Pupils use simulation to test hypotheses and experiment with random variation in the context of the controversial issue of speed cameras.
Do speed cameras reduce road casualties - or not? Even the experts do not agree, partly because the random nature of accidents makes it difficult to draw conclusions; this can lead to accidental - or deliberate - misrepresentations. Pupils use the context of media reporting to explore ideas of randomness and probability, to bring them alive and understand them and so help pupils draw conclusions from data. The Case Study uses video and newspaper resources to motivate discussion among pupils, combined with spreadsheets to model the reality of the random occurrence of accidents over a year. Pupils interpret and extrapolate from data and use data to support arguments they develop on speed cameras - and to examine the arguments of others.
Pupils realise that lower probabilities do not invariably lead to fewer accidents, and that the occurrence of more accidents in one year is not necessarily evidence of a higher probability. The Case Study helps them learn that random variation can obscure underlying probabilities; they develop a 'feel' for randomness and an ability to evaluate data critically.
Explore perceptions of randomness and relate this to the perceived effectiveness of speed cameras. Simulate the effects of different sitings of cameras.
Specific Key Stage 3 National Curriculum areas covered include:
- Key processes - represent and analyse a situation from the real world, with an emphasis on interpreting and analysing the data generated, reflecting on its meaning and communicating the results.
- Number and algebra - use rational numbers, their properties and different representations; use and apply ratio and proportion; accuracy and rounding.
- Statistics - apply the handling data cycle; use measures of central tendency and frequency; experimental and theoretical probabilities.
- Curriculum opportunities - thinking and reasoning; links to problems from other subjects; working collaboratively; group discussion and communicating mathematical reasoning.
Organisation and pedagogy
The Case Study supports four hour-long lessons of classroom activity, but could be extended, given the flexibility of the lesson plans. Where appropriate, homework tasks are suggested to reinforce the work done in the classroom. A mixture of whole class and small group work is involved. The context is 'real' and relates to the adult world and so may be less engaging for younger pupils. The mathematical demand can easily be extended for able post-16 students.
This Case Study contains a collection of lesson plans, handouts and other resources mainly presented as inter-linked MS Office documents.
- Lesson Plans
It is strongly recommended that teachers first look at the Overview and lesson plans onscreen rather than printing them on paper. Both documents contain a wealth of supporting resources, video recording, spreadsheet simulations, worksheets, teacher guidance and background information that can be accessed directly.
(including hardware & software)
Most lessons require a computer and data projector (or interactive whiteboard) with soundcard and speakers. The Case Study can be used on PC or Mac.
- Microsoft Word and Excel 2000 or later are required. For correct operation of the Excel spreadsheets, macros must be enabled. If the Excel macro security level (Tools/Macro/Security) is set to High it will need to be changed to Medium and Excel re-launched.
- QuickTime is needed to play the video: see http://www.apple.com/quicktime/.
- Some of the documents link to external websites with background information, so an internet connection is useful but not essential .