Snapshot
The calculator is useful, but overuse burns time. Rough work should capture structure, not every keystroke.
Calculator discipline
Use the calculator for arithmetic that is genuinely error-prone: division with awkward numbers, weighted averages, multi-step percentages, and compound growth. Do not use it for every small increase, rounded ratio, or obvious elimination. The calculator should execute your plan, not discover it.
A good scratch line looks like this:
$$\frac{\text{new value} - \text{old value}}{\text{old value}}$$
or:
$$\frac{\text{weighted sum}}{\text{sum of weights}}$$
or:
$$\frac{\text{part}}{\text{total}}\times 100$$
Bad rough work is a pile of numbers without labels. In review, you cannot tell whether a number was a numerator, denominator, intermediate value, or answer.
Screen habits
Numerical items often combine a stem, table, and options on one screen. Build a fixed eye movement:
- •stem first
- •table title and unit line
- •relevant row or column
- •answer options
- •stem again before final click
That final stem check catches many mistakes: "decrease" instead of "increase", "women" instead of "men", "average annual" instead of "total", "percentage points" instead of "percent".
Estimation before exact work
Before calculating, predict the answer region. If 120 rises to 150, the increase is about one quarter, so an answer near 25% is plausible. If options are 12%, 25%, 80%, and 125%, exact calculation is unnecessary. If options are 23.8%, 24.6%, 25.1%, and 25.8%, calculate.
Choose the calculation route
After choosing the base and unit, look at the shape of the numbers. A value near 100 may suit compensation; 12.5% may be one eighth; a total may split into easy multiples of its divisor. Write the ordinary operation first, then use the shorter route only if you can explain why it is equal. Use the calculator when numbers are awkward or answer options are close. Check the result against its unit and approximate size.
Calculation hint
Compensate in subtraction: 1204 − 398 = 1206 − 400 = 806. Adding 2 to both numbers keeps the difference unchanged and removes awkward borrowing.
Practice drill
For each wrong answer, write the first wrong action. Examples:
- •used calculator before choosing denominator
- •copied wrong year
- •ignored unit line
- •rounded too early
- •missed "percentage points"
Your rough work should make the mistake visible.