Common Mathematical Content Important Throughout KS3 and 4
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.