# BOWLAND

# MATHS

# Mathematics Assessment Resource Service

# How Risky
is Life?

# A Mathematics Case Study

## 1. Overview

This case study tackles something that affects people’s lives, liberties and happiness – the mismatch between real and perceived risk.

Pupils explore the risks of dying unexpectedly from various causes. They start from the fears they know and, by comparing them with real-life data, they recognise that these are often unfounded. Pupils learn how to 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 various kinds of variation in risk level between individuals and over time.

## 2. Mathematical content

Key Stage 3 National Curriculum areas covered include:

- Key Processes - Pupils are expected to represent a situation from the real world, analyse it using mathematical procedures, interpret and evaluate the evidence and communicate and reflect on their results
- Number and Algebra - Using rational numbers, their properties and their different representations; Using and applying ratio and proportion; accuracy and rounding
- Statistics - Applying the handling data cycle; Using measures of central tendency and spread; experimental and theoretical probabilities
- In addition, pupils are offered opportunities to: interpret very large and very small numbers; to use appropriate orders of magnitude; to use a range of representations, including tables and graphs of data, probabilities and distributions; to explore random variation and statistical inference from data.

## 3. Organisation and pedagogy

This case study supports 5-6 one-hour lessons of classroom activity, interspersed with modest amounts of homework, organised into 4 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.

## 4. Resources

This document provides the structure for the entire case study.

- 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
- O1: Base Risk of death by age: Slides for stage 3
- Software for PC and Mac: The Simulating Random Variations software is only needed for stage 4 - it can be run directly from this page
- Software installers: More details and options for getting the software onto pupils' machines
  Please double-check that the software works on pupils' machines in good time for the lesson

The Teacher's Guide looks best when printed double-sided, in colour, and bound into a booklet or ringbinder - but this is not compulsory. Some of the Handouts are best copied onto stiff paper and cut up into cards.

Running the software directly from this page requires Flash Player 8 or newer (see the software installers page for alternatives). PC users will need Adobe Reader to open the PDF files. Both can be downloaded from www.adobe.com.

© Bowland Charitable Trust 2008
Written by the Shell Centre for Mathematical Education at the University of Nottingham