To learn Mathematics Word Problems quickly and correctly, resist the urge to calculate as soon as you see a number. A word problem is a short story about quantities and relationships. Your job is to find out exactly what is known, what is missing and how those quantities connect. Once you translate the story into a bar model, table or equation, the arithmetic often becomes straightforward. These eduKateSG Quick Notes give you an easy repeatable reading-and-solving method for Primary and Secondary Mathematics.
- Read to understand: say in one sentence what is happening.
- Name the target: underline the precise quantity the question asks for.
- Sort facts: separate quantities, conditions and unneeded information.
- Draw or define: choose a small bar diagram, table or variable.
- Write the relationship: form the calculation or equation before solving.
- Check in the story: test the units, the total and whether the answer makes sense.
First, read the question twice for different reasons. On the first reading, understand the situation. On the second, look for the unknown and mark the important conditions. If a question asks how much money is left, your answer must describe a remainder, not just a total cost. If it asks how many more, you are comparing two values. Do not use a keyword alone to select an operation: the words “more than” can describe a comparison inside a longer question, so you still need to understand who has what.
Second, make a picture or write a simple relationship. A bar model can represent a total split into parts; a table can show changing quantities; an equation can express an unknown. For example, “three identical tickets and one $4 booking fee cost $49” becomes 3t + 4 = 49, where t is the price of one ticket. Naming t stops you from accidentally treating the fee as part of each ticket price. You do not need an elaborate diagram. Choose the smallest representation that makes the relationship clear.
Third, solve one step at a time and return to the original story. For 3t + 4 = 49, subtract the single booking fee from the total: 3t = 45. Divide by the three tickets: t = $15. Check: three $15 tickets cost $45, plus $4 gives $49. It matches. The checking sentence is as important as the calculation because it confirms that t means the right thing and that the answer fits every condition.
Worked example: a fraction of what remains
There are 48 stickers. Three-eighths are blue. One-third of the remaining stickers are green. How many stickers are neither blue nor green? Start with blue: 3/8 × 48 = 18. Remaining after blue = 48 − 18 = 30. Green = 1/3 × 30 = 10. Neither = 30 − 10 = 20 stickers. Check: blue 18 + green 10 + other 20 = 48. The crucial word is remaining; the one-third is not taken from the original 48.
Why choosing the right whole matters
Suppose a bag holds 40 counters in the ratio red : blue = 2 : 3. The total has five equal parts, so each part is 40 ÷ 5 = 8. Red = 2 × 8 = 16; blue = 3 × 8 = 24. You could represent this with five equal boxes, two red and three blue, before doing any arithmetic. This drawing prevents the mistake of taking 2/3 of the total when the ratio really has five parts.
A reliable six-question checklist
- Who or what? Identify the people, objects or measurements.
- How many or how much? List every given quantity with its unit.
- What is asked? Complete the sentence: “I need to find ___.”
- What connects them? Total, difference, equal groups, fraction, rate, ratio or percentage?
- What should I write? Use a short calculation, bar model, table or equation.
- Does it fit? Substitute the answer into all important conditions.
Choose a model that matches the situation
- A total split into shares: draw a bar model or ratio parts.
- A fixed fee plus equal items: form an equation such as total = fee + number × price.
- A change over time: use a two-row before-and-after table.
- A percentage change: label the original amount before multiplying.
- A distance, time and speed question: check compatible units and the relationship distance = speed × time.
- A geometry question: sketch the figure and mark known lengths or angles.
Common mistakes in word problems
- Using every number immediately: decide what each number represents first.
- Using the wrong base: distinguish a fraction of the total from a fraction of what remains.
- Forgetting a one-off fee: separate fixed costs from per-item costs.
- Changing units midway: convert before combining values.
- Stopping after the first calculation: check whether the question asks for an intermediate value or a final one.
- Writing only a number: attach the right unit and explain what was found.
Mini-test: translate before you calculate
- Four identical notebooks and a single $3 delivery fee cost $35. What is the price of one notebook?
- A shirt priced at $75 is discounted by 20%. What is its sale price?
- Sixty beads are shared between two children in the ratio 2 : 3. How many does the second child receive?
Answers with the relationship shown
1. 4n + 3 = 35, so n = (35 − 3)/4 = $8. 2. Twenty per cent of $75 is $15; final price = $60. 3. There are five ratio parts; one part is 60 ÷ 5 = 12, so the second child receives 3 × 12 = 36 beads. All three solutions work because the relationship was chosen before the calculation.
Your ten-minute word-problem practice
Choose one short story problem. Spend two minutes identifying the target, two drawing or writing the relationship, three solving, two checking against the story and one rewriting the question in your own words. The next day, change one condition and see whether the method still works. When you can explain why the method fits a new story, you have learned the Mathematics rather than memorised the example.
Keep learning: your next small step
Build the next foundation with Ratios, Percentages, Linear Equations, Mathematics. These Quick Notes work best when you study one idea, answer one question alone and return the next day without opening the example.
The longer school-learning context is Secondary 1 Mathematics Tutor Clementi | Small Groups Tutorials. That original reference remains unchanged.