How to Show Your Work

A rigorous guide to readable mathematical arguments: givens, definitions, transformations, conditions, units, and conclusions.

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Attempt → inspect → revise → retrieve. A first attempt produces evidence, the first incorrect step is diagnosed, one focused repair follows, and a delayed no-notes retrieval checks whether learning transferred.

Precise definition

Showing work means recording enough mathematical reasoning that a reader can identify the claim, verify each transformation, locate conditions, and see how the conclusion answers the question. Length alone is not rigor; relevant, ordered justification is.

Notation and mathematical language

A complete solution usually names variables, states a model or theorem, shows substitutions and equivalent steps, preserves domain restrictions, and ends with a contextual conclusion. Equality signs join equal expressions; implications connect logical steps; approximation signs mark rounding.

Conceptual picture

Good layout externalizes working memory and makes feedback precise. One transformation per line helps reveal sign or operation errors. Diagrams need labels; graphs need axes and scale; numerical answers need units and precision.

Fully worked example

Interpretation and application

Readable work supports partial-credit assessment, collaboration, proof, coding, and later self-correction. It demonstrates reasoning without requiring a specific ornamental style.