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Primary 6 Maths | Percentage: Discount and Profit: Tutor Lesson Guide | Cost, Marked Price, Selling Price
The trap in discount questions is that 20 percent off and a 20 percent reduction read differently but give the same number. The trap in profit questions is using the marked price as the cost, which wrecks every percentage that follows.
Objectives — Pupils can: (1) translate a discount into a multiplier, so 30 percent off means times 0.7 and 25 percent off means times 0.75; (2) find the selling price from a marked price and a discount; (3) find profit or loss from cost and selling price, and express it as a percentage of cost; (4) explain why a mark-up followed by a discount does not return to the original price.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Percentage and decimals | 20 percent is 0.2 | needed to convert discounts |
| Decimal multiplication | 400 times 0.8 | the workhorse of discount questions |
02 Lesson flow (40 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-5 min | Diagnostic | what is 20 percent of 100 | answer 20 |
| 5-13 min | The language of discount | marked price 400 with 20 percent off | times 0.8 is 320 |
| 13-22 min | Cost and profit | cost 250, selling price 320 | profit 70, rate 28 percent |
| 22-32 min | Mark-up then discount | cost 200, plus 25 percent, then 20 percent off | sells at 200, no profit |
| 32-40 min | Exit check | three questions | all correct |
03 Teaching script (read it out)
Scene 1: Act 1: A discount is the fraction you pay, not the amount removed
Ask what a 20 percent discount means. Pupils often answer that you take 80 percent away. Show a marked price of 400: 20 percent off means paying 80 percent, so 400 times 0.8 is 320. You save 80, not 8 and not 320. Then write the discount and the 20 percent reduction side by side and let pupils discover they are the same result in two wordings.
Tutor line: “A 20 percent discount is not 20 dollars off. You pay eighty percent, so 320 out of 400, and you save 80.”
Scene 2: Act 2: The profit rate always divides by cost
Cost 250, selling price 320. Profit is 320 minus 250, which is 70. The rate is 70 divided by 250, which is 0.28, so 28 percent. Pause here and deliberately compute the wrong version: 70 divided by 320 is about 21.9 percent, then ask why the selling price cannot be the denominator. Profit rate asks how much you earned relative to the money you put in, and that money is the cost. Get the denominator wrong and every later comparison is wrong.
Tutor line: “Profit rate compares the profit with the money you put in, not with the price tag. The denominator is always the cost.”
Scene 3: Act 3: A mark-up then a discount does not return to the original price
Cost 200, mark up 25 percent to a marked price of 250, then take 20 percent off: 250 times 0.8 is 200, exactly the cost, so profit is zero. Pupils assume that adding then removing the same percentage cancels out. The reason it does not is that the two percentages use different bases: the mark-up is based on cost, the discount is based on the marked price.
Tutor line: “The mark-up uses cost as its base and the discount uses the marked price, so they do not cancel. Here it lands exactly on cost, so you earn nothing.”
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Find the selling price | convert the discount, multiply the marked price, give the unit | 400 times 0.8 is 320 | |
| Find the discount | divide selling price by marked price, convert to percentage | 320 over 400 is 80 percent, so 20 percent off | |
| Find the profit rate | selling price minus cost, divide by cost, times 100 percent | 70 over 250 is 28 percent | |
| Find the cost from a loss | divide selling price by (1 minus loss rate) | 180 divided by 0.9 is 200 |
Sanity check (teach this): Write percentages to a whole number or one decimal. The denominator for profit and loss rates is always cost. The base for a discount is always the marked price. Do not mix half price and 50 percent off in the same question.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| Marked price 400, 20 percent off. Selling price? | 320 | 400 times 0.8 |
| Marked price 680, 25 percent off. Selling price? | 510 | 680 times 0.75 |
| Cost 250, selling price 320. Profit rate? | 28 percent | 70 over 250 |
| Cost 200, mark up 25 percent then 20 percent off. Profit? | 0 | marked 250, sells 200 |
| Selling price 180 at a 10 percent loss. Cost? | 200 | 180 divided by 0.9 |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Treating a discount as a subtraction | 400 minus 32 giving 368 | a discount is the share you pay: 320, not 8 percent off |
| Dividing profit by selling price | 70 over 320 giving 21.9 percent | the denominator is cost, and your cost is 250 |
| Assuming mark-up then discount cancels | expecting a 25 percent gain after the discount | the bases differ; work it out and you land on 200 with zero profit |
| Writing a loss as a gain | selling at 180 with cost 200 and calling it a 20 profit | selling below cost is a loss of 20, say so explicitly |
07 Homework (paper, section and question numbers)
- Independent practice in this chapter (questions 1 to 5 above) — questions 1 to 2: discount; 3 to 5: profit rate, the trap, reverse cost
- Primary Maths chapter index (related chapters at this level) — questions 6 to 8: write one discount, one profit and one loss question
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| Marked price 500, 40 percent off. Selling price? | 300 | if wrong: reteach the multiplier 0.6 |
| Cost 400, selling price 460. Profit rate? | 15 percent | if wrong: reteach cost as denominator |
| Cost 300, mark up 20 percent then 20 percent off. Selling price? | 288 | if wrong: reteach the two bases, a loss of 12 |
09 Tutor FAQ
Should the two wordings be taught together?
Yes, side by side. The same result in two wordings stalls pupils who only recognise one of them.
Why not start with the formula?
The formula is short but the idea of a base is abstract. Once pupils can name the base out loud, the formula stops going wrong.
Is reverse cost worth teaching?
School papers ask it often. There is one method: divide the selling price by 1 plus or minus the rate. Never guess.
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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.