# How risky is life?

Pupils explore the risk of dying unexpectedly from various causes. Using realistic data, they calculate risks and how they vary with time.

# Overview

Pupils start from fears and risks they know about and, by comparing them with real- life data, recognise that the fears are often unfounded and that their perceptions of the risks tend to be driven by presentations in the media. Pupils work with real data; they deduce information about small probabilities and use measures of average and spread in real life. Pupils calculate the risks involved for various activities and how these are related to the base risk of death for typical people of different ages and genders. The emphasis is on order-of-magnitude comparisons, reflecting the variations in risk between individuals and over time. Pupils learn that mathematical thinking is essential to put risks in perspective, which can affect how people live, and that the media usually focus on stories rather than on information.

The Case Study deals with potentially sensitive issues and, although the materials were well-received during trials, teachers may wish to consult with colleagues in PSHE before starting.

# Mathematical content

Compare perceptions of the causes of death with actual statistics. Interpret very large and very small probabilities. Decide what these say about behaviour and attitudes. Explore random variation.

Specific Key Stage 3 National Curriculum areas covered include:

• Key processes - represent a situation from the real world, analyse it using mathematical procedures; interpret and evaluate the evidence and communicate and reflect on the results.
• Number and algebra - use rational numbers, their properties and their different representations; use and apply ratio and proportion; accuracy and rounding.
• Statistics - apply the handling data cycle; use appropriate orders of magnitude; use measures of central tendency and spread; experimental and theoretical probabilities.
• Curriculum opportunities - use open and closed tasks in a variety of contexts; explore random variation and statistical inference from data; interpret very large and very small numbers; use a range of representations, including tables and graphs of data, probabilities and distributions.

# Organisation and pedagogy

The Case Study supports five to six hour-long lessons of classroom activity, interspersed with modest amounts of homework, organised into four stages. A mixture of class, group and individual work is involved. Stage 4 requires computers - the rest of the study is paper-based.

It is most suitable for pupils in Years 8 or 9. Stage 4 is more challenging mathematically than the first three, but is designed to be valuable in different ways to pupils at different levels.

# Resources provided

This Case Study contains a collection of printable and ICT resources comprising:

• Teacher's Guide (PDF): read this first for a more complete overview and detailed lesson plans.
• Pupil handouts (PDF): copy masters for all handouts and worksheets.
• Base risk of death by age: "slides" for Stage 3.
• Simulating Random Variations software (only needed for Stage 4).
• Software installers which offer alternative ways for getting the software onto pupils' machines.

# Resource requirements (including hardware & software)

• The Teacher's Guide looks best when printed double-sided, in colour, and bound into a booklet or ring-binder.
• Some of the handouts are best copied onto stiff paper and cut up into cards.
• If no data projector/interactive whiteboard is available then an overhead projector may be useful.
• Stage 4 requires a computer with data projector/interactive whiteboard and, optionally, one computer for each pair or small group of pupils, running the supplied software.
• The software is compatible with Windows PCs or Apple Mac.
• To run the software online or in a web browser requires Flash Player 8 or later (available from www.adobe.com). Internet Explorer may warn about "Blocked Content" when running the browser-based version of the software from disc. Users must choose to allow this. Installing the stand-alone PC version avoids these issues.