How to Check Your Math Answers: 5 Methods That Catch Mistakes
Stop losing easy marks. Learn 5 proven checking methods that catch careless mistakes before you submit your PSLE or O-Level math paper.
How to Check Your Math Answers (Without Wasting Time)
You solved the question correctly. You wrote the right method. Then you copied “54” instead of “45” — and lost 2 marks. Sound familiar? Here are 5 checking methods that catch mistakes before you hand in your paper.
Why “Just Check Your Work” Doesn’t Work
Teachers say “check your answers” — but nobody teaches you how. Most students re-read their working and think, “Yeah, that looks right.” That is not checking. That is just reading the same thing twice.
Real checking means attacking your own answer from a different angle. If you solved it going forward, check it going backward. If you used algebra, check with numbers. If you got a number, ask: does this even make sense?
💡 The Checking Mindset
Pretend you are marking someone else’s paper. You would be more critical, right? That is exactly the mindset you need when checking your own work.
Here are 5 methods — ranked from fastest to most thorough. Use the right one for the right question.
Method 1: The Estimation Sanity Check (5 seconds)
Best for: Any question with numbers — especially word problems, percentages, and measurement.
Before you move on, glance at your answer and ask: “Is this answer even reasonable?”
Round the numbers, do a quick mental calculation, and see if your answer is in the right ballpark.
Example: Percentage Word Problem
Question:
A bag costs $248. During a sale, it is sold at a 35% discount. What is the selling price?
Your answer: $161.20
Estimation check:
- $248 is roughly $250
- 35% of $250 = about $87.50
- $250 − $87.50 = about $162.50
Your answer of $161.20 is very close to $162.50 — it passes the sanity check.
If your answer was $86.80 or $334.80:
Those are nowhere near $162.50. You either found the discount instead of the selling price, or added instead of subtracted. The estimation instantly flags the error.
⚠️ Common Estimation Traps
- Percentage questions: Did you find the percentage or the final amount? The question usually asks for one, not the other.
- Speed/distance: If a car travels at 60 km/h for 2.5 hours, the distance should be around 150 km — not 15 km or 1500 km.
- Area vs perimeter: Area should be much larger than perimeter for big shapes. If your area is smaller than the perimeter, something is wrong.
Method 2: The Reverse Operation (15 seconds)
Best for: Arithmetic, fractions, percentages, speed-distance-time, and any “find the value” question.
The idea is simple: undo your answer using the opposite operation.
| If you used… | Check with… |
|---|---|
| Addition | Subtraction |
| Subtraction | Addition |
| Multiplication | Division |
| Division | Multiplication |
Example: Speed-Distance-Time
Question:
A cyclist travels 36 km in 2.4 hours. Find his average speed.
Your working: Speed = Distance ÷ Time = km/h
Reverse check: Speed × Time = Distance → km ✓
The reverse gives back the original number, so you are correct.
Example: Fraction Subtraction
Question:
Your answer:
Reverse check: Add your answer back →
✓
You get back the original number, so the subtraction is correct.
Method 3: The Substitution Check (20 seconds)
Best for: Algebra — solving equations, simultaneous equations, inequalities.
Once you find the value of (or ), plug it back into the original equation. If both sides are equal, you are correct.
Example: Linear Equation
Question:
Solve
Your answer:
Substitution check: ✓
Left side equals right side — confirmed correct.
Example: Simultaneous Equations
Question:
Solve: and
Your answer: ,
Substitution check (both equations):
- Equation 1: ✓
- Equation 2: ✓
Both equations balance — you nailed it.
💡 Substitution is the Most Powerful Check for Algebra
For algebra questions, substitution is almost guaranteed to catch errors. It takes 20 seconds and can save you 2–4 marks. There is no reason not to do it.
Method 4: The “Read the Question Again” Check (10 seconds)
Best for: Word problems, multi-step questions, and any question where you might answer the wrong thing.
This sounds obvious, but it catches the #1 reason students lose marks: solving correctly but answering the wrong thing.
The 3 Things to Re-Read
-
What is the question actually asking?
- “Find the remaining amount” — did you give the amount taken away instead?
- “How many more” — did you give the total instead of the difference?
- “Express as a fraction” — did you give a decimal or percentage?
-
Are your units correct?
- The question asks for metres but you answered in centimetres.
- The question asks for hours and minutes but you gave just minutes.
-
Did you answer ALL parts?
- Some questions have (a) and (b). Did you answer both?
Example: The Classic Trap
Question:
Ali had 240 marbles. He gave 25% to Ben and 30% to Chandra. How many marbles did Ali have left?
Common wrong answer: 132 (that is 25% + 30% = 55% → )
But the question asks for marbles left, not marbles given away!
Correct answer: marbles
The 10-second re-read catches this instantly.
❌ The Most Expensive 10 Seconds You'll Ever Skip
In a typical PSLE or O-Level paper, 2–4 questions are designed to trip you up with tricky wording. Re-reading the question takes 10 seconds. Losing those marks takes your grade down a notch. The math is obvious.
Method 5: The Different Method Check (30–60 seconds)
Best for: High-value questions (3–5 marks) where you have time, and questions you are not 100% sure about.
Solve the question a completely different way. If both methods give the same answer, you can be very confident.
Example: Ratio Word Problem
Question:
The ratio of Amy’s money to Ben’s money is 3 : 5. They have $240 altogether. How much does Amy have?
Method 1 (Unitary):
- Total units = 3 + 5 = 8
- 1 unit = $240 ÷ 8 = $30
- Amy = 3 units = $90
Method 2 (Fraction):
- Amy’s share = of $240 = = $90
Both methods give $90 — confirmed correct. ✓
This method takes the longest, so save it for questions worth 3 marks or more, or questions you are uneasy about.
The Checking Game Plan: How to Manage Your Time
Knowing the 5 methods is useless if you have no time left to use them. Here is how to build checking into your exam.
The 80-20 Rule for Exams
| Phase | Time | What to Do |
|---|---|---|
| Solve | 80% of exam time | Work through all questions. Skip any that take too long. |
| Check | 20% of exam time | Go back and check using the methods above. |
For a 1-hour PSLE paper, that is about 48 minutes solving + 12 minutes checking.
For a 2h 15min O-Level paper, that is about 108 minutes solving + 27 minutes checking.
💡 What to Check First
Don’t check in question order. Check in this order:
- High-mark questions first (3–5 marks) — most marks at stake
- Questions you felt unsure about — highest chance of errors
- Quick estimation pass on remaining questions — catches silly mistakes
The Dot System
As you work through the paper, mark each question with a small dot:
- No dot = confident, just needs a quick estimation check
- One dot (·) = slightly unsure, needs a reverse operation or substitution check
- Two dots (··) = very unsure or skipped, needs a full re-attempt or different method check
When you enter checking time, start with the two-dot questions, then one-dot, then skim the rest.
Quick Reference: Which Method for Which Question?
| Question Type | Best Checking Method | Time |
|---|---|---|
| Arithmetic (add, subtract, multiply, divide) | Reverse Operation | 15 sec |
| Fractions & Decimals | Reverse Operation | 15 sec |
| Percentages & Discounts | Estimation + Re-read | 15 sec |
| Speed, Distance, Time | Reverse Operation | 15 sec |
| Algebra (solve for ) | Substitution | 20 sec |
| Simultaneous Equations | Substitution (both equations) | 20 sec |
| Ratio Word Problems | Different Method or Estimation | 30 sec |
| Multi-step Word Problems | Re-read Question + Estimation | 15 sec |
| Area, Perimeter, Volume | Estimation (does size make sense?) | 10 sec |
| Geometry & Angles | Do angles add to 180° or 360°? | 10 sec |
The 3 Marks You Keep Losing (And Which Method Fixes Each)
1. “I got the method right but wrote the wrong number”
Fix: Reverse Operation check. If does not give you back 36, you copied a number wrong somewhere.
2. “I solved for the wrong thing”
Fix: Re-read the Question check. Circle the key word in the question (“left”, “more”, “fraction”, “percentage”) before solving.
3. “My answer was way off but I didn’t notice”
Fix: Estimation Sanity Check. A 3-second glance would have told you that a Primary 5 student cannot have $45,000 in their savings account.
Build the Checking Habit: Practice Drill
Checking is a skill. Like any skill, it improves with practice. Here is a simple drill:
- Do 5 practice questions (any topic)
- After each question, use at least one checking method before looking at the answer key
- Record your results: Did the check catch a mistake? Which method did you use?
- Track your checking accuracy over 2 weeks
After 2 weeks, you will notice two things:
- Your checking speed increases dramatically
- You start catching mistakes while solving, not just after
💡 Pro Tip: Check During Solving, Not Just After
The best students don’t wait until the end to check. They do mini-checks at each step:
- After finding “1 unit”, quickly estimate if it makes sense
- After solving for , immediately substitute back
- After a long calculation, round the numbers and verify the ballpark
This catches errors early, before they cascade into bigger mistakes.
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