S1 Maths — Percentages Basics: Lesson Prep Guide for Tutors (conversions, reverse calculation, add-then-cut trap)

2026-11-14

Tutor lesson-prep guides · Secondary Maths

Students who say a 15% rise followed by a 15% cut returns to the original price are treating a percentage as a fixed number, when its base keeps moving. This lesson uses a $240 wallet to run both steps and then divides back to 240, so the 5.4 dollar gap is visible.

Objectives — By the end students can: (1) convert 3/8, 7/20 and 9/25 into 37.5%, 35% and 36% and state the divide-then-multiply-by-100 order; (2) use 40 students with 25% girls to get 10 girls and 30 boys and note that 25% plus 75% is exactly 100%; (3) compute 240 raised by 15% to 276, then cut by 15% to 234.6, a 5.4 gap from the original, and divide 276 by 1.15 to recover 240.

01 Prerequisites (3-minute check)

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

Skill	Quick check	Pass mark
Fraction to decimal	What is 3 divided by 8?	0.375, carried to the decimal places
Decimal multiplication	What is 240 times 1.15?	276, not 27.6
Reading percentages	What fraction is 25%?	One quarter, that is 1/4

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	Estimate first	Write on the board: a $240 wallet rises 15% then is cut 15%; does the price change? Ask for a show of hands	One sentence of reasoning each, wrong is fine
5-13 min	What per hundred means	Write the class of 40 on the board and draw a 100-square strip with 25 squares shaded	Say the shaded 25 squares are one quarter, so 10 students
13-22 min	Two different bases	Compute 240 plus 15% to get 276, then ask what 15% of 276 is	Work out 41.4, giving 234.6
22-32 min	Reverse to the original	Show 276 divided by 1.15 is 240: multiply going forward, divide coming back	Write the division 276 over 1.15 themselves
32-40 min	Three independent questions	Hand out three questions (conversion, part, reverse) and scan for the first written step	Write the division or multiplication before pressing keys
40-45 min	Exit check	Three quick oral questions; note any student who misses two	Answer aloud with a reason

03 Teaching script (read it out)

Scene 1: Act 1: a percentage is per hundred

“A percentage tells you how many out of every hundred. 25% means 25 out of 100, which is one quarter. So in a class of 40, 25% girls is 40 divided by 4, which is 10 girls. A percentage and a fraction are the same idea written differently. To go from a fraction to a percentage you do two steps: divide first, then multiply by 100. Three divided by eight is 0.375, times 100 is 37.5%.”

Students repeat: divide first, then times 100

Scene 2: Act 2: the base moves

“240 plus 15% adds 15% of 240, which is 36, giving 276. When the price is cut, the cut is 15% of 276, which is 41.4, giving 234.6. Same one and a half tenths, but 36 up and 41.4 down, because the base grew. So up then down leaves the wallet cheaper by 5.4.”

Students repeat: the rise uses the old price, the cut uses the new price

Scene 3: Act 3: reverse means divide

“Going backwards: if you only know the price after the rise is 276, do not take away 15%. That gives 234.6, which is the price after the cut. Divide 276 by 1.15 and you get 240. Remember: forward you multiply, backwards you divide, and the divisor is 1 plus the percentage.”

Students repeat: backwards means divide by 1 plus the percentage

04 Question types and worked steps

Type	Example	Steps	Answer
Fraction to percentage	Write 7/20 as a percentage	(1) Divide the numerator by the denominator (2) get 0.35 (3) multiply by 100 (4) write the percent sign	7 / 20 = 0.35, so 35%
Find a part	In a class of 40, 25% are girls. How many girls?	(1) Identify the whole as 40 (2) 25% is 0.25 (3) multiply (4) give the unit, students	40 x 0.25 = 10 girls
Find the whole (reverse)	After a 15% rise the price is 276. What was it?	(1) Forward is times 1.15 (2) backwards is divide by 1.15 (3) 276 / 1.15 (4) check 240 x 1.15 = 276	276 / 1.15 = 240
Percentage change	A price goes from 240 to 300. What is the increase?	(1) Difference is 60 (2) divide by the original 240 (3) times 100 (4) say “compared with the original”	60 / 240 = 0.25, a 25% increase

Sanity check (teach this): Reasonableness checks: a fraction-to-percentage answer must sit between 0 and 100, so 37.5% is fine and 3.75% means the times-100 step was skipped; a part must be smaller than the whole, and 10 is smaller than 40; two shares must total 100%, and 25% plus 75% does; after a rise and a cut the price 234.6 is below 240, so an answer of 240 means the changing base was ignored; a reverse answer must multiply back, and 240 times 1.15 is 276.

05 Independent practice (3 questions)

Question	Answer	What to watch
Write 9/25 as a percentage	9 / 25 = 0.36, so 36%	An answer of 3.6% means the times-100 step was skipped
In a class of 40, 75% are boys. How many boys and how many girls?	40 x 0.75 = 30 boys, and 40 – 30 = 10 girls	Both answers are needed, plus the note that 25% and 75% total 100%
After a 15% cut an item sells for 234.6. What was the price?	234.6 / 0.85 = 276	Adding or subtracting 15% fails; divide by 0.85

06 Common mistakes and what to say

Mistake	Student writes	Say this
Believing a rise then a cut cancels out	“240 up 15% then down 15% is back to 240.”	“The rise was 15% of 240 and the cut was 15% of 276. You cut a bigger number, so the wallet ends up 5.4 cheaper.”
Skipping the times-100 step	“3/8 is 3.75%.”	“3 divided by 8 is 0.375, not 3.75. Multiply by 100 and you get 37.5%. Yours is ten times too big.”
Using subtraction to reverse	“276 minus 15% is 234.6, so the original price is 234.6.”	“That is the price after the second cut. To get back divide: 276 over 1.15 is 240, and 240 times 1.15 checks out.”
Thinking above 100% must be wrong	“After a 15% rise it should be 115%, which looks too big.”	“115% is perfectly normal. It just means the new price is above the old one, so more than the original amount.”

07 Homework (paper, section and question numbers)

Redo the three conversions from Act 1, writing both steps: divide, then times 100 — Chapter practice, question 1
Use your own class size and work out the boy and girl percentages, which must total 100% — Chapter practice, question 2
Preview: raise 240 by 25% then cut 20% and see whether it returns to 240; write both lines — Chapter practice, question 3

08 Exit check (last 5 minutes)

Question	Answer	Decision
What is 3/8 as a percentage?	37.5%, divide then times 100	An answer of 3.75% means Act 1 again
240 up 15% then down 15%: dearer, cheaper, or the same?	Cheaper, 234.6, a 5.4 gap	Answering “the same” means Act 2 again
After a 15% rise the price is 276. What was it?	276 / 1.15 = 240	Using subtraction means Act 3 again

09 Tutor FAQ

May students use the percentage key on a calculator?

Yes, but they must write the expression on paper first. The key gives the answer, the written line earns the method marks, and exams want both.

Should 25% and 0.25 be taught together?

Yes. Say three times in the lesson that a percentage divided by 100 becomes a decimal, then do every multiplication with decimals so nobody multiplies by 15.

Does this chapter cover discount questions later?

It does. A discount is a percentage decrease with a moving base, so once Act 2 lands, discount and profit questions follow naturally.

Find a tutor — free Tutor Registration →

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.