You’ve done hundreds of practice papers. You’ve memorised every formula. You sit down, flip to the first page, and breeze through the first few questions.

Then you hit that question.

It doesn’t look like anything from your assessment book. The wording is strange. You read it once, twice, three times — and your mind goes blank.

Sound familiar? You’re not alone. And here’s the thing: this question was designed to do exactly that.

Why Exams Have “Never-Seen-Before” Questions

Here’s a truth most students don’t realise: examiners deliberately include unfamiliar questions. It’s not a mistake. It’s not unfair. It’s the entire point.

About 60% of PSLE Paper 2 tests non-routine problem solving — questions that can’t be answered by memorising steps alone. O-Level papers are even more demanding, with higher-order application questions worth 6-10 marks each.

The good news? These questions almost always use concepts you already know — just dressed up differently. A ratio question might be hidden inside a story about sharing pizza. A percentage question might appear as a discount-on-discount scenario you’ve never practised.

The concepts are familiar. Only the packaging is new.

And that means you can learn a system to “unwrap” any unfamiliar question. We call it the SOLVE framework.

The SOLVE Framework

SOLVE is a 5-step system for attacking any question that makes you think “I’ve never seen this before.” It’s based on the same principles that mathematician George Pólya identified in his famous problem-solving research, adapted specifically for Singapore Math exams.

Step	Action	Time
S	Stop and read again	30 sec
O	Organise what you know	30 sec
L	Link to something familiar	30 sec
V	Visualise with a diagram	1 min
E	Execute and show everything	remaining

Total setup time: about 2.5 minutes before you start solving. That investment pays back massively.

Let’s break down each step.

---

S — Stop and Read Again

Your first instinct when you see a strange question is to panic. Your heart rate spikes, your brain screams “I don’t know this!” and you either freeze or rush into a calculation.

Don’t.

Instead: put your pen down. Take one slow breath. Then read the question again — slowly, word by word.

Here’s what to do on your second read:

• Circle every number and quantity
• Underline exactly what the question is asking for
• Box any keywords that hint at the math topic (e.g., “remaining,” “ratio,” “increased by,” “altogether”)

Ask yourself these three questions:

1. What information am I given?
2. What do I need to find?
3. Are there any conditions or constraints? (e.g., “at least,” “not more than,” “whole numbers only”)

If you can answer these three questions, you’ve already conquered the hardest part — understanding the problem.

---

O — Organise What You Know

Now take everything you identified in Step S and write it down neatly. This isn’t “working” yet — it’s preparation. Think of it like laying out your ingredients before cooking.

Write down:

• All given values with labels (e.g., “Ali’s stickers = 120, Ben’s stickers = ?”)
• Any formulas that might be relevant (even if you’re not sure yet)
• What type of math this could involve (ratio? percentage? algebra? geometry?)

For PSLE students, organise into a simple list:

Given: Total stickers = 120, Ali has 3 times as many as Ben
Find: How many stickers does Ben have?
Type: Ratio / Multiples

For O-Level students, also note:

• Which topic(s) might apply
• Whether you need exact values or can use a calculator
• If it’s a “show that” question (your answer is already given — you need to prove it)

---

L — Link to Something Familiar

This is the most powerful step — and the one most students skip.

Ask yourself: “What does this remind me of?”

Every unfamiliar question is built on familiar foundations. Your job is to find the connection. Here are three techniques:

Technique 1: Simplify the Numbers

Replace the scary numbers with simple ones. If the question uses 37.5% and $\frac{7}{12}$, mentally swap them for 50% and $\frac{1}{2}$. Can you solve the simpler version? If yes, use the same method with the real numbers.

Technique 2: Strip the Story

Remove the context entirely. “A bakery sells muffins in boxes of 6 and cupcakes in boxes of 8. They sold 120 items total…” becomes “Two groups of items, one in 6s and one in 8s, total 120.” Suddenly you might recognise it as a simultaneous equation or a guess-and-check problem.

Technique 3: Work Backwards from the Answer

If you’re told to “find the ratio,” think: “What kind of question gives me a ratio as the answer?” That’s probably a before-and-after problem, or a comparison problem. Now you know which tools to use.

---

V — Visualise with a Diagram

If Steps S, O, and L haven’t cracked the question yet, this step almost certainly will. Draw something.

The Singapore Math curriculum emphasises heuristics — and the single most powerful heuristic is drawing a diagram. The MOE prescribes 12 problem-solving heuristics, and visual representation appears in nearly every one.

What to draw depends on the question type:

Question Type	Best Diagram
Sharing / Comparison	Bar model
Before and After	Two bar models (before & after)
Speed / Distance / Time	Timeline or journey diagram
Geometry	Sketch with labels
Fractions / Ratios	Bar model with units
Patterns / Sequences	Table of values
Algebra word problems	Let statements + bar model

Rules for good diagrams:

1. Label everything — numbers, units, unknowns
2. Keep it simple — rough sketches are fine, not art class
3. Show relationships — which is bigger? What’s equal? What changes?

---

E — Execute and Show Everything

You’ve read carefully, organised your information, linked to familiar concepts, and drawn a diagram. Now it’s time to solve.

But here’s the critical rule for unfamiliar questions: show every single step.

Why Showing Working Matters More Than Ever

For familiar questions, you might skip steps because the method is obvious. For unfamiliar questions, every line of working is potential marks.

PSLE: Markers award marks for correct methods even if the final answer is wrong. Writing “15 cubes $\times$ 8 cm$^3$ = 120 cm$^3$” earns you marks even if you make a calculation error later.

O-Level: Method marks (M marks) are explicitly awarded. A 5-mark question might give M1 for setting up the equation, M1 for the correct method, A1 for intermediate values, and A2 for the final answer. You can score 3/5 without getting the final answer right.

The “Something Is Better Than Nothing” Rule

If you’re stuck halfway through:

1. Write down what you’ve calculated so far — don’t erase it
2. State what you would do next — even “I would divide by 5 to find one unit” shows understanding
3. Write a reasonable estimate if you can’t get the exact answer

The Final Check

After solving, spend 30 seconds on a sanity check:

• Does the answer make sense? (A person can’t be 450 years old. A ratio can’t be negative.)
• Did you answer what was actually asked? (The question asked for Ben’s stickers, not Ali’s.)
• Are the units correct? (cm vs m, minutes vs hours, $ vs cents)

---

SOLVE in Action: Full Worked Examples

Let’s walk through two complete examples — one PSLE-level and one O-Level — using every step of the SOLVE framework.

---

The Secret: Most “New” Questions Are Old Questions in Disguise

Here’s a cheat sheet of common disguises that examiners use:

It Looks Like…	It’s Actually…
A confusing story about sharing food	A ratio question
Something about filling pools or tanks	A rate question
A weird pattern with shapes or numbers	A number pattern / sequence
A long paragraph about buying and selling	A percentage (profit/loss) question
A question about folding paper or shadows	A geometry (similar triangles) question
”After giving away… he had…”	A before-and-after bar model
Two people working together	Combined rates (add the rates)

Once you identify the disguise, you already know how to solve it.

---

What NOT to Do When You’re Stuck

Knowing what to do is important. Knowing what to avoid is equally important.

1. Don’t stare for 5+ minutes. If SOLVE doesn’t crack it in 3 minutes, skip it strategically and come back later. Your subconscious will keep working on it.

2. Don’t erase everything and restart. Your first attempt often contains useful working. Build on it — don’t destroy it.

3. Don’t leave it completely blank. Even writing “Volume of cubes = 15 $\times$ $2^3$ = 120 cm$^3$” on an otherwise unsolved question could earn you a mark.

4. Don’t let one hard question ruin the rest of your paper. The biggest danger isn’t getting one question wrong — it’s letting the frustration cause careless mistakes on the easy questions that follow.

---

Quick Reference: The SOLVE Poster

Save this for your revision notes:

Step	What to Do	Key Question
Stop	Read again. Circle, underline, box.	”What am I given? What must I find?”
Organise	List values, formulas, math type.	”What type of math is this?”
Link	Connect to familiar problems.	”What does this remind me of?”
Visualise	Draw a diagram, model, or table.	”Can I see the relationships?”
Execute	Solve step-by-step. Show everything.	”Does my answer make sense?”

---

Start Practising SOLVE Today

The SOLVE framework isn’t something you use only on exam day. The best way to master it is to practise it on purpose:

1. Pick a question from an unfamiliar topic in your assessment book
2. Cover the solution
3. Walk through all 5 steps of SOLVE, writing each one out
4. Compare your approach with the given solution

Do this 2-3 times a week, and unfamiliar questions will stop feeling scary. They’ll start feeling like puzzles — and you’ll have the tools to solve every one.