Modelling resources for Cambridge International Mathematics (IGCSE)

Modelling resources for Cambridge International Mathematics (IGCSE) 0607 Weblinks Care is needed here because many web-based materials come in at a much higher level than IGCSE, and involve skills at AS/A2 and above. We are modelling at a more basic level using IGCSE knowledge.

Modelling packages Shell centre materials developed by University of Nottingham - graphs and functions http://www.mathshell.com/scp/lfg50.htm - this deals with modelling problems through graphs. The materials were written about 15 years ago but have received very good reviews. Priced at £25 with a teacher’s guide and photocopiable masters this covers a range of topics.

Books There are IGCSE modelling type questions in many of the current texts where students have to use algebra to model real life situations. The IGCSE text by Rayner (Mathematics for IGCSE: Extended Mathematics for IGCSE, 2005, Oxford University Press, ISBN: 0199149941) has some specific problems that can be used – look at the Investigations/practical problems and puzzles section at the back of the text. ! ! ! !

Number 29 stopping distances – adapt to graph Number 2 - Hiring a car – graphing problem Number 3 - Running a business Number 4 – How many of each?

Contexts The following topic areas are good contexts for modelling – but relevant data will need to be sourced and the modelling task set up by the teacher. Financial modelling !

Compound interest and simple interest, graphing and using formulae to represent the growth ! Household finance – electricity/ gas bills, could model two different company rates – linear relations ! Mobile phone tariffs – use company data, graph prices + find the rule ! Depreciation of car prices for different makes of cars

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Travel costs Hire charges – cars, equipments etc Hire purchase – To buy? or to rent? – exploring graphical models and contrasting the two

Speed distance time !

World record times – try the 1 mile record using data over the past 50 years – is there a model that fits it – could apply this to any record in sport - would be good because the model has limitations ! http://www.tsm-resources.com/xls/Data/Sports.xls !

Astronomical data – planetary distances from the sun, times for orbits, diameters of planets. Kepler’s 3rd law etc

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Falling objects – Newton’s laws and kinematics

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Braking distances for different speeds/weather conditions

Scientific/geographical modelling ! ! ! ! ! ! .

Modelling the greenhouse effect – increase in temperature over time Carbon footprints over time Population growth of people/ animals/ bacteria etc Carbon dating Cooling against time http://www.galileo.org/math/investigations/markov.html - this is a good practical introduction to the Markov process