A newly born rabbit is
capable of reproducing at one month old (when it matures). Suppose the
rabbit never dies, and it continues reproducing one new rabbit every month.
So, when the rabbit is born, it has one member in its own family. After a
month, it matures, and by the second month it adds a new born member to its
family. In the third month, the rabbit produces another offspring; its
first child also matures and will be ready to have an offspring in the next
The sequence named by Fibonacci (1,1,2,3,5,8,13,21,...)
can describe the number of members in the rabbit's family at each month.
How does the number of rabbits
produced in a certain month relate to the number of rabbits produced in the
months prior to that?
Solve/Investigate the Problem
Continue the diagram started in
the problem to include the 4th, 5th and 6th
month. Look for a pattern.
of the Problem
I set up the diagram that was
included in the explanation of the problem. I extended the pattern to include
the number and types of rabbits found in months 4, 5 and 6. In month 4 there were 3 mature
rabbits and 2 newborn rabbits for a total of 5 rabbits. In month 5 there
were 5 mature rabbits and 3 newborn rabbits for a total of 8 rabbits. In month 6 there were 8 mature
rabbits and 5 newborns for a total 13 rabbits. Each month the total number of
rabbits will be equal to the total number of rabbits in the month before in
addition to the number of rabbits the month prior to that. This pattern is
that of the Fibonacci Sequence.
Extensions of the Problem
In the Extension portion of
this problem I compared the ratios of consecutive numbers in the sequence
as suggested: 1/1, ½,
2/3, 3/4, etc… After the
24th term number I noticed that the ratio became a continuous
This ratio is known as the Golden Ratio.
Author & Contact
Insert name and contact information.
Link(s) to resources, references, lesson plans, and/or other
This page discusses real-world
applications associated with the Fibonacci numbers and golden section.
This worksheet from Mathematics Teaching
in the Middle School leads students to discover the golden ratio by making
various measurements and calculations.
Important Note: You should compose your write-up
targeting an audience in mind rather than just the instructor for the
You are creating a page to publish it on the web.