Teach me this properly

Teach me this: [TOPIC]

Assume I am smart and know nothing about it specifically. Work in this order:

1. What problem does this exist to solve? What did people do before it?
2. The core idea, in plain language, before any terminology.
3. Now the terminology, mapped onto the idea you just explained.
4. A worked example I can follow all the way through.
5. What people usually get wrong about this, and why the mistake is tempting.
6. How I would know I have understood it — a question I should be able to answer.

Stop and check with me after step 3 rather than delivering all six at once.