Mathematical modelling: Playing with fire
View Sequence overviewMathematical models help us make informed decisions by providing useful estimates and predictions. There are also practical factors that influence our decisions and must be considered alongside the mathematics.
Whole class
Playing with fire PowerPoint
Playing with fire Spreadsheet (Teacher)
Each group
Playing with fire Spreadsheet (Student)
Access to computers, at least 1 between 3 students
Lesson
Teacher note: While written as a single lesson, this activity could be delivered over two sessions. In the first, students determine when towns should evacuate; in the second, they present their findings to the class.
Explain to students that in this lesson they will take on the role of emergency services experts responsible for deciding when to evacuate. In the scenarios provided, bushfires start 20 km away from the towns. Students must determine when an evacuation should be announced (how long after the fire starts). Emphasise that the townspeople are reluctant to leave their homes and will only evacuate when they feel there is no other option, so immediate evacuation is not possible.
To make their decision, students need to draw on the rules of thumb and/or the mathematical equations they have learned throughout the sequence.
Each group will present their findings to the class, and in their presentation, they must justify both the methods they used (rules of thumb and/or equations) and the timing of their evacuation decision. Their reasoning should reflect an understanding of fire behaviour and the impact of environmental conditions on the rate of spread.
Show students slides 34-35 of Playing with Fire PowerPoint which presents the two town scenarios:
- Town 1: On flat ground surrounded by dry eucalypt forest.
- Town 2: On top of a hill surrounded by dry eucalypt forest.
Allow students to work in their groups to determine when each town should evacuate. Students should also have access to the Playing with fire Spreadsheet (Student) if they believe it will be useful.
As they work, prompt students to consider additional factors that could influence their decision, such as:
- The uncertainty in estimating the rate of spread, due to the complex and often unpredictable nature of fire behaviour.
- The time needed for a safe evacuation, including possible delays, traffic congestion, and the importance of issuing early warnings.
Remind students that leaving immediately is not an option because the townspeople are reluctant to abandon their homes until they feel they have no other choice.
Encourage students to weigh these factors alongside their calculations to make well-reasoned, realistic recommendations.
Invite each group to present their decision on how long after a fire starts should an evacuation be announced. Ask them to justify their decisions using their calculations and reasoning.
As a class, compare the different solutions and discuss the justifications each group provided. Highlight the similarities and differences in their approaches and explore how uncertainty and safety considerations influenced their decisions.
Conduct a final discussion to evaluate whether the rules of thumb and the equations offer adequate and sensible solutions for determining when a town should evacuate. Consider the contexts in which rules of thumb may be appropriately applied and those where the use of equations would be more important.