Problem-solving
- Syllabus
- 2017
- Topic
- —
- Level
- Higher
Learning objectives
Translate a problem into mathematics
Problem-solving begins by converting a situation into a mathematical model: identify what is known and required, represent the relationships, carry out a connected process, then interpret the result in the original context.
| Stage | Question to ask |
|---|---|
| understand | What is known, unknown, constrained and being asked? |
| represent | Would a variable, equation, diagram, table, graph or ratio expose the relationships? |
| plan | Which ordered mathematical steps connect the facts to the unknown? |
| execute | Can each step be carried out accurately with units and sufficient precision? |
| interpret | What does the result mean in context? |
| validate | Is it feasible, correctly rounded and consistent with the original conditions? |
Translate phrases into relationships before calculating. For example, 'three more than x' is x+3, 'shared in the ratio 2:5' means seven equal parts, and a fixed total creates an equation whose parts sum to that total.
A series of processes may cross topics: form an equation from a diagram, solve it, substitute the value into a formula, convert units, then make a decision. Record the chain so every result has a clear source.
Use bounds and common sense: lengths and counts cannot be negative, a probability must lie from 0 to 1, dimensions must use compatible units, and a rounded answer must satisfy the requested accuracy.
Do not start with an operation just because a number appears in the question. A correct calculation on the wrong model does not solve the problem; the final answer must address the stated unknown and context.