The Rabbit Problem

This is a representation of the classic Fibonacci problem of reproducing rabbits. The problem of how many pairs of rabbits you will have after 1 year if you start with 1 pair and they each take 1 month to mature and produce 1 other pair each month afterwards is illustrated through a calendar. The paper engineering is creative, and the narrative is told through a series of “problems” that the ever-increasing population experiences each month. A small sign keeps the reader updated as to how many pairs are now living in Fibonacci’s Field. The extras, like The Ration Book and The Newspaper, contain great launch items for statistics discussions.

1.

Prior to reading, present the rabbit problem. (It is on the inside cover.)

If a pair of baby rabbits are put into a field, how many pairs will there be: a) at the end of each month, and b) at the end of one year? Criteria: Rabbits are fully grown at 1 month and have another pair of bunnies at 2 months. Each pair is comprised of 1 male and 1 female, and no rabbits die or leave the field. 

This is the classic rabbit problem Fibonacci used to generate the sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

2.

Ask students to work together in pairs and estimate the number of pairs they will have at the end of one year.

3.

You could further set the context for the book by having students explore the sequence and see if they can discover a rule for generating the next number (each number is the sum of the previous two numbers), or you could discuss some biographical or mathematical ideas related to Fibonacci the mathematician.

4.

After a first reading, quickly flip through a second time, demonstrating how the pairs of rabbits are illustrated as unorganised sets. Ask students to work together to create an illustration of how the population has expanded over one year. Their diagram needs to be organised so that the set for each month is easily found. Try not to give too many directions about this assignment, as it will be a valuable assessment opportunity to see how students think about organising a pattern.

• What do they know about using a tree diagram or a flow chart?
• Do they see it as a “branching” scheme, a layering scheme, or a more linear scheme?
• There are many ways to create a schematic representation, and encouraging creative responses to this may provide you with surprises.

       a) The

5.

Ask students to present their diagrams to each other and locate the common elements and the differences between them. Generate some agreed-upon criteria for representing sequential patterns:

• What makes for a clear and easily understood diagram?

6.

As a follow-up, you may want to explore the sequence as it is found in nature or as the spiral generated by a series of squares working out from a centre.