Teach a concept through believable mistakes

Teach [CONCEPT] to [LEARNER LEVEL] through four plausible wrong attempts, ordered from intuitive to subtle. For each, show what the learner might say, why that idea is tempting, the exact point it fails, and a small counterexample. Then provide one correct worked example and a fresh check-for-understanding question with answer hidden below a divider. Keep feedback respectful and avoid pretending the learner made these mistakes. Return a one-page teaching handout and a facilitator note. Use [SOURCE OR CURRICULUM] for technical facts and mark any curriculum mismatch.