Translate the problem
Read once for the situation and again for the mathematical relationships. Circle the quantity requested, list known values with units and sketch a diagram or table when useful. Identify information that is irrelevant or missing. Restating the task prevents a familiar number from triggering the wrong method before the question is understood.
- Convert units only after writing the original values
- Label unknowns with clear symbols
- Estimate the likely size or sign of the answer
Choose and show a method
Name the relevant principle, formula or pattern and explain why it applies. Substitute values carefully and write intermediate steps so an error can be located. For algebra, keep operations balanced; for geometry, mark used properties; for data, state what the measure represents. If stuck, solve a simpler case or work backwards from the requested quantity.
- Write the formula before inserting numbers
- Keep exact values until rounding is required
- Use brackets to make calculator input unambiguous
Check more than arithmetic
Recalculate with a second route where possible, verify units and compare the result with the earlier estimate. Substitute solutions back into equations and check whether a probability, length or percentage is physically possible. When reviewing errors, identify whether the issue was interpretation, method, manipulation or calculation, then practise a new problem that targets that cause.
- State rounding and units in the final answer
- Reject extraneous solutions created by algebraic steps
- Record recurring mistakes in a correction list
Questions, answered.
What should a learner do when they cannot choose a method?
Write what is known, what is required and any relationship that connects them. Draw a representation, recall a similar principle rather than an identical question, and attempt a smaller case. After receiving help, solve a fresh example independently.