An answer with no visible reasoning is a rumour: it might be true, but nobody — including you, three weeks later — can tell why. In this course the reasoning is the work. Multi-step problems, models built from data, and triangle solutions all live or die on whether a reader can follow the chain, and showing it is a concrete skill with named parts.
The four-part habit on paper
- Restate — one line saying what the problem actually asks, in your own words. “Find when the account first doubles” is a different job from “find the balance after ten years” — half of all wrong answers are right answers to a misread question.
- Reason — the steps in order, with a word about why each move is legal. “Divide both sides by 500 to isolate the growth factor” beats a bare arrow — and in a modelling task like The Tide Problem, the why behind every parameter is the whole product.
- Units — carried through every line, not sprinkled on at the end. A Money Over Time answer should arrive in dollars and years; a Ferris wheel height should arrive in metres. Units that arrive wrong have found your error for you.
- Answer sentence — a full sentence a stranger could read on its own: “The deposit doubles during the twelfth year; after that, growth outpaces anything the account saw in its first decade.” A boxed answers nothing by itself.
At the whiteboards
One rule does most of the work: the person holding the marker writes only other people’s ideas. It forces reasoning out loud — you cannot write what nobody has said — so every line on the board has already survived one listener. And cross out rather than erase: a corrected line is a record of thinking, which is what the board is for, as Mistakes Are Data argues at length.
The checklist
- Could someone follow this without me standing beside it?
- Is there a why beside every non-obvious step?
- Do the units survive from the first line to the last?
- Does it end in a sentence answering the actual question?
- Are my crossed-out attempts still visible?