Duration and Setting 30 minutes & 1.5 hours (approximately 2 lessons).

Summary
This activity enables students to understand the Fibonacci sequence and how it occurs in nature by relating it to rabbit breeding trends.

Student outcomes
Students will be able to:

• Learn about the Fibonacci Sequence and how this relates to rabbit breeding
• Research the impact of the introduction of European rabbits to Australia.

Background notes for teachers
Rabbits were first brought into Australia by the First Fleet, however they did not successfully become established until 1859 when Victorian grazier Thomas Austin imported 24 rabbits from England and released them on his farm with the belief that "the introduction of a few rabbits could do little harm and might provide a touch of home, in addition to a spot of hunting" 2.

Within a decade of the rabbit release, their numbers had multiplied so much that millions could be eradicated each year without having any noticeable effect on the population. Rabbits held the record for the fastest spreading mammal anywhere in the world and their impact on Victorian agriculture is estimated (in 1998) to be $360 million 1.

Fibonacci, an Italian mathematician investigated how fast rabbits could breed under ideal circumstances. This activity is a way of demonstrating the Fibonacci sequence to students while also showing them how, in a short period of time, rabbit populations under certain conditions can increase to explosive proportions. This can lead to discussions with students about the devastating impacts rabbits have on Australia's environment.

In 1202 Fibonacci recognised mathematical patterns in nature and developed the Fibonacci sequence. A Fibonacci number sequence is a sequence where the subsequent number is the sum of the two preceding numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. For example 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3. In nature, these values often show up in the form of numbers of seeds, petals, segments or spirals. For instance, pinecones usually have 8 spirals going around in one direction and 13 in the other.

1 The State Barrier Fence of Western Australia (2001), Department of Agriculture Western Australia website
2 Rabbits and their Impact (1999), Tim Bloomfield, Department of Primary Industries, Attwood

Materials

• Calculator
• Pen and paper
• Graph paper or Microsoft Excel

next» Fibonacci and Rabbit Breeding - Part 2