Mathematical Modelling: How Risky is Life?

ACMSP228; ACMSP252; ACMSP253; ACMNA208; ACMNA210; ACMSP283; ACMSP226;
This unit How Risky is Life? is one of 5 units making up the Special Topic “Mathematical Modelling”.
This 'descriptive modelling' unit introduces concepts of statistical modelling, with a focus on the interpretation of data and evaluation of the inferences drawn from it. Throughout the unit the goal is to develop students' ability to work and think independently, and to develop an informed scepticism about dramatic claims on risk.
 
Students consider risk in everyday life and investigate the relative probability of various causes of death - unnatural and natural - including terrorism, disease and accidents of various kinds. They consider how factors such as age affect the data, and discuss the usefulness of the model to predict a particular person’s future.
 
For classes who have not recently done Unit 1 Introduction to Modelling, a single ‘quick start’ lesson is provided.
 
Read the Teachers’ Guide (included in the download package) before using this resource.

 

Lesson 1: Perceptions of Risk

Students consider how statistical representations (such as a description of a typical Australian) can be considered as mathematical models of reality. They begin to build other such models through discussion of dangers that worry them, and they analyse risk as a combination of probability of occurrence and hazard (the seriousness of the event). They then focus on potentially fatal hazards, and rank the causes of unexpected death, estimating numbers of Australians who will die in a year from each cause. They express the number of people in various ways in proportion to the population.

Lesson 2: Sudden Death - The Data

Students are given the official numbers of people who died in 2015 from selected ‘unnatural’ causes. They compare them with their perceptions, going on to calculate the risk of dying from these causes in various ways numerically and represent them visually. It emerges that unexpected deaths are very unlikely in Australia.

Lesson 3: The Bigger Picture

This lesson focuses on the ‘base’ probability of dying in a year, the total risk of death broken down only by age and gender. This is dominated by illness-related deaths, which are strongly age-dependent. The overall picture is built up from further data on various causes of death in various age bands. Students read and interpret graphs and tables, and express risk in multiple ways (probability, proportion, percent). They use data to evaluate statements.

Lesson 4: Phoney Figures?

This lesson first relates the analysis from previous lessons to the modelling process and diagram. Students then move on to a series of exercises in critiquing the interpretation and evaluation of data, done mainly in think-pair-share groups. The aim is to practise looking at data sensibly, seeing the story presented in a direct reading of the data but then looking through it make more sophisticated interpretations.

Lesson 5: How Risky for Me?

This lesson explores variation and prediction. Students use a computer simulation to explore the random variation that may be expected in the data, getting a feel for whether reported changes (e.g. in number of drownings) are significant, or likely to have happened by chance. The unit closes by reflecting on the extent to which overall probabilities apply to individuals. Finally, students summarise their mathematical understanding of risk on a poster.

 

Last updated November 9 2018.