Media :
- Statement of the famous problem of rabbits Fibon accident
- a biography of the mathematician
Material:
drawings rabbit s couples (adults and babies) to paste on feui Islands
worked Skills:
- understanding u n statement;
- solve problems problems using logical reasoning;
- monitor and iscuter relevance or likelihood of a solution;
- argue to prop bones of the validity of a solution;
- concept of double;
- read No large mber.
Statement:
The Tuscan mathematician Fibonacci, said iff Leonardo of Pisa, in 1202 poses the "problem of the rabbits'
a couple of rabbits, born on 1 st January, gives na wth another pair of rabbits every month, when he reached the age of two months. The new coupled 're following the same law of reproduction.
How will he rabbits on 1 st January of next year, assuming no torque has disappeared in the meantime? .
There A 1 the number of couples at the beginning (that is to say that A 1 = 1) and A n the number of neck ples of rabbits during the nth month.
Give 1 ° A 2, A 3, A 4, 5 and A
2 in. Explain urquoi for n ≥ 3, A n = A n-1 = A n-2 .
3 Calculate s A 6, 7 A, A 8 ... 13 A . Reply to Fibonacci problem.
Spark 1st Hachette Education
course we can present only the first part of el'énoncé!
For my part I decided to give them to read the entire en ounce, so that students envision that are other ways Res owder problems they discover " later."
Immediately after first reading it does me one said: "We do not understand anything. "" Really nothing? "I told them. I have therefore ls admitted able to understand the beginning. It took a few clarifying words vocabulary: couple, reproduction and clarify the "Assuming that N o couple has disappeared in the meantime" that fai t here the difference between "real life" and the "world of mathematical s' (same for the regularity of the supposed a reproduction).
procedure :
- reading and exchanges to understand the statement
- representation by pasting on sheets the c ouple rabbits in January (rabbits), on a separate sheet for FE February (Still too young to breed), then look what happens in March and represent (the first pair has grown up and has given rise to e 2 new bunnies) ... Rate whenever clearly e number of pairs of rabbits and
He quickly became born necessary to take stock on how to count the rabbits, some students unhesitatingly counting the same rabbits shown in different months. My students have chosen to put their s birthmarks color for recognize (you can name them ...) This also allows for precautionary e check over the work that some rabbits are not forgotten a month on the other (no one dies)
- when the representation map e begun to become laborious it is time to bring students to discover that the s numbers pairs found are those of the Fibonacci example by making them read the biography the m athématicien
Although évidemme nt can not be expected of students in primary school they find themselves uls operation of the suite.
- we verify that it "really works" in seeking another month or two then you problem using the Rmin following
Find in this article the magazine "Entertainment & Education" in a desc OCCE riptif very complete the first session. Thank you to Marie-France 
Attempted explanation
Why is the number of couples (and rabbits for that matter) it follows the Fibonacci sequence?
can try to explain to students (with the help of the support of the posters): every month there are the rabbits of the previous month + children. These children are as numerous as rabbits having at least two months, the number of rabbits present two months ago.
Number of rabbits from month n = number of rabbits from month n-1 + number of rabbits from month n-2
Extension possible:
Using the small program concocted by my son (who gave me an excellent idea of treating this problem with my students, thank you ;-) Florian) we can seek to students after how many months it exceeds one million rabbits then 1 billion. As spaces are not marked in the program is an ideal location to work on reading large numbers and realize the great value of space the various classes. The program with a presentation austere, Florian has also scheduled a nice wallpaper on the subject of rabbits to brighten up the computer at work.
This situation will be presented by my students in the 6 th Science Forum [1] organized by Maison des Sciences de Chatenay-Malabry 30 and 31 May.
[1] The Science Forum is an event that takes place every year for 6 years at the end of the school year on the town of Chatenay-Malabry. It is organized by the association "La Maison des Sciences" in partnership with the Academic Achievement of Chatenay-Malabry, Ecole Centrale de Paris, the Graduate School of Optics, the school inspectorate in the Hauts-de-Seine the town of Chatenay-Malabry, CNRS, the Hands-On, Andra, Paris Observatory in Meudon. Throughout the school year classes in the district are invited to work in science with "The House of Science" (place with a teacher and scientific equipment) and / or students from colleges that enliven science workshops in schools. Then these classes present their work at the forum of science for a day and a half in the form of one or more experiences offered to visitors. Visitors are students from other classes, teachers, students and parents. 3 years, some classes are also mathematical activities.
