From the sale price back to the original: money
The Short Answer
Money questions are word problems with two extra traps: mixed units, and working backwards. Put everything into pounds or everything into pence before starting. And remember that a sale price is not the original minus the discount percentage of the sale price — to go back you divide, rather than adding the percentage on again.
What makes money questions their own topic?
They are word problems, so everything in that topic applies — read twice, count the steps, answer what was asked.
Money adds two difficulties of its own: mixed units, and working backwards.
Same unit first
Pounds or pence, and the same one all the way through.
For 35p pencils and a £5 note, pence is easier: 500 ÷ 35. For a £48 coat with a percentage off, pounds is easier.
Mixing them mid-calculation is the single commonest way to produce an answer that is a hundred times out — and because both £4.50 and 450p are perfectly plausible amounts of money, nothing about the answer looks wrong.
Going backwards is where everybody trips
This is worth doing slowly, because the instinct is so strong and so wrong.
Comparing value honestly
Six pens for £2.70, or ten for £4.20?
Comparing the totals tells you nothing — of course the ten-pack costs more. Comparing how much you save is worse, because it depends on what you were going to buy anyway.
Find the cost of one. 2.70 ÷ 6 = 45p each. 4.20 ÷ 10 = 42p each.
The ten-pack is better value. And notice it did not look it: £4.20 is a bigger number than £2.70, and packs on real shelves are often arranged so the better value is the one that looks dearer.
Where do pupils lose marks?
Adding a percentage back on instead of dividing.
Mixing pounds and pence mid-calculation.
Comparing totals rather than unit prices.
Writing £24.4 instead of £24.40, which is right arithmetic and a lost mark.
Try it yourself
Same unit first. Label every amount with what it buys. Count the steps before calculating.
- A coat costs £48 and is reduced by 25%. What is the sale price?
- A coat is £36 in a sale after 25% off. What was the original price?
- Which is better value: 6 pens for £2.70, or 10 pens for £4.20?
- Ravi has £5 and buys pencils at 35p each. How many, and what change?
- Why is adding 25% back onto £36 the wrong way to answer question 2?
- £36. 25% of 48 is 12, so the sale price is 48 − 12. Or in one step: he pays 75%, and 75% of 48 is 36.
- £48. The £36 is 75% of the original, so divide: 36 ÷ 0.75 = 48. Equivalently, 36 is three quarters, so one quarter is 12, and four quarters is 48.
- The 10-pack. 2.70 ÷ 6 is 45p each; 4.20 ÷ 10 is 42p each. Comparing totals tells you nothing — you must find the cost of one.
- 14 pencils, 10p change. Convert first: £5 is 500p. Then 500 ÷ 35 = 14 remainder 10, and the remainder is the change.
- Because 25% of £36 is £9, giving £45 — and £45 is not the original. The discount was 25% of the larger number, not of the sale price. Going backwards is a division, and treating it as an addition is the commonest error on this topic.
How much practice does this type need at home?
Shopping. Genuinely — this is the one topic where the real world does the teaching for you.
In front of a shelf, ask which is better value and make your child divide. At the till, ask what the change should be before it appears. In a sale, ask what the original price was, then check the ticket.
That last one is the hardest question on this topic and it is printed on the label, which means your child gets an immediate answer to how they did.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
Why can't my child just add the discount back on?
Because the discount was a percentage of the original, not of the sale price. Take 25% off £48 and you get £36. Now add 25% of £36 — that is £9 — and you get £45, which is not where you started. The percentages are of different numbers. To go backwards, ask what fraction of the original the sale price represents: £36 is 75% of it, so divide by 0.75, or recognise that three quarters is 36 so one quarter is 12.
What is the reliable way to compare two pack sizes?
Find the cost of one item, or the number of items per pound — either works, but do the same thing to both packs. Six pens for £2.70 is 45p each; ten for £4.20 is 42p each. Comparing the totals, or comparing how much you save, produces confident wrong answers, and packs are frequently designed so the larger one looks worse until you divide.
Pounds or pence?
Whichever makes the numbers easier, and the same one throughout. For 35p pencils and a £5 note, pence is easier: 500 ÷ 35. For a £48 coat with a percentage off, pounds is easier. What is never acceptable is mixing them mid-calculation, which is the single commonest source of an answer that is a hundred times out.
How should the answer be written?
As money looks. £24.04 rather than £24.4 or 2404p, unless the question asked for pence. Two decimal places, and the right symbol. It is worth a final glance, because a numerically correct answer written as £24.4 can lose the mark and is entirely avoidable.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
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