How to approach word problems: a systematic strategy that works

Word problems are where students either shine or stumble. The issue isn’t usually the mathematics itself - it’s extracting the mathematics from the English. Here’s the systematic approach I use in my tutoring sessions that transforms word problem performance.

Why Word Problems Feel Hard

Students often say “I understand when you show me, but I can’t start on my own.” This is the classic symptom of not having a systematic approach. Word problems require:

1. Reading comprehension (understanding what’s being asked)
2. Mathematical translation (converting words to equations)
3. Problem-solving strategy (knowing which technique to use)

Most curricula teach the maths, but not the extraction process.

My 3-Point Framework

I teach every student the same framework, regardless of their age or subject. It works for GCSE algebra problems, A-level physics scenarios, or university-level word problems.

Point 1: Read Twice, Underline Once

First read: Understand the story. What’s actually happening in this scenario?

Second read: Hunt for numbers and relationships. Underline all numbers, and circle words that indicate mathematical relationships:

• “is” means equals
• “more than” means plus
• “less than” means minus
• “twice” means 2×
• “half of” means divide by 2

Common trap: Students start working before they understand. Make understanding mandatory, not optional.

Point 2: Variables First, Then Equations

The number one mistake? Writing equations before identifying variables.

The process:

1. Read the problem
2. Ask: “What are we trying to find?” (Define variables)
3. Ask: “What do we know?” (Write down given information)
4. Ask: “How are these connected?” (Write equations)

Example: Sarah has twice as many apples as John. Together they have 30 apples. How many apples does each have?

Variables first:

• Let $j$ = number of apples John has
• Let $s$ = number of apples Sarah has

Then equations:

• $s = 2j$ (Sarah has twice as many)
• $s + j = 30$ (Together they have 30)

Only NOW do we solve.

Point 3: Check Your Answer Makes Sense

This isn’t optional homework advice - it’s problem-solving gold. Your answer should make sense in the original context.

Checklist:

• Is your answer positive when it should be?
• Does it satisfy the original conditions?
• Is it the right magnitude? (e.g., £1500 feels right for a laptop, not £1.50 or £15000)

Real Example: From Last Week’s Session

Student: Mia, Year 10, stuck on this problem

Original problem: “A train travels 120 km in 1 hour 30 minutes. Another train travels 90 km in 1 hour. If they start at the same time from opposite stations 315 km apart, when will they meet?”

Mia’s first attempt: She tried guessing, got frustrated.

Our framework approach:

Step 1 - Read twice:

• First train: 120 km in 1.5 hours
• Second train: 90 km in 1 hour
• Distance between stations: 315 km
• They start simultaneously in opposite directions

Step 2 - Variables:

• Let $t$ = time until they meet (in hours)

Step 3 - Equations:

• First train’s speed: $120 \div 1.5 = 80$ km/h
• Second train’s speed: $90 \div 1 = 90$ km/h
• When they meet, combined distance = 315 km
• Distance = speed × time
• So: $80t + 90t = 315$
• Therefore: $170t = 315$
• $t = 315 \div 170 = 1.85$ hours

Step 4 - Check:

• First train goes: $80 \times 1.85 = 148$ km
• Second train goes: $90 \times 1.85 = 166.5$ km
• Total: $148 + 166.5 = 314.5$ km ✓ (rounding!)

The satisfaction when Mia checked this and it worked? That’s the breakthrough moment.

Subject-Specific Variations

Physics Problems

The framework stays the same, but the variables are physical quantities:

• What are we finding? (force, velocity, etc.)
• What do we know? (given values, constants)
• Which equations connect these? (SUVAT, forces, energy)

Common trap: Students try to remember which equation to use. Instead, ask “What am I finding, and what do I know?” - this naturally leads to the right equation.

GCSE Algebra

Often involves constructing equations from descriptions of relationships:

• “Five more than x” → $x + 5$
• “The sum of twice x and three” → $2x + 3$

The tip: Break complex descriptions into smaller phrases.

The Confidence Build

Here’s what I notice: students who master this framework stop saying “I’m bad at word problems.” They start saying “I need to read this more carefully” or “Let me define my variables.”

That’s the real win - not just solving the problem, but building a reliable process.

Advanced Technique: Working Backwards

For harder problems, sometimes it helps to think backwards:

1. What’s the final answer format?
2. What information do I need to calculate that?
3. Do I have that information? If not, what else do I need?

This is especially powerful for multi-step physics problems.

The Pattern Recognition Phase

After doing enough word problems, students start noticing patterns:

• “How long?” often means find time
• “How far?” often means find distance
• “How much/many?” often means find a quantity

But this pattern recognition comes AFTER mastering the framework. Don’t skip the systematic approach hoping to jump straight to shortcuts.

Tips for Different Learning Styles

Visual learners: Draw diagrams! For motion problems, sketch the scenario. For algebra, use boxes or lines to represent variables.

Sequential learners: Write out the steps explicitly. Number your steps. Check off as you go.

Kinesthetic learners: Act it out or use physical objects (counters, etc.) to model the situation.

Common Pitfalls and How to Avoid Them

1. Jumping to calculations - Force yourself to define variables first
2. Not reading carefully - “more than” vs “less than” trips up 90% of students
3. Ignoring units - If the answer should be in hours and you get a large number, check your conversions
4. Not checking - Always substitute back into the original problem

The Meta-Lesson

This approach teaches more than just word problems. It’s about:

• Systematic thinking
• Breaking down complex tasks
• Checking your work
• Building confidence

These skills transfer to any problem-solving situation.

Next Steps

Practice with progressively harder word problems. Start with simple number relationships (GCSE), move to motion problems (A-level), then tackle multi-part scenarios. Each time, apply the framework. Over time, it becomes automatic.

Remember: the goal isn’t to be fast - it’s to be reliable. A methodical approach that you can always fall back on is worth more than quick tricks that sometimes fail.