Fibonacci+Numbers

=Fibonacci Numbers = = Due by February 24 = //__Directions:__ Follow the following steps. You will add your responses under the //red text // and we will add comments, thoughts or suggestions under the //blue text //. //

1) How does this sequence of numbers continue? Add at least three numbers to the pattern and explain how you got your answer.

0, 1, 1, 2, 3, 5, 8, 13, 21,

The next numbers in the Sequence are: 34,55,89

Explanation By adding two previous numbers, I got the next number. It did not take long because I have heard of the Fibonacci sequence before. I thought through this by thinking about the relationship of a number to the numbers preceding it.

Thoughts, Comments and / or Suggestions from Mrs. Fazzino and Mr. Luthultz :

Andy- Did it take you long to figure this out? Under the explanation section above, can you explain to me how you thought through figuring out this pattern?

This sequence is called the Fibonacci Sequence. The term that mathematicians use for the type of rule followed to obtain the numbers in the sequence is called an //algorithm//. This series of numbers developed by Leonardo Fibonacci as a means of solving a practical problem: In 1202, Fibonacci wanted to determine the rate at which pairs of rabbits would reproduce in ideal circumstances, so.....


 * 2) Let's look at Fibonacci's Rabbits [[image:801793.jpg width="510" height="227" align="right"]] **

__The Problem:__ Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">The puzzle that Fibonacci posed was...

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">How many pairs will there be in one year?

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">Explain your answer in words or using a graphic created in Kerpoof or Comic Life.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">If you choose to use a graphic, post your work on this page. Directions for posting work on the wiki, can be found by clicking here. Since you are posting your graphic on the wiki, please either make your own drawings or use [|http: schools.clipart.com] for images.

<span style="color: #ff0000; font-family: 'Comic Sans MS',cursive; font-size: 110%;">Your answer and explanation: 144 pairs of rabbits, because I know after the first month the pair of rabbits doesn't make any new offspring until after the third month. After two months though, the total number of pairs is 2 pairs. However, at the third month, the parents give birth to 1 new pair of rabbits. The first born pair has no offspring until the 5th month. The total number of pairs is now 2 pairs. At the fourth month, the parents have one pair that month. The total number of pairs is now 3. Then at the fifth month, the parents have a new pair of babies and the first born pair also have a pair of babies. This keeps on going and every pair older than two months will have a pair of babies. It followed the Fibonacci pattern, so I can summarize below: 1st month---> 1 pair 2nd month---> 1 pair 3rd month> 2 pairs (1 pair of parents, 1 pair of babies) 4th month-> 3 pairs (1 pair of parents, 2 pairs of babies) 5th month-> 5 pairs (2 pairs of parents, 3 pairs of babies) 6th month-> 8 pairs (3 pairs of parents, 5 pairs of babies) 7th month-> 13 pairs (5 pairs of parents, 8 pairs of babies) 8th month> 21 pairs (8 pairs of parents, 13 pairs of babies) 9th month---> 34 pairs (13 pairs of parents, 21 pairs of babies) 10th month--> 55 pairs (21 pairs of parents, 34 pairs of babies) 11th month-> 89 pairs (34 pairs of parents, 55 pairs of babies) 12th month---> 144 pairs (55 pairs of parents, 89 pairs of babies)

<span style="color: #0000ff; font-family: 'Comic Sans MS',cursive; font-size: 110%;">Thoughts, Comments and / or Suggestions from Mrs. Fazzino and Mr. Luthultz :

<span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 110%;">3) Click [|here] to read more about Fibonacci's Rabbits and see the graphic they created to describe the answer to Fibonacci's problem. Please stop reading at the yellow bar on the website. <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">

<span style="color: #800080; font-family: 'Comic Sans MS',cursive; font-size: 110%;">4) Post a response to the questions under the Discussion Tab above.