Home/Curriculum resources/Mathematics of bushfire/Activity 1 - The geometry of fire

Subject:

Mathematics

Year level:

Level 9

Suggested timing:

30-minute discussion on concepts, theory and example problems. Two 30-minute sessions to work on assigned problems in handout.

Required resources:

Handout

# Activity 1 - The geometry of fire

This activity is a part of the Mathematics of bushfire resource.

*Burnt Banksia Plant. Blue Mountains, Dharug country. Photographer: Andrew Merry. Source: Getty Images. Used under licence.Â *

### In this activity, students will explore the concept of an ellipse, focusing on its characteristics and formula for area, which will be applied to understand the geometry of wind-driven fires. They'll relate wind speed to length-to-breadth ratios, draw fire shapes based on wind conditions, and estimate the areas of large fires using scientific notation, enhancing their understanding of fire behaviour.

**Required resources**

**Suggested**** supporting resources**

### Step by step guide

Students are introduced to the concept ofâ€¯an ellipse as a generalisation of a circle. The concept of length-to-breadth ratio is introduced along with semi-major and semi-minor axes and the formula for area.Â

The ellipse is linked to the basic shape of a wind-driven fire (usingâ€¯land asâ€¯examples) and the basic anatomy of a fire is introduced (head fire, flanks, etc). In particular, students consider the head fire as the fastest moving part of a fire.Â

Introduce the relationship between length-to-breadth ratio and wind speed via graphical handout and get students to assign wind speeds to various elliptical shapes and vice versa.Â

Get students to draw various fire shapes based on information about wind speed and direction (using Cartesian plane/compass points).Â

Estimate areas of very large fires, expressing answers using scientific notation.Â

## Related activities within this resources:

## Activity 2 - Fire behaviour (Part one)

In this two-part activity, students will delve into the concept of head fire rate of spread and explore the factors affecting it, such as wind, temperature, humidity, and topographic slope.

Suggested timing:

40 minute discussion on concepts and theory. One 40 minute session to work on problem set 1 and one 40 minute session to work on problem set 2 in handout.Â

Required resources:

Handout

## Activity 3 - Fire behaviour (Part two)Â

In this two-part activity, students will explore concepts like flame angle, flame height, and fire intensity, delving into the factors influencing them, such as fuel load.

Suggested timing:

40 minute discussion on concepts, theory and examples. One 40-minute session to work on problem set in handout. 15 minutes class discussion on the two inquiry questions listed below after watching the video.

Required resources:

Handout, Laptop/tablet, Projector

## Activity 4 - Fire and climate

In this activity, students delve into fire danger ratings, examine the forest fire danger index, analyse historical fire weather changes, interpret data, and make informed decisions, deepening their comprehension of the fire-climate connection.

Suggested timing:

40 minute discussion on concepts, theory and examples. One 30 minute session to work on problem set 1, and one 40 minute session to work on problem set 2 in handout. Problem set 2 can involve broader class discussion and students working in groups.â€¯

Required resources:

Handout, Laptop/tablet and internet connection