Key Stage 3 science · Working scientifically

KS3 science units, equations and calculations explained

Science is a measuring subject, and in Key Stage 3 pupils get fluent with the language of measurement. They learn the standard SI units and how to convert between them, the internationally agreed system for naming chemicals, how to use and rearrange simple equations such as speed or density, and how to summarise a set of results with basic statistics like the mean and range.

Units, equations and calculations, explained

SI units are the international standard for measurement, so that scientists everywhere describe things in the same way. The base units include the metre (length), the kilogram (mass), the second (time) and the ampere (electric current); the kelvin (temperature) and the mole (amount of substance) mostly come later, at GCSE. Other units are built from the base units, such as the newton (force), the joule (energy), the watt (power) and the pascal (pressure). Day to day, science lessons at this stage often use grams, centimetres, litres and degrees Celsius too, and pupils must be able to convert, for example 2,500 g to 2.5 kg.

Chemistry has a similar agreed language. IUPAC, the international body for chemistry, sets the naming rules, which is why chemical names follow patterns. A name ending “-ide”, such as sodium chloride or magnesium oxide, usually means a compound of two elements only. A name ending “-ate”, such as copper sulfate or calcium carbonate, means the compound also contains oxygen. Prefixes show numbers: carbon dioxide has two oxygen atoms for each carbon, carbon monoxide has one. Pupils will also notice that sulfur is spelled with an f.

Pupils use equations as short descriptions of relationships, usually first as word equations: speed = distance ÷ time, density = mass ÷ volume. They substitute numbers with their units, calculate and give the answer with the right unit. They also rearrange an equation to find a different quantity, and derive simple equations for themselves from data, noticing, for example, that when mass doubles, extension doubles, so extension is proportional to mass. Many schools teach rearranging by doing the same thing to both sides, because it carries on working with harder equations later.

Basic data analysis covers the mean (add the readings and divide by how many there are), the range (largest minus smallest), and in many schools the median and mode, plus choosing a sensible number of decimal places. Pupils should be able to say whether an answer is sensible: a person running 100 m in 2 seconds, or a glass of water with a mass of 5 kg, tells you to check the working.

Words your child will hear

SI unit: A unit from the international system of measurement, such as the metre, kilogram or second.
Conversion: Changing a measurement from one unit to another, such as 3,200 m to 3.2 km.
Word equation: A relationship written in words, such as speed = distance ÷ time.
Subject of an equation: The quantity on its own on one side. Rearranging changes which quantity this is.
Density: How much mass there is in a given volume of a material, often in g/cm³.
Mean, median, mode: Three kinds of average: the total divided by the number of readings, the middle value and the most common value.
Nomenclature: The agreed system for naming things; IUPAC sets the one for chemical compounds.

What the National Curriculum says

In Key Stage 3, pupils should be taught to:

Understand and use SI units and IUPAC (International Union of Pure and Applied Chemistry) chemical nomenclature
Use and derive simple equations and carry out appropriate calculations
Undertake basic data analysis including simple statistical techniques

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

Try it: using and rearranging the density equation

A metal block has a mass of 270 g and a volume of 100 cm³. (a) Calculate its density. (b) What would be the mass of 50 cm³ of the same metal? (c) Give the density in kg/m³.

Write the equation and check the units. Density = mass ÷ volume. With grams and cm³, the answer will be in g/cm³.
Substitute and calculate (a). Density = 270 g ÷ 100 cm³ = 2.7 g/cm³. This is close to the density of aluminium, which suggests the answer is sensible.
```
density = mass ÷ volume
        = 270 ÷ 100
        = 2.7 g/cm³
```
Rearrange for (b). Multiply both sides by volume, so mass = density × volume.
```
mass = density × volume
     = 2.7 × 50
     = 135 g
```
Check (b) against common sense: 50 cm³ is half the original volume, so the mass should be half of 270 g, which is 135 g.
Convert for (c). A cubic metre is 100 cm × 100 cm × 100 cm = 1,000,000 cm³. At 2.7 g in every cm³, that is 2,700,000 g, and dividing by 1,000 turns grams into kilograms. So 2.7 g/cm³ is 2,700 kg/m³. A useful shortcut: multiply g/cm³ by 1,000 to get kg/m³.
```
1 m³ = 1,000,000 cm³
mass = 2.7 × 1,000,000
     = 2,700,000 g
     = 2,700 kg
density = 2,700 kg/m³
```

(a) 2.7 g/cm³. (b) 135 g. (c) 2,700 kg/m³.

Common mistakes and how to help

Dropping the units or mixing them in a calculation

Pupils concentrate on the numbers, then divide centimetres by seconds, or grams by cubic metres, and the answer is wrong by a factor of a thousand or a million.

What helps: Write the unit next to every number. Convert everything to one system before calculating, then check that the unit of the answer makes sense.

Using “weight” and “mass” as the same thing

In everyday language we say we “weigh” 50 kg. In science, mass is the amount of matter, in kilograms, and weight is a force in newtons caused by gravity.

What helps: Use mass for kilograms and weight for newtons. A person’s mass is the same on the Moon, but their weight is smaller.

Rearranging equations by memorising a triangle without understanding it

The triangle trick works until the equation has more than three quantities, and then pupils have nothing to fall back on.

What helps: Practise “do the same to both sides”. If distance = speed × time, dividing both sides by time gives speed = distance ÷ time.

Thinking every name ending in “-ide” is a simple compound of two elements

Most are, such as sodium chloride, but hydroxides like sodium hydroxide contain more than two elements, and pupils expect a neat rule that is never broken.

What helps: Teach it as a useful pattern with a few well-known exceptions, and encourage pupils to check the formula, such as NaCl for sodium chloride, when in doubt.

How to help at home

Cook with conversions. Ask your child to scale a recipe up or down and convert the units: grams to kilograms, millilitres to litres. Check each answer by asking whether it is sensible.
Calculate your own speed. In a park or garden, with an adult nearby, measure out 20 m with a tape or by counting paces of known length. Time a walk, jog or cycle with a phone stopwatch and work out the speed in metres per second.
Sink or float with numbers. Drop safe household objects into a bowl of water at the sink and ask which will float. Water has a density of 1 g/cm³, so an object that floats is less dense than 1 g/cm³ overall.
Find the mean of your own data. Measure the same thing five times, such as how many seconds your child can balance on one leg, and calculate the mean and range. Which reading would you remove if you suspected a mistake?
Read the labels. Look at nutrition labels, bus timetables or energy bills together. What units are used, and what do they mean? Ask your teenager to convert one measurement into another unit.

Builds on

Years 5 and 6: Working scientifically

Leads on to

Key Stage 4: The development of scientific thinking
Key Stage 4: Experimental skills and strategies
Key Stage 4: Analysis and evaluation
Key Stage 4: Units, symbols and nomenclature