1. Begin by discussing the Fibonacci sequence, using a simple example like the number of petals on flowers. Introduce the idea of using the Fibonacci sequence to calculate rabbit breeding trends. Fibonacci made the following assumptions when he came up with his mathematical pattern:

• Begin with one male and one female rabbit. Rabbits can mate at the age of one month, so by the end of the second month, each female can produce another pair of rabbits.
• The rabbits never die.
• The female produces one male and one female every month.

2. Work with the class to see if students can develop the sequence themselves. Remind them that they're counting pairs of rabbits, not individuals. Work as a class through the first few months of the problem by referring to Figure 1: Fibonacci and Rabbit Breeding

• Begin with one pair of new born rabbits. (1)
• At the end of the first month, still only one pair exists. (1)
• At the end of the second month, the female has produced a second pair, so two pairs exist. (2)
• At the end of the third month, the original female has produced another pair, and now three pairs exist. (3)
• At the end of the fourth month, the original female has produced yet another pair, and the female born two months earlier has produced her first pair, making a total of five pairs. (5)

3. Write the pattern that has emerged on the board: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...

Discuss the sequence: Help students understand that to get the next number in the sequence, you add the previous two numbers. As a class, continue the sequence for the next few numbers.

4. Using Excel or graph paper, get students to graph the Fibonacci sequence. Use this graph as a way of introducing types of graphical curves. How many rabbits will there be after two years (24 months)?

5. Have students develop a 'rule' for the Fibonacci sequence in relation to the rabbit breeding example, making up their own symbols for the 'rule'.

Is the sequence a realistic way of calculating rabbit numbers over a period of time? Make a list of all the errors in Fibonacci's assumptions in relation to what would actually occur in nature.

Research rabbit control methods. Discuss reasons why these methods became ineffective over time and why it is necessary to use a combination of methods for effective eradication.

Investigate why rabbits have so successfully adapted to the Australian environment compared to other countries. This should include demonstrating your understanding of the different types of adaptations - behavioural, structural and physiological.

Use the 'Finding Fibonacci Patterns in Nature' activity (Learning in the Garden activity booklet on the LandLearning CD) to investigate Fibonacci numbers in the school grounds

Visit www.tallpoppies.net.au/education/pdf/sci_heroes_p46_51.pdf for a number of rabbit-related activities

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