It Stands to Reason
In this regular feature, an element of the mathematics curriculum is chosen and we collate for you some teaching ideas and resources that we think will help your pupils develop their reasoning skills. If you’d like to suggest a future topic, please do so to firstname.lastname@example.org or @NCETMsecondary.
When a relatively small football club is scheduled to play one of the giants of the game, for instance when little Crawley Town played Manchester United in the FA Cup a few years back, we are provided with just the situation to create a bit of cognitive conflict for some of the pupils we teach. What would your pupils say about this statement: is it true or false or can we not be sure?
This statement comes from the resource Evaluating Probability Statements, which comprises ten statements that pupils are asked to consider. Other statements are linked to the lottery, situations with dice, coin throwing and other familiar situations – ripe for misconception! – associated with classical probability. To introduce pupils to the idea of sampling, the problem Counting Fish gives a real life context. The teachers’ notes suggest a way of simulating the situation using cubes to support pupils develop their understanding.
You may have already looked at Placing Numbers from the NCETM microsite What Makes A Good Resource.
The relatively simple activity of placing products of pairs of numbers on a grid may not immediately suggest a probability resource, however, the task can be extended to consider the sample space of outcomes to inform the placing of the products – a more complex task altogether!
Pupils may be familiar with buying lottery tickets in the UK. This is a rich source of mathematics, particularly with the support of the Lottery Simulator from NRICH. The Number Tumbler allows you to pick up to 6 numbers from up to 49 numbers and simulate up to 1000 draws which should allow you to build up to the actual UK lottery draw scenario (picking 6 from 49) but start as small scale as you like. You may like to explore the Key Stage 2 problem Winning the Lottery for further ideas for Year 7 and 8 pupils.
Further resources include:
- The NRICH article Probability Through Problems: a new approach to teaching probability
- Some real-life contexts are outlined in Conditional Probability Is Important for All Students!
- your pupils could use their knowledge to solve this mystery
- The Probability Computer Games include some Flash resources to use in the classroom. Working through these resources introduces the idea of tree diagrams in a logical sequence.
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