Time, money and measures
Maths · Key Stage 2 · The School
Metric units are all tens
The metric system runs on 10, 100 and 1000, which is what makes it easy. 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km. 1000 g = 1 kg. 1000 ml = 1 litre. Converting is multiplying or dividing by a power of ten, so the digits stay the same and only their position moves — which is place value doing the work again.
Time is the awkward one
Time does not run on tens: 60 seconds to a minute, 60 minutes to an hour, 24 hours to a day. So durations cannot be worked out by subtracting like ordinary numbers. From 10:45 to 11:20 is not 11:20 − 10:45 = 75. Count up instead: 15 minutes to 11:00, then 20 more, so 35 minutes. Counting up through the hour boundary is reliable and avoids the trap entirely.
Money is decimals with a rule
£3.45 means 3 pounds and 45 pence, so pounds and pence are two decimal places, always written with two digits: £3.40, not £3.4. To find change, count up from the price to the amount given — from £3.45 to £5, count 5p to £3.50, 50p to £4, then £1, giving £1.55. Shopkeepers have counted up like this for centuries because it is quicker and harder to get wrong.
Do not subtract, because time is not decimal. Count on in stages. 10:45 to 11:00 is 15 minutes. 11:00 to 12:00 is 1 hour. 12:00 to 12:20 is 20 minutes. Total: 1 hour 35 minutes. Now see what subtraction would have given: 12:20 − 10:45 treated as digits gives one hour and seventy-five minutes, which is not a time at all — and 1.75 hours would be 1 hour 45 minutes, ten minutes wrong.