Word Problems
Turn words into maths, then solve
Reading the problem carefully is half the battle. The other half is writing a clear number sentence before calculating.
See It in Action
The Problem
Mia has 3 bags with 14 apples each. She gives 11 apples to her friend and eats 2. How many apples does she have left?
Common Mistake
3 × 14 = 42. 42 − 2 = 40.
The student forgot to also subtract the 11 apples given away. The problem has two subtractions: giving away AND eating.
Correct Approach
Total apples: 3 × 14 = 42. Apples removed: 11 + 2 = 13. Apples left: 42 − 13 = 29.
Answer: 29 apples
3 bags × 14 = 42. Gave away 11, ate 2: total removed = 13. 42 − 13 = 29. ✓
The Core Concept
Word problems fail in a predictable order: (1) misreading which quantity the question asks for, (2) choosing the wrong operation, (3) including irrelevant numbers, (4) forgetting units in the answer. Fix the first two and most errors disappear.
The reliable strategy is to annotate before calculating. Read the problem once for the story. Read it again and underline the numbers. Circle the question (the last sentence usually). Label each number with what it represents. Then write a number sentence using symbols before doing arithmetic.
Watch out for irrelevant numbers — NSW selective tests sometimes include information you don't need, to check if you can identify what matters. Also watch for multi-step structures: "First... then... finally..." tells you there are multiple calculations in sequence.
Common Mistakes to Avoid
Answering a different question than the one asked
Circle the final question before starting. "How many apples does she have LEFT?" means you need the remaining total, not the amount removed.
Using all the numbers given without checking relevance
Some numbers in a problem are context, not data you need. Label each number with its meaning before deciding whether to use it.
Multi-step problems treated as single-step
"First... then..." signals multiple operations. Solve in the order the events happen, keeping track of the running total.
Forgetting units in the answer
"29" is incomplete. "29 apples" answers the question. Always include units.
Try It Yourself
A cinema has 12 rows of 15 seats. 87 seats are already sold. How many seats are still available?
Hint: Step 1: find the total number of seats. Step 2: subtract the sold seats.
Key Tips
Circle the question (last sentence) before doing any calculation.
Label each number: "14 = apples per bag, 3 = number of bags..." so you know what you're using.
Write the number sentence in symbols first: 3 × 14 − 11 − 2 = ?
Ready to practise Word Problems?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.