Topic 06 · 16 lessons

Measurement

A measurement is a number plus a unit. "Five" means nothing on its own, but five metres, five litres and five minutes are all useful facts. Measurement is where maths meets the physical world.

This section covers the units we use for length, mass, capacity and time, how to calculate area and volume, and how to convert between units without getting lost.

Lessons in this topic

6.1Units of MeasurementA measurement is a number and a unit. Choosing the right unit makes numbers sensible and comparable.
6.2Comparing Length, Mass and CapacityYou can compare two things without any numbers: longer or shorter, heavier or lighter, holds more or holds less. Counting equal units tells you by how much.
6.3Measuring Length with a RulerLine one end of the object up with zero, then read the number at the other end. The small marks between the numbers show millimetres.
6.4Metric Length: mm, cm, m and kmMetric length units are linked by tens, hundreds and thousands: 10 mm make 1 cm, 100 cm make 1 m and 1000 m make 1 km.
6.5Mass: Grams and KilogramsMass is measured in grams and kilograms. There are 1000 grams in 1 kilogram, so convert by multiplying or dividing by 1000.
6.6Capacity: Millilitres and LitresCapacity is how much a container holds. There are 1000 millilitres in 1 litre, so convert by multiplying or dividing by 1000.
6.7Time and ClocksTime runs on sixties and twelves, not tens. Once you know that, clocks, timetables and durations fall into place.
6.8Quarter Past, Quarter To and Five-Minute TimesThe minute hand counts in fives around the clock face. Say minutes past the hour up to half past, and minutes to the next hour after that.
6.9Calendars, Days and MonthsA calendar shows the days of a month in rows of seven. Knowing the days, months and a few facts about them lets you find any date.
6.1012-Hour and 24-Hour TimeThe 24-hour clock counts from 00:00 at midnight to 23:59. For times after noon, add 12 to the hour of the 12-hour time.
6.11Elapsed Time and TimetablesElapsed time is the time between a start and an end. Jump to the next hour, then add the remaining hours and minutes on a number line.
6.12Unit ConversionsConverting units means multiplying by a fraction equal to one. Let the units guide you and you cannot go wrong.
6.13Area and VolumeArea counts squares that cover a surface and volume counts cubes that fill a space. A cuboid has volume length times width times height.
6.14Surface Area of Cubes and CuboidsSurface area is the total area of all the faces of a solid. A cube has 6 equal faces, so its surface area is 6 times side squared.
6.15Temperature and ThermometersTemperature tells us how hot or cold something is. We read it in degrees Celsius on a scale, and numbers below zero mean colder than freezing.
6.16Speed, Distance and TimeSpeed is distance divided by time. Rearrange the formula to find distance or time, and always use matching units.

The big ideas

a)Always carry the unit: Write units at every step. They catch mistakes. If an "area" comes out in metres rather than square metres, something has gone wrong.
b)Metric is built on tens: Kilo means $1000$ , centi means $\tfrac{1}{100}$ and milli means $\tfrac{1}{1000}$ . The same prefixes work for metres, grams and litres.
c)Dimensions multiply: Length is one dimension, area is two and volume is three. That is why $1\text{ m}^2 = 10\,000\text{ cm}^2$ , not $100$ .
d)Time is not decimal: An hour has $60$ minutes, so $1.5$ hours is $1$ hour $30$ minutes, not $1$ hour $50$ minutes.

Worked example

Filling a fish tank

A tank measures $60\text{ cm} \times 30\text{ cm} \times 40\text{ cm}$ . How many litres does it hold?

Volume of a cuboid: length × width × height $= 60 \times 30 \times 40 = 72\,000\text{ cm}^3$ .
One litre is $1000\text{ cm}^3$ .
Divide: $72\,000 \div 1000 = 72$ .

Answer: The tank holds $72$ litres.

Where you will meet it

Cooking, DIY, travel, medicine doses, fuel economy and buying flooring all depend on measuring accurately and converting units correctly.

The wider field

Measurement also covers these ideas, which build on the lessons above:

Mass and weight
Capacity
Temperature scales
Speed, distance and time
Metric vs imperial
Accuracy and rounding