Problem-solving
- Syllabus
- 2016
- Topic
- —
- Level
- —
Learning objectives
Translate a problem into a mathematical process
Problem-solving begins by replacing the context with quantities, relationships and a planned sequence of mathematical operations. The model must preserve what each statement means, not merely reuse its numbers.
| Context clue | Mathematical translation |
|---|---|
| total, altogether | addition or a sum equation |
| difference, fewer than | subtraction with order checked |
| each, per, rate | multiplication or a ratio |
| shared equally | division |
| percentage increase/decrease | multiplier applied to the original quantity |
| fixed total with unknown parts | define variables and form simultaneous relationships |
- State what is known and what is required. 2. Define unknowns with units. 3. Translate one sentence at a time into expressions, equations, diagrams or tables. 4. Choose and order the required techniques. 5. Calculate with units and appropriate precision. 6. Interpret and check the result against the context.
Check that units are consistent, every condition has been used, the answer has a plausible size and sign, and substituting it back satisfies the original relationships. If a result is impossible in context, revisit the model rather than forcing an interpretation.
A correct calculation applied to the wrong model does not solve the problem. Do not assume a diagram is to scale, introduce an unstated relationship, round before the final stage, or give a bare number without answering the contextual question.