Intermath | Workshop Support

Write-up


Title
Multiplying Rabbits

Problem Statement
A newborn rabbit is capable of reproducing at maturity which is one month old.  If the rabbit never dies and continues reproducing each month is there a sequence that describes the number of members in the rabbit’s family.

 

Problem setup

Explain how the Fibonacci sequence (1,1,2,3,5,8,13,21,...) describes the number of members in the rabbit's family at each month.

Plans to Solve/Investigate the Problem

The problem page provided a graph depicting the rabbit’s birth month and subsequent birth of additional family members.  The initial step included continuing the graph on paper and using an excel spreadsheet to compare the number of family members to the Fibonacci sequence.

 

Investigation/Exploration of the Problem

 

The following example is a graph completed by hand on the reproduction of the rabbit’s family.  The graph completed by hand was also reproduced in excel which follows.  N = new rabbit, M=mature rabbit

 

Months             Fibonacci               Rabbits

0                                          1                         1N

1                                          1                         1M           

2                                          2                         1M-IN

3                                          3                         1M-1N, 1M

4                                          5                         1M-1N, 1M, 1M-1N

5                                          8                         1M-1N, 1M, 1M-1N, 1M-1N, 1M

 

 

Term

Fibonacci

Ratio

1

1

 

2

1

1

3

2

0.5

4

3

0.666667

5

5

0.6

6

8

0.625

7

13

0.615385

8

21

0.619048

9

34

0.617647

10

55

0.618182

11

89

0.617978

12

144

0.618056

13

233

0.618026

14

377

0.618037

15

610

0.618033

16

987

0.618034

17

1597

0.618034

18

2584

0.618034

19

4181

0.618034

 

 

 

 

Extensions of the Problem

When the problem was extended to 100 using excel, rounding or truncated errors appeared at number 55. 

 

53

53316291173

0.618034

54

86267571272

0.618034

55

1.39584E+11

0.618034

 

Author & Contact
Susan R. Kelly


Link(s) to resources, references, lesson plans, and/or other materials

Golden Exploration Worksheet -
This worksheet from Mathematics Teaching in the Middle School leads students to discover the golden ratio by making various measurements and calculations.
[ web page ]
http://www.nctm.org/mtms/1999/01/worksheets.htm

 

U Important Note: You should compose your write-up targeting an audience in mind rather than just the instructor for the course.

                                   You are creating a page to publish it on the web.

 

 

writeup.htm Failed! Click Here To Go Back!writeup_temp.htm Failed! Click Here To Go Back!