hundred nineteen. And my estimate was around eight hundred. It fits the neighbourhood." They exhaled. "A hundred seventy-nine was nowhere close. If I'd estimated first, I'd have known my first answer was garbage before I even trusted it." Rounda nodded warmly. "Now you always will. Guess the size, then check the exact answer moved into the right street."