Primary 6 Maths | Discount, Profit and Loss: Tutor Prep Guide | 45 minutes from marked price to profit percentage

2026-11-08

Tutor lesson-prep guides · Primary Maths

Marks are not lost on percentages here. They are lost on which number is the 100 per cent. For a discount it is the marked price; for profit it is the cost. Mix the two and every step looks right while the answer is wrong.

Objectives — Pupils can: (1) find the selling price from the marked price and a discount; (2) work backwards from selling price to discount percentage; (3) take the cost as 100 per cent and find profit or loss percentage; (4) explain why marking up ten per cent then taking twenty per cent off is 64 dollars more than a straight twenty per cent discount.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Percentage to decimal	Write 75 per cent as a decimal	0.75
Multiplying by a decimal	0.8 x 400	320
Dividing by a whole number	70 divided by 250	0.28
Fraction to percentage	Write 7/25 as a percentage	28 per cent
Spotting the original amount	Twenty per cent off. Which number is the original?	The marked price

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0–7 min	Starter: a 400 dollar jacket at twenty per cent off	Pupil says what twenty per cent off means before writing anything	Says pay eighty per cent, writes 400 x 0.8
7–15 min	Fix the two hundreds	Two columns on the board: discount uses marked price, profit uses cost, one example each	Names which number is 100 per cent
15–24 min	Three discount questions	Model selling price, discount percentage, and marked price backwards	States the 100 per cent in each
24–32 min	Profit and loss	Cost 250, sold 320: profit 70, then divide by cost 250	Writes 70 divided by 250
32–41 min	Trap: mark up then discount	Marked price 800, up ten per cent to 880, then take twenty per cent off to 704, beside a straight discount of 640	Explains the 64 dollar gap
41–45 min	Exit check	Three quick questions, each needs the 100 per cent named	Answers independently

03 Teaching script (read it out)

Scene 1: A discount is multiplication, not subtraction

Pupils see twenty per cent off and write 400 minus 80, reading the offer as take 80 away. Say clearly: you pay eighty per cent, so multiply by 0.8. Subtracting 80 only works by luck on a 400 dollar item; try 500 and it collapses.
Every time, ask what fraction of the price is paid, write that down, then multiply.

Pupil says: what fraction do I pay, and which number do I multiply?

Scene 2: Profit percentage divides by cost, not by selling price

Pupils compute 70 divided by 320 because 320 looks friendlier. Ask: you put down 250, you made 70, so what are you comparing against?
Give the extreme case: cost 1 dollar, sold 2 dollars. Divided by cost is 100 per cent, divided by selling price is 50 per cent. A child immediately sees which one means doubled your money.

Pupil says: profit is compared with which number?

Scene 3: Marking up then discounting is not the original price

Marked price 800, up ten per cent gives 880, twenty per cent off that gives 704, not 800. Pupils assume the two moves cancel. Put the numbers side by side: straight discount is 640, the round trip is 704, a 64 dollar difference.
One sentence explains it: the second discount multiplies 880, not 800.

Pupil writes both lines and circles what is being multiplied.

Scene 4: Working backwards still uses the marked price as 100 per cent

Selling price 320 after twenty per cent off, find the marked price. Pupils multiply 320 by 0.8 and get 256, the wrong direction. Teach division: 320 divided by 0.8 is 400.
Self-check: the marked price must be larger than the selling price. If the answer is smaller, the direction is wrong.

Pupil says: should the marked price be bigger or smaller than the selling price?

04 Question types and worked steps

Type	Example	Steps	Answer
Find the selling price	Marked price 400, twenty per cent off	Discount means paying eighty per cent, so multiply by 0.8	320 dollars
Find the discount percentage	Marked price 400, sold 320	Marked minus selling, divided by marked price	20 per cent
Find the profit percentage	Cost 250, sold 320	Profit divided by cost, times 100 per cent	Profit 70 dollars, 28 per cent
Mark up then discount	Marked price 800, up ten per cent, then twenty per cent off	Multiply by 1.1 first, then by 0.8; never merge the two steps	704 dollars, 64 more than a straight discount

Sanity check (teach this): Reality checks: the selling price is below the marked price except in mark-up questions; profit percentage always divides by cost; discount percentage always divides by marked price; a backwards marked price must exceed the selling price; mark up then discount must cost more than a straight discount; percentages carry the per cent sign and the answer ends with a sentence about the situation.

05 Independent practice (3 questions)

Question	Answer	What to watch
Five selling price and discount items	Three forward, two working back to the discount percentage	Check that the 100 per cent is named first
Four profit and loss items	Two profit, two loss, cost and selling price both given	Check the divisor is the cost
Two comparison items	Same marked price: straight discount against mark up then discount	Check the pupil can explain the difference

06 Common mistakes and what to say

Mistake	Student writes	Say this
Reading twenty per cent off as minus 80 dollars	400 minus 80 equals 320, which happens to work	Which number is the whole? Twenty per cent off means you pay eighty per cent, so multiply.
Dividing profit by selling price	70 divided by 320 is 21.9 per cent	You put down 250 and made 70. Profit is compared with what you put down, not with what you took in.
Treating mark up then discount as a wash	Answers 800 for the round trip	The second discount multiplies 880, not 800. Write both lines side by side.
Multiplying when working backwards	320 times 0.8 is 256	The marked price must be larger than the selling price. Your answer is smaller, so the direction is wrong.

07 Homework (paper, section and question numbers)

Primary 6 maths paper drills — Section on what each paper tests: pull ten percentage and discount questions, mark them straight away

08 Exit check (last 5 minutes)

Question	Answer	Decision
Marked price 400, twenty-five per cent off. Selling price?	400 x 0.75 = 300 dollars	Wrong: reteach that a discount is multiplication
Cost 500, sold 425. Loss percentage?	75 divided by 500 = 15 per cent	Wrong: reteach dividing by cost
Marked price 800, up ten per cent then twenty per cent off. Selling price?	880 x 0.8 = 704 dollars	Wrong: reteach the comparison pair

09 Tutor FAQ

Which year does this topic belong to?

Primary 6 in Hong Kong, as an extension of percentage applications. Primary 5 can use it later in the year once percentages to decimals are secure.

Is 45 minutes enough?

Yes. There are only two hundreds to teach. Fewer questions with the 100 per cent named every time beats ten rushed items.

Is there a matching worksheet?

Yes. The homework section links to our Primary 6 maths drill guide, and every practice and exit item on this page carries an answer.

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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.