DoRevision
Log in Sign up free

Units, Time and Compound Measures

Metric units step by tens, so converting them moves a decimal point. Time steps by sixty, so a decimal point in a time does not mean what it seems to, and that one difference explains the traps in this topic.

⏱️ 22 min 🎯 16 activities
Best used for
Intervention Mock preparation Cover lesson

Get the method right under pressure

Free interactive practice on the steps that lose marks under exam pressure.

Start revising free

What you'll cover

Time does not count in tens

Most of the measures you use are metric, and metric units are built so that each one is ten, a hundred or a thousand times the next. That is why converting them only ever moves a decimal point. Time was never built that way. A minute holds sixty seconds, an hour holds sixty minutes and a day holds twenty-four hours, so a decimal point in a time means something quite different from what it appears to mean. A calculator does not know this. It will happily subtract one clock time from another as if they were ordinary numbers, or show a journey as 2.4 hours, and both answers need translating before they mean anything. This module is about three habits that stop those slips. Before converting anything, decide whether the new unit is larger or smaller, because a smaller unit always needs a larger number. Treat anything involving time as counting in sixties, not in tens. And at the Higher end, remember that a unit of area or volume is built from more than one length, so the length factor is used more than once. Every offset, equivalence and figure in this module is given inside its question, as an exam supplies them, and none is a real timetable or a real place.

Five measures words

Two of these are about clocks, two are about families of units, and one is about measures built from other measures.

Match each units job to its method

  • Changing 3.5 kilometres into metres
  • Changing 150 minutes into hours
  • Changing 4 square metres into square centimetres
  • Changing a distance in kilometres into miles, when told that 8 kilometres is about 5 miles
  • Giving a sensible estimate of the height of a classroom door
  • Multiply by 1000, since the new unit is smaller and so there must be more of them
  • Divide by 60 rather than 100, since that is how many of the smaller unit make one of the larger
  • Use the factor of 100 twice, once for each of the two lengths that make up the unit
  • Use the given equivalence as a ratio, and remember the answer is only as exact as the equivalence
  • No conversion at all: compare it with something familiar, such as the height of an adult, and give a round figure

When does the film finish?

A film starts at 19:45 and lasts 2 hours 30 minutes. What time does it finish, written in the 12-hour clock?

  • 10:15 pm
  • 10:15 am
  • 9:75 pm
  • 22:15 pm

Tens against sixties

The two families of measures behave differently, and treating one as if it were the other is where the traps in this topic come from. Set side by side, the difference is plain.

How long is the train journey?

A train leaves at 14:47 and arrives at 17:18 on the same afternoon. How long does the journey take, in MINUTES?

Count up to find a time interval

Five steps for finding how long something lasts, without ever subtracting clock times as if they were ordinary numbers. Put them in order.

  • Write both times in the 24-hour clock, so that morning and afternoon cannot be confused
  • Count the minutes from the start time up to the next whole hour
  • Count the whole hours from there up to the last whole hour before the end time
  • Count the minutes from that hour up to the end time
  • Add the pieces together, turning every 60 minutes into an hour

Where measures go wrong

There are a small number of places where a measures answer can go wrong, and every one is avoidable once you know where to look. Subtracting clock times directly gives nonsense: 17:18 take away 14:47 as ordinary numbers gives 271, which is not a number of minutes and not a time. A calculator answer in hours has to be read as a fraction of an hour, so 2.4 hours is 2 hours and 24 minutes, because four tenths of sixty is twenty-four. The hours near midday and midnight need care: 12:30 am is half an hour after midnight, and 12:30 pm is half an hour after midday. A time zone that is ahead needs hours added, one that is behind needs hours taken away, and either can move you into a different day. And at the Higher end, a square metre is 100 centimetres by 100 centimetres, so it holds ten thousand square centimetres, not a hundred; a cubic metre holds a million cubic centimetres for the same reason. The check that catches most of these is one question asked at the end: is the answer the right size? A journey of just over two and a half hours cannot be 271 minutes long.

Convert an area

A rug covers 2.5 square metres. How many SQUARE CENTIMETRES does it cover?

Spot the two broken conversions

Six statements about units and time. Tap the TWO that are wrong.

  • 3.2 kilometres is the same distance as 3200 metres.
  • A time of 1 hour 45 minutes can be written as 1.75 hours.
  • A calculator showing 2.3 hours means 2 hours and 30 minutes.
  • Half past nine in the evening is 21:30 on the 24-hour clock.
  • A floor of 3 square metres has an area of 300 square centimetres.
  • If 1 gallon is about 4.5 litres, then 10 gallons is about 45 litres.

Counting by the dozen

A baker sells eggs by the dozen, and a customer asks for one and a half dozen. Nobody behind the counter hands over fifteen eggs. Half of a dozen is six, so one and a half dozen is eighteen, and the baker knows that without thinking because the grouping is twelve and not ten. Now suppose the order is written down as 1.5 and passed to someone who has never sold eggs. They might well read the point as if it split tens from units and count out fifteen. The number on the note was right; the reading of it was wrong, because the reader assumed the wrong size of group. Any quantity that is counted in groups other than ten carries the same risk, and the only protection is to know the size of the group before reading what comes after the point.

Complete the time and units rules

An hour is split into _____ minutes, so 1.5 hours is 1 hour and _____ minutes. Changing from a larger unit to a smaller one always makes the number _____. To change square metres into square centimetres, multiply by _____.

sixty thirty larger ten thousand a hundred fifty smaller a thousand

Read the calculator display

A calculator gives a journey time of 2.75 hours. Choose the option in each gap to turn that into a proper answer with its reason.

The measures run

Five quick questions on time, units and compound measures. Three lives.

A call across time zones

You are arranging a video call with a cousin who lives in a city whose clocks are 7 hours BEHIND yours. Work through three decisions.

  • Your cousin says they are free from 08:00 on their own clocks. You need to know what time that is on yours before you can agree. Which time do you work out?
  • The call is booked for 15:45 on your clocks and is expected to last 1 hour 50 minutes. You have to tell someone at home when you will be finished. Which end time do you give?
  • For the next call, your cousin tells you their clocks have gone forward one hour for the summer, and yours have not changed. You need to decide what the gap between you is now. What do you conclude?

Explain the journey time

A friend worked out a journey from 14:50 to 17:15 by typing 17.15 take away 14.50 into a calculator. The display showed 2.65, and they wrote the answer as 2 hours 65 minutes. Explain what went wrong, then work out the journey time properly, showing the method in your explanation.

  • Say why clock times cannot be subtracted like decimals
  • Explain why 2 hours 65 minutes cannot be a correct way to write a time
  • Work out the journey time by counting up in pieces, showing each piece
  • State the journey time in hours and minutes, then in minutes
  • Finish with the general rule about time that this case shows