Common Mathematical Content Important Throughout KS3 and 4

Age 11 to 16

Some mathematical content runs throughout science at key stages 3, 4 and 5. It is worth remembering that good lessons in these areas can indirectly benefit students in other subjects, particularly if students are made aware of the connections in lessons.

Converting units of length, mass, capacity

The use of units is a key issue in science.  Dimension-ful answers should always be given with units (otherwise they are meaningless).  The ability to convert between units is extremely important.  nm and microns need to be recognised in Sc; mm, m, cm, km need to be converted between.

In Ma we use 1000 as the usual conversion between adjacent units, recognising that cm are an anomaly.

In Sc converting periods of time is important, eg to turn a number of minutes and seconds into a number of seconds.

Standard index or scientific form

In Sc this links closely with the conversion of units.  For example, MW (megawatts) are 106 Watts, nm are 10-9m, etc.

In Ma standard form tends to be introduced and used with reference to measurements, for example to record very large distances (solar system data) or very small measurements (size of microbes), but then proceeds to abstract calculations.

Using and converting compound measures

Speed and density are used in Ma.  Are pupils made aware that speed cannot be measured directly, but has to be calculated from the ratio between the distance travelled and the time taken?

Sc uses other compound measures too (pressure, work, etc).

The units can be used to help remember the formulas (eg m/s has metres ÷ seconds, so we calculate distance ÷ time).

Rounding/approximation/estimation

In Sc rounding to sig figs and dp are both important, including knowing when it is appropriate to round and to what degree.

In Ma: approximation is done by rounding figures (and maybe then carrying out calculations on them), whereas estimation involves deciding on a value for something.

'The length of my classroom is about 6m' is an estimate.  'My classroom is approximately 6.0m long' is an approximation.

In Sc when there is lots of data we might talk about the 'best estimate' for the 'true value'.

In Ma, at KS4, pupils need to realise that measurements have already been rounded by their very nature, whether this is explicitly stated or not.  They need to be able to work out the upper/lower bounds for measurements.  They also need to play the examination game, realising that if they are given a triangle and asked to work out the area, or to use trigonometry, then they should treat the measurements as being accurate, while remembering to give the final answer to the degree of accuracy asked for.

Using indices

Sc: positive whole number powers, eg for volume formulas.  x-1 for rate calculations (higher tier GCSE).  Again there is a link with units (volume units are m3, etc, so they involve multiplying three lengths together).

Proportion and ratio

Sc: direct and inverse proportion only.  Ma: higher GCSE includes square and inverse square too.  In Sc the links between the graph and the proportion it implies are important.

Using algebra

In Sc this includes substituting, rearranging, solving equations etc.  NB: the units are still important! Formula triangles are often used in Sc (eg for speed, density, etc) and in Ma (for trigonometrical formulae).

Drawing graphs

In Sc this involves: Drawing and labelling axes; plotting graphs; reading values from graphs; creating scatter graphs and the line of best fit; relating a table of values to a graph; drawing graphs for a particular proportional relationship; bar charts

The data handling cycle and the investigation cycle

There are considerable links between these, with initial hypotheses being expressed in both, then data collected, analysis of the data (using graphs and calculations) and an evaluation of what it means, perhaps then leading to a new hypothesis and a second cycle.

Calculations, including using fractions/decimals/percentages

Sc: in Yr 11 percentages are particularly important

Use of a calculator

Entering calculations in the correct order, finding the right keys (eg for cube root) and using brackets as appropriate.

Converting units of area/volume

Ma: important at KS4

Calculating perimeters, areas and volumes

Important for Sc and for Ma

The mean and range

These are used in Ma and Sc; Sc does not use mode/modal/median

Probability

In Ma pupils must use fractions (or an equivalent) to describe probabilities and may not use words. In Sc pupils can explain, using the language of probability, how likely it is that a particular result true or meaningful.