PSLE Learner’s Guide · Vol 0390 · Percentages, discounts and transaction states
Find the exact decision this guide helps you make
This guide helps a Primary 6 learner separate the discount amount from the sale price by fixing the original price as 100 percent and naming whether the question asks for money saved or money paid. The short rule is original price is 100 percent; discount is the removed part; sale price is the remaining percentage. You will learn the mechanism, see worked examples, repair common misconceptions, practise in stages and use a compact examination routine.
Choose a reading route
- Understand why the error happens
- Use the step-by-step method
- Study eight worked cases
- Build practice and delayed transfer
- Use the examination-control routine
- Guidance for parents and tutors
- Read the FAQs and choose the next route
This is an examination-performance guide, not a replacement for full topic teaching. Use the PSLE Learning Guide for the wider sequence and the Mathematics Learning Hub for deeper subject instruction.
For complete teaching, worked practice and topic progression beyond this performance decision, continue through the Mathematics Learning Hub. The PSLE discounts, GST and reverse-percentage guide gives a focused canonical route for the underlying topic. This volume keeps a narrower job: it helps the learner recognise, execute and check one examination decision without competing with the wider owner. Use the complete PSLE Learner’s Guide volume directory as the permanent series route. For a nearby published performance routine, continue to Vol 0129 on predicting whether an answer must be greater or smaller.
A careful note about the current examination year
This article is written for the 2026 PSLE preparation context. SEAB’s official 2026 formats page lists English Language as subject 0001, revised Mathematics as 0008 and revised Science as 0009. Format details can change, so confirm any paper-specific timing, component or administrative instruction with the current official SEAB 2026 source and your school. The reasoning routine taught here is deliberately broader: it strengthens how you read evidence, make a decision and check an answer.
Why this mistake happens
A 20% discount does not mean the sale price is 20% of the original. Twenty percent is removed, so eighty percent remains to be paid. Learners often calculate the discount correctly and report it as the price, or subtract when the question asks only for the saving. The repair is to label three transaction states: original price, discount amount and sale price.
The mind likes a fast label. A familiar word, operation, result or rule triggers an answer before the conditions have been checked. That shortcut sometimes works in easy practice, so it becomes a habit. In a demanding question, however, a nearby distractor preserves the surface pattern while changing one important condition. The learner then performs a correct-looking move on the wrong object. The repair is to slow only the decision point: identify what is being linked or measured, preserve its labels, test the conditions, and then continue at normal speed.
Think of the method as a chain with four locks. Object: what exact idea or quantity is under discussion? Relationship: how are the relevant parts connected? Condition: what must be true for the move to be valid? Claim: what is the strongest conclusion the evidence actually supports? A weak answer often skips from object to claim. A strong answer makes the two middle locks visible.
The one-line operating rule
Original price is 100 percent; discount is the removed part; sale price is the remaining percentage. Say it before the first practice set. During timed work, shorten it to four cue words you can recall without stopping.
The step-by-step method
Step 1: Identify the original marked price and label it 100 percent
Identify the original marked price and label it 100 percent. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 2: Circle the discount rate and decide whether the question asks for saving or payment
Circle the discount rate and decide whether the question asks for saving or payment. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 3: Calculate the discount amount as the stated percentage of the original price
Calculate the discount amount as the stated percentage of the original price. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 4: Find the sale price by subtracting the discount from the original, or multiply by the remaining percentage
Find the sale price by subtracting the discount from the original, or multiply by the remaining percentage. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 5: Keep currency units and decimal places appropriate for money
Keep currency units and decimal places appropriate for money. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Step 6: Check that a positive discount makes the sale price lower and that original equals discount plus sale price
Check that a positive discount makes the sale price lower and that original equals discount plus sale price. Do this on the page, not only in your head. A brief arrow, label, unit, underline or condition note makes the decision inspectable. If you later find an error, you can repair the exact step instead of restarting the entire answer.
At this stage, do not decorate the answer with extra facts. Ask one diagnostic question: “What evidence would make this step wrong?” If you can name a possible failure, check it now. If the failure is absent, continue. This negative check prevents confidence from replacing proof.
Misconceptions to diagnose and repair
Misconception 1
Tempting move: Reporting the discount amount when the question asks for sale price. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Misconception 2
Tempting move: Treating a 20 percent discount as paying 20 percent. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Misconception 3
Tempting move: Taking the percentage from a later sale price instead of the original marked price. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Misconception 4
Tempting move: Subtracting the percentage number directly from the dollar amount. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Misconception 5
Tempting move: Forgetting that successive discounts use a changing base. This feels efficient because it removes a decision. It is unsafe because the question may have changed the reference, unit, interval, definition or strength of claim.
Repair: return to the line, number, setup or statement that supplies the condition. Mark it with a short label. Then rebuild only the affected link. Keep all earlier work that remains valid. The purpose of checking is targeted correction, not anxious repetition.
Eight worked cases
Worked case 1: Twenty percent off 80 dollars
Scenario. An item marked $80 has a 20% discount.
The tempting error. Reporting $16 as the sale price. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. $16 is the discount amount. The remaining 80% is $64. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. Discount $16; sale price $64. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. $80=$16+$64. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 2: Find only the saving
Scenario. A $150 bag is reduced by 30%.
The tempting error. Continuing to calculate the price when only saving is asked. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The discount is 30% of $150, which is $45. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. Amount saved: $45. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. State the sale price only as an optional check. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 3: Remaining percentage
Scenario. A book is 15% off.
The tempting error. Multiplying the original by 15% for the amount paid. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The customer pays 100%-15%=85% of the original. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. Sale price equals 85% of marked price. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Explain why the multiplier is 0.85. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 4: Reverse marked price
Scenario. A sale price of $72 is after a 10% discount.
The tempting error. Adding 10% of $72 to recover the marked price. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The $72 represents 90% of the original, not 100%. Divide by 0.9. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. Original price is $80. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Check that 10% of $80 is $8. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 5: Successive discounts
Scenario. A $200 item receives 20% off, then 10% off the reduced price.
The tempting error. Adding the rates and taking 30% off $200. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. First price is $160. The second discount is 10% of $160, or $16. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. Final price is $144. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Compare with one 28% discount. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 6: Discount then fee
Scenario. A $100 service receives 25% off, then a fixed $5 fee.
The tempting error. Taking 25% off the fee too. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. The sequence matters: discounted service is $75, then fixed fee gives $80. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. Final amount $80. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Write the transaction states in order. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 7: Compare two offers
Scenario. Shop A gives 20% off $90; Shop B cuts $15 from $90.
The tempting error. Comparing 20 and 15 without units. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. Shop A saves $18; Shop B saves $15. Compare dollars with dollars. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. Shop A is $3 cheaper. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Calculate both sale prices. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Worked case 8: Reasonableness check
Scenario. A learner gets $108 after a 10% discount on $120.
The tempting error. Rejecting it because 108 seems far from 120. The response may contain relevant knowledge, yet it does not answer the precise decision because one label or condition has been lost.
Work the mechanism. Ten percent of $120 is $12; subtracting gives $108. The answer is lower and the parts recombine. Write the decisive evidence beside the step where it is used. This makes the reasoning readable to another person and prevents a later sentence from quietly changing the meaning.
Answer form. $120=$12+$108. Notice that the answer carries both the conclusion and the reason that licenses it. It is complete without becoming a list of everything you know.
Check. Re-read the command word, substitute the conclusion into the original situation and ask whether every noun, number and comparison still has the same referent or unit. If the answer is stronger than the evidence, narrow it.
Delayed transfer. Estimate first with ten percent. Do this variation after a gap, not immediately, so retrieval rather than imitation drives the solution.
Practice progression: from recognition to transfer
Round 1: mark only
Use six short items. Do not answer them. Mark the object, reference, unit, interval, condition or rule that controls the decision. The goal is accurate noticing without the burden of full writing.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 2: explain the choice
Solve four items and add one sentence beginning “This is valid because…”. If the sentence merely repeats the answer, the condition is still hidden.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 3: repair a wrong answer
Take four plausible wrong answers. Identify the earliest faulty link, preserve the correct work and rewrite only what must change. This develops error diagnosis rather than answer copying.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 4: mixed questions
Mix this job with two older skills. Remove headings that reveal the topic. Decide which routine applies before solving. Selection is part of performance.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 5: timed set
Use a small timed set with a fixed check budget. Mark a cue at the decision point, finish the answer, then perform one positive check and one rejection check.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
Round 6: delayed transfer
Return after two or three days with different surface details. Before seeing notes, write the one-line rule from memory and solve. Compare the new error pattern with the earlier one.
Record the result as one of four codes: N for noticing error, M for method error, I for interpretation error, and C for checking error. Practise the weakest code with a fresh item. Do not repeat an entire worksheet when only one decision needs repair.
A compact practice log
- Question source and date
- Decision cue you marked
- Your first answer in one line
- Earliest wrong link, if any
- Corrected rule in twelve words or fewer
- Date for delayed transfer
- Whether the new item was solved without notes
A useful log is small enough to maintain. It should help you predict the next mistake, not become a scrapbook of completed pages.
Graded independent practice with explained answers
Practice item 1: Direct sale price
Prompt. $60 with 25% off.
Answer. $45
Why. The customer pays 75% of $60.
Check or extension. Check discount $15.
Practice item 2: Saving
Prompt. $240 with 15% off. Find saving.
Answer. $36
Why. 15% of $240 is $36.
Check or extension. Do not report $204.
Practice item 3: Reverse
Prompt. $54 is the price after 10% off. Find original.
Answer. $60
Why. $54 represents 90%.
Check or extension. Divide by 0.9.
Practice item 4: Successive
Prompt. $100 with 20% off, then 25% off reduced price.
Answer. $60
Why. $100→$80→$60.
Check or extension. Do not add rates blindly.
Practice item 5: Compare offers
Prompt. $80: 15% off or $10 off.
Answer. 15% off saves $12 and is better by $2.
Why. Convert both to dollars.
Check or extension. Compare final prices $68 and $70.
Practice item 6: Delayed transfer
Prompt. Explain why a 30% discount means paying 70%, not 30%.
Answer. The original is 100%; removing 30% leaves 70%.
Why. Discount and payment are complementary parts.
Check or extension. Draw a 100-unit bar.
Checking that tests meaning, not neatness
A check should have a target. First run a positive test: identify the evidence, calculation or condition that supports your answer. Then run a rejection test: name the closest tempting alternative and the exact reason it fails. This pair is more powerful than rereading the same line while hoping to feel certain.
Use a reverse check where possible. Reconstruct the original amount, replace a connector with its expanded meaning, map a conclusion back to the data, or apply the repaired rule to the apparent exception. Reverse checking exposes lost labels and unsupported leaps because the answer has to return to its source.
Stop when the check has answered a real question. Repeatedly changing a sound answer because it feels unfamiliar is not checking. If the object, relationship, condition and claim all remain consistent, keep the answer and move on.
Examination control
When time is tight, use the cue ORCC: Object, Relationship, Condition, Claim. Write only the smallest useful mark—an arrow, a unit, a time interval, a boundary or a qualifying word. The mark should prevent the known error without slowing the rest of the paper.
- Read the command word and identify the decision.
- Mark the object or quantity that must keep its identity.
- State the relationship or operation in plain language.
- Check the condition that makes it valid.
- Give the claim at the strength supported by evidence.
- Use one positive and one rejection check, then stop.
If you become stuck, do not produce a longer answer immediately. Shorten the task: write what is known, what must be decided and what condition separates the two best options. A precise partial structure often unlocks the next step and also makes any partial credit more defensible.
A seven-day delayed-transfer plan
- Day 1: learn the one-line rule and complete two worked cases with notes.
- Day 2: solve four short items without notes; classify errors by N, M, I or C.
- Day 3: mix two new items with two older PSLE skills and hide the topic labels.
- Day 4: explain one case aloud to a parent, tutor or imaginary learner in under two minutes.
- Day 5: complete a timed mini-set and use the ORCC marks only at decision points.
- Day 6: rest this skill or practise a different subject so memory has to consolidate.
- Day 7: attempt one unfamiliar transfer item, then write the smallest rule revision needed.
Success on Day 7 matters more than fluency immediately after reading. Delayed transfer shows whether you can retrieve the method, recognise its job under new surface details and control it without a model beside you.
Guidance for parents and tutors
Ask for the decision, not a performance speech. Useful prompts are: “What exactly are you deciding?”, “Which word, unit or condition controls it?”, “What is the closest wrong option?” and “How can you check without starting again?” These questions keep ownership with the learner while making thinking visible.
When an error occurs, locate its earliest point. Praise accurate diagnosis even before the final answer is corrected. If the learner repeatedly loses the same label, introduce one stable notation: arrows for reference, units beside remainders, interval brackets for rates, or boxes around claim conditions. Avoid adding several new routines at once.
Build variation gradually. Begin with clean examples, then add one plausible distractor, then mix the skill with older content, and finally delay the next attempt. A learner who succeeds only when the worksheet title names the method has learned recognition, not transfer.
Keep emotional temperature low. A surprising exception or remainder is information, not proof that the learner is “bad at” a subject. The practical question is which link changed. Once that link is named, practise a small set that isolates it and then return to mixed questions.
The independent-reader test
Before you call the skill secure, explain one solution to a reader who cannot see your thoughts. Name the starting information, the decision, the condition that controls it and the reason the rejected alternative fails. If the explanation depends on “you know what I mean”, a label is still missing. Add that label to the answer, then remove any sentence that does not help the reader follow the chain.
Next, cover the worked example and rebuild the method from a fresh prompt. Do not copy the surface details. Recover the sequence of decisions. This separates genuine control from familiarity with one page. A learner who can transfer the decision routine to new names, numbers or apparatus has a more dependable examination skill than a learner who can reproduce only the model answer.
Finally, compress the method without losing its safety condition. Write one sentence of no more than fifteen words, then test that sentence against an awkward case. If the short rule gives the wrong result, restore the missing condition. Good compression keeps the mechanism available under time pressure while the awkward case prevents the cue from becoming a careless shortcut.
A timed diagnosis drill
Set aside twelve minutes and choose three unfamiliar questions that could trigger this error. Spend the first minute identifying the decision in each question without solving it. Mark the object, relationship, condition and permitted claim. This preview is not wasted time: it prevents you from entering a long method before you know what the method must preserve.
Solve the three questions in the next eight minutes. After each answer, write one tiny prediction about what a correct answer should preserve: a reference word, a whole-number boundary, a pathway, a unit, a direction or an observable result. Then compare the finished answer with that prediction. If they disagree, repair the earliest link and keep the later work only when its meaning remains valid.
Use the final three minutes to classify the errors. A noticing error means the controlling detail was never marked. A method error means the right information was present but the wrong operation or reasoning chain was used. An interpretation error means the result was calculated or observed correctly but described at the wrong level. A checking error means the answer contained a detectable contradiction that the final audit missed.
Repeat the drill a week later with different surface details and without looking at the old corrections. Improvement is not merely a higher score. Look for a shorter pause at the decision point, fewer unnecessary restarts, more stable labels and a clearer reason for rejecting the nearest wrong answer. Those are signs that the performance routine is becoming portable.
Frequently asked questions
What is the difference between discount and sale price?
Discount is money removed; sale price is money paid after removal.
What amount is 100 percent?
Usually the original marked price unless the question states another base.
Can I multiply directly for sale price?
Yes, by the remaining percentage.
Why do successive discounts not simply add?
The later discount is taken from a changed price.
How do I recover an original price?
Treat the known sale price as its remaining percentage and divide.
What is the fastest check?
Original price must equal discount amount plus sale price.
Should a discounted price be higher?
No, not from the discount alone. Additional fees must be handled separately.
What should I study next?
Use the Mathematics Learning Hub and the discount/GST guide.
Your next route
Use this guide until you can state the rule, solve an unfamiliar case and explain why the closest alternative fails. Then move to a deeper subject route: the English Learning Hub, Mathematics Learning Hub, Science Learning Hub, or the full learning-hubs directory. Return to the PSLE Learning Guide when you want to place this skill inside a broader revision sequence.
The Mathematics guide continues the object-label discipline by keeping money saved separate from money paid.