STEM Teacher Pages

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• General ideas for lessons and learning

  Many of the stemNRICH tasks can be used in the ways described here. We will provide guidance and suggestions for appropriate use in the teachers' notes to the tasks.

  1. Data collection in SET then analysis of the data in maths; possibly with a feedback into SET.
  2. Create an equation/make a prediction/do a calculation for a physical process in a maths lesson and then test out the prediction by performing the experiment in science.
  3. Introduce a task in a SET lesson (to ensure the pupils all have the SET knowledge required), continuing to work on it in a maths lesson (using maths skills) and then complete it for a double homework - marked by both maths and SET teacher with their particular subject focus.
  4. Introduce a short, regular and scheduled 'discussion' or circle time in both maths and SET lessons (perhaps 10 minutes a fortnight). Give students a chance to comment on the SET that they have noted in maths and vice versa and also to ask teachers/other students of wider questions concerning the mathematics they have seen in SET or the SET that they have seen in maths.
  5. Set a half-termly cross-curricular review homework:
     1. Maths: Review SET books for mathematical content; make links with the mathematics that they have learnt during the term.
     2. SET: Review maths books and suggest SET links or connections with the material covered. Look for parts of maths which have the most common uses.
  6. Joint poster project: Choose a theme and work on the same poster in both a maths and SET lesson, where the focus is finding the maths/SET related to a big theme, such as global warming.
  7. Use snippets of problems/weekly challenges as starters when students enter room. Choose topic to give a flavour of the main theme of the day and plan for appropriate content in schemes of work.
  8. Include some cross-curricular display material in corridors and classrooms.
  9. Ask student newspaper to interview members of science and maths departments to find out their 'STEM history' in terms of the STEM experience at university, hobbies or other jobs.
  10. Build on the clear links between 'investigation cycles' in science, 'design pentagon' in D&T and 'data handling cycles' in maths.
  11. Use data loggers, light sensors, paper and other patterns, and other hands-on technology in maths.
  12. Show a picture of an experiment/activity as used in SET to act as stimulated recall in maths at the appropriate time.
  13. Have meaningful end of term cross-curricular activites.
  14. Have AsSTEMblies - assemblies which focus on some aspect of STEM
  15. Form a STEM club or a maths club or both. Form links between these clubs and clubs from other schools.
• Curriculum area offering rich opportunities for collaboration

  These are the main curriculum areas offering natural STEM links as identified by our focus group of science and maths teachers - this will be enlarged after our focus group of D&T and maths teachers has met in July 2011.

  • Graphs
  • Data handling and representation
  • Formula rearranging
  • Units of measurement
  • Standard form
  • Percentages, ratio and proportion
  • Scale drawing
  • The topics covered in functional skills
  • The historical links between mathematics and SET
  • The present day links between mathematics and SET
• Specific examples of curriculum links by year

  These examples will hopefully give you an idea of some of the natural cross-over points between subjects at specific points during the year.

  This will also be augmented after our Maths/D&T focus group has met.

  	Science	Maths
  Y7	Variation (Y7 Biology)	Bar charts/line graphs (L3-6) Interpreting graphs (L4-6)
  Y7	Mass & Weight, Speed, Pressure (all years Physics)	Reading scales (L3-4) Distance/time and mass/weight graphs (L5-6) Rates of change and compound measures (L7-8, Unit 2 GCSE)
  Y7	Forces :Hooke's Law, Friction, Speed.  Direct proportion as a concept appearing.  From a maths viewpoint links to initial use of equations and basic algebraic substitution.
  Y7	Classification & food webs -Could link the idea of classification in Science to classification of 2D shapes or quadrilaterals in maths.  Statistics built in with the science content through use of data collection with quadrants, calculating averages when investigating the food webs.  Possible connections to area as well e.g. estimating areas of different size leaves.
  Y7	In KS3 Sc uses trolleys and light-gates to calculate speed.  Sc could make a video of this the next time it happens for Ma to use to help the pupils recall this.
  Y7/8	Negative numbers for boiling and melting points of elements; which stay solid for largest range of temperatures? This incorporates differences between negative numbers.
  Y7/8	Balancing Equations (Y7 & 8 Chem)	Ratios Unitary method (L3-4) Simplify ratios, divide quantities into two parts (L4-5) Divide into quantities of more than two parts (L5-6, Unit 2 GCSE) Interpret ratios in a range of contexts (L6-7, Unit 2 GCSE)
  Y8	Solar System (Y8 Physics) Swirling water tub with balls to demonstrate orbits. Relative sizes, distances from the sun, temperatures, orbital period	Loci (all levels) Circumference/area of a circle (L6-7, Unit 2/3 GCSE) Standard form Orbits (KS5)
  Y8	Graphing, sequences from experiments such as measurement of temperature.
  Y8	Liquid soap: how watered down does soap need to be before just slipping of hands/surfaces at various angles.	Angles of elevation, ratios, rearranging, averages from repeated measurements.
  Y9	Building on the clear links between the Investigation Cycle in science and the Data Handling Cycle in maths by having a joint maths/sci project in Yr 9.
  Y9/10	Attach data loggers to a pupil and watch as they attempt to create particular distance/time graphs.  Pupils are used to seeing the x and y axes as spatial axes, which means the graph creates a picture of what we would see in real life.  A distance/time graph is different, but some pupils assume it shows someone climbing a hill, for example.
  Y9	Dinosaurs, percentages, ratio, scales and scale drawing; timelines.  There could be links to Y7 fossils in science.
  Y9	Pressures, forces & moments, formulae rearranging
  Y9	Chemical Patterns, concentration of solutions, ratio.
  Y9	Reaction Times,Drugs & Behaviour/Quest for Y9 Intelligence data handling.  Science look at the effects of caffeine on reaction times.  In maths could have a data handling project where collecting reactions times provides one set of data to investigate hypotheses comparing boys' and girls' 'abilities'
  Y10+	Air Quality/pollutants (GCSE Chem, 21st Century)	Averages, range, outliers, repetition of trials (probability), reliability of results/comments and comparisons  of results (Unit 1 GCSE)
  Y10+	Risk (IAS 5 21st Century)	Percentages, ratio, proportionality, sampling (Unit 2 GCSE)
  Y10+	Parallax Error, trigonometry.  Linking initial discovery into trigonometrical ratios with this.  Also could be developing concept of accuracy and bounds.
  Y10+	Standard Form, Astronomical distances / cell biology.
  Y10+	Lens formula, focal points / telephoto lens &enlargements.  Interesting area, with links to formulae, angles and transformations.
  Y10+	Crystal formation, 3D coordinates, angles between bonds, 3D Geometry.
  Y10+	Kinematic Equations, rearranging formulae / real-life formulae
  Y10+	Samples (Health Studies 21st Century)	Sampling (Unit 1 GCSE) [NB Sci just random, Ma includes stratified]
  Y10+	Electrical Circuits (P5 21st Century)	Transposition of formulae, straight line graphs (Unit 2 GCSE)
  Y10+	Correlation and cause (IAS2 21st Century)	Lines of best fit, correlation, types of graph (Unit 1 GCSE)
  Y10+	Energy and the Environment (all levels Chem)	Scale drawing, percentages, graph skills, budgeting, area (all levels)

• 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.

  This will also be augmented after our Maths/D&T focus group has met.

  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 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 need the 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.

  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?

  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.

   

• Content uses specific to university biology/chemistry

  If you take a look at the bigger picture then many students will choose to study science at university and the mathematics they learn at school will become fundamentally important to them. Here we give a comprehensive list of the important subjects in mathematics compiled from all of the NRICH maths content tags by a second-year undergraduate - NRICH has the capability to be searched according to these tags. This list will be relevant to KS3/4/5 science and should be made known to students who might consider studying biology or chemistry at university.

  Maths content	Applications
  Extremely important
  Processing and representing data	Many various
  Interpreting data	Many various
  Handling data	Many various
  Data logging	Many various
  Data collection	Many various
  Sampling	Many various
  Types of data	Many various
  Experimental design	Many various
  Working systematically	A very important skill to have!
  Calculating with ratio and proportion	Generally very important
  Very important
  Game theory	Behaviour
  Speed	Rate of reaction, physiology
  Volume and capacity	Related to surface area
  Surface and surface areas	Uptake of nutrients etc
  Angle properties of shapes	Bond angles
  Angles at a point or line	Bond angles
  Angles	Bond angles
  Laws of logs	Various
  Log functions	Many various
  Exponential function	Many various
  Exp growth and decay	Cooling curves, modelling,
  Sketching	Many various
  Gradients	Many various
  Graphs	Data handling, modelling
  Trial and improvement	Modelling, experiment
  Investigations	Experiment
  Selecting and using information	Designing experiments
  Recording mathematics	Experiment
  Making and testing hypotheses	Experiment, investigation
  Some understanding needed
  Cartesian equations of lines	Modelling
  Co ordinates	Data handling
  Cubic functions	Modelling
  Composition of functions	Various
  Inverses	Various
  Quadratic functions	Modelling
  Linear functions	Modelling, data handling
  Transformation of functions	Modelling, linearisation
  Asymptotes	Modelling
  Indices	Modelling, data handling
  Algebraic fractions	Modelling, data handling
  Solving equations graphically	Modelling, data handling
  Other equations	Modelling, data handling
  Quadratic	Modelling, data handling
  Simultaneous equations	Modelling, data handling
  Linear equations	Modelling, data handling
  Factorisation	Modelling, data handling
  Expanding brackets	Modelling, data handling
  Manipulation	Modelling, data handling
  Creating expressions	Modelling, data handling
  Introducing algebra	Modelling, data handling
  Using symbols	Modelling, data handling
  Formulae	Modelling, data handling
  Generally	Modelling, data handling
  Estimating and approximating	Data handling
  Multiplication + division	Data handling
  Addition + subtraction	Data handling
  Approximate solution	Useful when doing an experiment
  Direct and inverse proportion	Data handling, modelling
  Ratio	Data handling
  Equivalent fractions, decimals and percentages	Data handling
  Mixed fractions, decimals and percentages	Data handling
  Calculating with percentages	Data handling
  Calculating with decimals	Data handling
  Calculating with fractions	Data handling
  Percentages	Data handling
  Decimals	Data handling
  Fractions	Data handling
  Standard index form	Data handling
  Powers and roots	Data handling, experiment
  Rounding	Data handling
  Used occasionally
  Optimisation	More advanced topics
  Chi squared tests	Usually population-related
  Statistics generally	ANOVA testing, understanding how reliable a result is
  3D	Chemistry - orbital geometry, shapes of molecules
  Max/min/optimise	Chemical reactions, optimisation
  Curve fitting	Data handling, modelling
  Matrices	Game theory: payoff matrices
  Making and proving conjectures	Experiment
  Mathematical modelling	Making predictions
  Complex numbers	Wave and diffusion equations

• Get started on cross curricular planning

  To get started on STEM in your school it can be useful simply to get the views of interested parties. These simple questions can be a good focus for discussion.

  • What do you think might be key elements of good STEM practice?
  • What do you think might be key obstacles hindering cross-curricular teaching?
  • What curriculum areas do you think might offer rich opportunities for collaboration?
  • Can you suggest any practical ways for the departments to work together/to support teachers?
  • Do you have any general ideas for lessons and learning?
  • Do you see any potential sources of confusion between departments?
• Acknowledgements
  
  

  We are indebted to the following teachers for contributing to the initial development of the KS3/4 STEM pages:

  Samantha Armsby, Sawston Village College

  Alissa Baldwin, PGCE Trainee, Cambridge University

  Mark Dawes, Comberton Village College

  Rachel Dixon, Tudhoe Grange school

  Cecilia Freer, Swavesey Village College,

  Tabitha George, Swavesey Village College

  Sarah Glover, Tudhoe Grange school

  Luke Pendlebury, St. Faith's School

  Euan Willder, Comberton Village College

   

  We are also grateful to the many students who have worked with us thus far on developing these scientific mathematics materials.

  We thank the Cambridge University Faculty of education for inviting us to speak to their science and maths PGCE students about stemNRICH, from which many developments have followed.

  We are also very grateful to the Clothworkers' Foundation for funding this significant and important project at KS3/4.

  Finally we are grateful to the Cambridge University Transkills project which provided funding for the development of the KS5 stemNRICH pages where the concepts around which the STEM: secondary pages are to be created were invented, tested and refined; many of the resources in STEM: secondary will form a direct link with these more advanced resources leading to coherent links from years 11 to 18