Money Problems

El método, paso a paso

1. 1

   Convert everything to one unit first

   £2.40 + 75p → £2.40 + £0.75 = £3.15

   Mixing pounds and pence in one calculation is the most common error. Choose one unit, convert everything into it, and only then calculate — the conversion is worth writing as its own step.

2. 2

   Always write two decimal places

   £3.50, not £3.5 · £4.00, not £4

   Currency conventionally shows both the pounds and the pence, so an answer of £3.5 is wrong notation. Exam marks are lost to this even when the arithmetic is entirely correct.

3. 3

   Find change by counting up

   £6.35 from £10 → 65p to £7, then £3 to £10 → £3.65

   Counting up to the next pound and then in whole pounds is faster and more reliable than column subtraction with a decimal point, and it mirrors how change is actually given.

4. 4

   Compare value by finding a common basis

   6 for £4.50 → 75p each · 4 for £3.20 → 80p each

   Best-buy questions need a unit price, or a common quantity. Finding the cost of one is the unitary method again, and it makes any two offers directly comparable however they are packaged.

5. 5

   Work multi-step problems in order

   total the costs, then subtract from the budget

   Budget questions usually combine several operations. Doing them in a written sequence rather than mentally keeps the intermediate values available for checking and earns method marks where they are offered.

The notation rule

Money is written with exactly two decimal places when using pounds. £3.50 shows three pounds and fifty pence; £3.5 shows the same value in a form that is not how currency is written, and it is marked wrong.

The related rule is never to mix symbols: £3.50 or 350p, but never £3.50p. Both errors are notation rather than arithmetic, which makes them frustrating and easy to eliminate.

• Convert to one unit before calculating
• Always two decimal places with £
• Never write £ and p together
• Change: count up, do not subtract
• Best buy: find the cost of one

Why counting up works better

Subtracting £6.35 from £10.00 in columns requires exchanging across the decimal point twice, which is exactly where errors appear. Counting up to £7 and then to £10 requires no exchange at all.

It also matches how change is handed over in a shop, so students find it intuitive. Methods that mirror the real situation tend to be remembered better than ones that only exist on paper.

Comparing offers

Best-buy questions give two packages of different sizes and prices and ask which represents better value. The reliable method is to find the price of one item in each, then compare — or, where the numbers are awkward, to scale both to a common quantity.

The answer should always state the comparison explicitly: which is better value and by how much per item. A bare calculation without a conclusion frequently loses the final mark.

How we teach money problems

We mark the two-decimal-place convention strictly from the start. It is the cheapest mark on any money question and the one students most often give away, and habits formed early do not need correcting later.

We teach change by counting up rather than by column subtraction, because it removes the exchange across the decimal point that causes most errors, and because it is what students will actually do outside a classroom.