Six verification habits
- Plug it back in. Substitute your answer into the original problem statement, not just your final equation.
- Check units and dimensions. An area shouldn’t come out in linear units; a probability shouldn’t be dimensionless where a count was expected.
- Check parity/modulo behavior. If the problem structure guarantees an odd answer, an even result signals an error.
- Test extreme or boundary inputs. Does your formula behave sensibly as a variable approaches 0 or infinity?
- Check order of magnitude. Does the answer’s size roughly match a quick mental estimate?
- Check sign and direction. A distance, length, or count should never be negative.
Common careless-error categories
Most avoidable point losses fall into a short list: sign flips during algebra, simple arithmetic slips, mismatched units, violating a constraint implied by the problem (like a probability over 1), an answer with the wrong order of magnitude, or a geometrically impossible result (negative length or area).
Applying it
Scenario: You compute the area of a triangle and get a negative number from the shoelace formula.
Response: This is expected if you listed the vertices in clockwise rather than counterclockwise order — the shoelace formula’s sign depends on orientation. Take the absolute value, and treat a negative raw result as a built-in sanity check rather than a final error.
Practice problems
1.You solve for a probability and get 1.3. What verification habit catches this, and what does it tell you?
2.A problem asks for the number of ways to arrange some objects, and your formula gives a non-integer answer. What does this suggest?
3.You compute the side length of a square from its area and get a negative number. What check would have caught this earlier?
4.Why is 'plug the answer back into the original problem' more reliable than just double-checking your algebra steps?