Number problems

A 5-mark problem is a chain of small steps. Before you start, write down what you are aiming for and what you need to get there.

1. aim: the cost of the paint
2. need: the area to paint, the number of coats, how much a tin covers, the price of a tin
3. area: 4.5 × 2.4 = 10.8, minus the door 0.9 × 2 = 1.8, gives 9 m²
4. paint: 9 × 2 coats = 18 m², and 18 ÷ 5 = 3.6 tins
5. tins come whole: round up to 4, so 4 × £12.50 = £50

Each line is a method mark on a paper. If the last line goes wrong, the earlier ones still score.

• Write each calculation, not just its answer: "18 ÷ 5 = 3.6" earns a mark that "3.6" alone may not.
• Keep full accuracy until the end; round only the final answer, as the question asks.
• Round up for whole things you must buy (tins, rolls, bags, packs) and down for whole things you can make.
• Finish with a sentence when the question asks you to decide: "Offer B is cheaper, by 6p for each pen."

The usual slip: a percentage taken off twice, or a reverse percentage done forwards. If 80% of the price is £60, the price is £60 ÷ 0.8 = £75, not £60 × 1.2.

To decide whether a speed could be over a limit, find its upper bound: the biggest distance divided by the smallest time. A distance of 90 km to the nearest km is between 89.5 and 90.5 km.