Why word problems feel harder
The maths in a word problem is usually easier than the maths in the exercise above it. The difficulty is translation: turning English into an equation. Treat that as its own skill and practise it separately.
The five steps
Use the same five steps every time, in order, even when the problem looks easy.
- 1. Read once for the story, then again with a pen, underlining numbers and units.
- 2. Write down what you are asked to find, and name it with a letter.
- 3. Translate each sentence into an equation, one sentence at a time.
- 4. Solve, keeping units attached.
- 5. Read the question again and check your answer is sensible and answers what was asked.
Translation dictionary
'Is / was / will be' means =. 'Of' usually means ×. 'More than' and 'increased by' mean +. 'Less than' means − but flips the order: '5 less than x' is x - 5, not 5 - x. 'Per' means ÷. 'Twice' means 2×. 'Consecutive integers' means n, n + 1, n + 2.
Worked example — ages
Maya is 4 years older than Sam. In 3 years the sum of their ages will be 30. How old is Sam now?
Let Sam's age be s. Then Maya's age is s + 4. In 3 years they are s + 3 and s + 7. Their sum: (s + 3) + (s + 7) = 30, so 2s + 10 = 30, 2s = 20, s = 10. Sam is 10 and Maya is 14. Check: in 3 years, 13 + 17 = 30. Correct.
Worked example — rate
A train travels 240 km in 3 hours, then 150 km in 2 hours. What is the average speed for the whole trip?
Average speed is total distance ÷ total time, never the average of the two speeds. Total distance = 390 km, total time = 5 hours, so the average speed is 78 km/h.
The habit that fixes most mistakes
Before writing any equation, say the answer's units out loud: 'the answer will be in dollars', 'the answer will be a number of students'. If your working produces something in the wrong units, you have caught the error before it costs you marks.