Work through an example, showing the decisions

When you understand a technique in the abstract but not how to apply it.

Work through a concrete example of the technique below.

Structure:
1. Set up a realistic problem, not a toy one. State the inputs explicitly.
2. Solve it step by step. At every step, say what you are doing and why you chose that over the alternative you also considered.
3. Mark the steps that are mechanical and the steps that require judgement. The judgement ones are what I need.
4. Show one place where a beginner would plausibly go wrong, and what the result would look like if they did.
5. Give me a second problem of similar difficulty, with the answer hidden until I ask, so I can try it myself.

Technique:
Context I care about:

Practice, not reading. Worked examples, exercises and Socratic sessions that make you do the thinking.