How to Show Your Work in Math (And Why It Matters)
Showing your work isn’t busywork — it’s how teachers (and the AP exam graders) figure out where you went wrong, and it’s the only way to earn partial credit on a problem you don’t fully solve.
Quick answer
Show one step per line. Each line should be either (a) a new equation that follows from the line above, or (b) a one-sentence label of what you’re doing. Keep arithmetic on the side. Final answer goes at the bottom, boxed or circled.
Why teachers care
- Partial credit: a wrong final answer with correct setup can score 60-80%. A wrong final answer with no work scores 0%.
- Debugging: when you re-read your work, you can find the exact step where you went wrong.
- Patterns: showing work reveals which mistakes you make repeatedly, so you can target them.
The standard format
Example: solve 3(x − 2) = 21.
- Line 1: 3(x − 2) = 21 (the original equation)
- Line 2: 3x − 6 = 21 (distribute the 3)
- Line 3: 3x = 27 (add 6 to both sides)
- Line 4: x = 9 (divide both sides by 3)
- Final: x = 9 (boxed)
For word problems
Add labels: “Let x = the number of apples.” “Given: 3 apples + 2 oranges = 14. Find: number of apples.” Even one sentence of setup is worth points.
For geometry
Draw the figure. Label sides. State what theorem or formula you’re using before applying it. Example: “By the Pythagorean theorem, a² + b² = c². Substituting…”
For calculus
State the rule you’re using. “Applying the chain rule:” then write the work. The AP graders specifically look for this.
Common mistakes
- Writing only the final answer when work was expected.
- Writing a wall of arithmetic with no labels.
- Erasing wrong steps instead of crossing them out (teachers can see the journey).
- Skipping multiple steps in one line — split each operation into its own line.