Mathematical Reasoning and Problem Solving: Word Problems and Modelling
What you must be able to do
Translate a word problem into an equation or expression. Identify the unknown, give it a letter, write down the relations stated in the text, and solve. Common models include: age problems (differences stay constant), motion problems (distance = speed × time), work problems (rates add), mixture problems (amount × concentration), and money problems (value = quantity × unit price).
Justify your steps: state the rule or property used, and finish with a sentence answering the question asked, in the correct units. Check whether the answer is reasonable in context - a negative length or a fractional number of people signals an error.
For percentage problems, remember the base: a price increased by 20% then decreased by 20% does not return to the original. For consecutive integers, write n, n + 1, n + 2.
Traps that appear in questions
- Answering a sub-question instead of the one asked (e.g. giving the number of adults when children were requested).
- Mixing units (minutes and hours, grams and kilograms).
- Setting up the equation with the wrong direction, such as speed of current added instead of subtracted.
- Rounding an intermediate result and losing accuracy.
- Forgetting to state units or to check the answer against the conditions.
Rule of thumb
After solving, re-read the question and verify that your value satisfies every stated condition, not just the equation you wrote.
Worked example
A father is 30 years older than his son. In 6 years the father will be three times as old as the son. Let the son be x now: x + 36 = 3(x + 6), so x + 36 = 3x + 18, giving x = 9. The son is 9 and the father 39.