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'The Car That Passes' printed from http://nrich.maths.org/
Why do this problem?
is very appropriate when starting off the topic of probability, as is In the Playground
. They both give the opportunity for pupils to make their own decisions and discover some important issues in this area of mathematics. This investigation will need to take place over a
period of several days.
This really needs to be presented as part of a class discussion. Pose the question, adapting it appropriately to suit your setting. Pupils will need to listen to each other's ideas and decide on what action needs to be taken. A 'brainstorming' session may be the result with learners suggesting surveying the traffic, focusing on, for example:
The car's colour
Who is driving the car
The direction the car is traveling in
The number of passengers in the car etc. etc.
The pupils will probably need a few days to gather their information, perhaps in pairs or small groups, and then time to analyse it. They will then need to be given the chance to come up with their statements. Look out for children who use vocabulary associated with probability appropriately (such as 'very likely', 'likely', 'certain' etc.) and justify their statements using the data they
have gathered. This work would make a fantastic wall display.
Ask the class how they will know if their statements are true. The only way is to test them at the specified time! Children can then reflect on their work. This reflection time is just as important as the previous stages and you can pose several questions, such as:
- Was the car as we expected?
- Can we explain why some of the statements turned out to be true and some false?
- What might have happened if we had collected data just for one day? Why?
- What might have happened if w'?d collected data for longer? Why?
What things are you going to do to find out information?
Will you decide beforehand what you particularly want to look at when gathering information?
(After the event) What can you now say about the data you collected and what you have seen just now?
Ideas for further investigation may well come from the pupils when the event is over and you've had a chance to discuss the appropriateness of the data collected.
Some pupils may need support in gathering their information in a practical sense. This task is not intended to 'test' particular recording or presentation methods, rather it is intended to focus on the process of data collection and interpretation as a whole.
You can read about some of the issues which might arise when teaching probability in this article.