Twelve people, everyone shakes hands with everyone else once. Almost everybody answers 132 first. The answer is 66, and the reason is worth more than the number.
The answer key prints on a separate page.
132 is 12 × 11, and it is not a careless answer — it is the right count of something else. Each of the twelve people shakes eleven hands, so that product really does count every handshake. It counts each one twice, once from each end, because a handshake belongs to two people. Halving is not a correction to a mistake; it is the last step of a method that was right all along.
So the sheet also asks the version where halving is wrong. When every team plays home AND away, a match at A against B and a match at B against A are different matches, and the answer is the full 12 × 11. Both shapes appear on the same page on purpose: a child who has learned "divide by two" as a rule meets the question that rule does not fit, and has to decide instead of apply.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Counting pairs, step by step