Feat: import de la séquence sur Pythagore
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4e/03_Pythagore/B1_Puzzle_Pythagore.pdf
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65
4e/03_Pythagore/index.rst
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4e/03_Pythagore/index.rst
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|
|||||||
|
Découverte du théorème de Pythagore avec les 4e de Mouthe
|
||||||
|
#########################################################
|
||||||
|
|
||||||
|
:date: 2021-09-21
|
||||||
|
:modified: 2021-09-21
|
||||||
|
:tags: Geométrie, Pythagore
|
||||||
|
:category: 4e
|
||||||
|
:authors: Bertrand Benjamin
|
||||||
|
:summary: Découverte du théorème Pythagore, du carré et de la racine carré.
|
||||||
|
|
||||||
|
|
||||||
|
Étape 1: Mesure de l'hypoténuse
|
||||||
|
===============================
|
||||||
|
|
||||||
|
On dessine 3 triangles rectangles avec 2 longueurs à chaque fois et on demande de calculer la longueur du 3e côté (l'hypoténuse). Au début, la seule méthode possible est de tracer et mesurer. Il faudra s'assurer qu'il y est au moins un triangle qui ne puisse pas être tracé sur le cahier (trop grand ou trop petit). On discutera ensuite la limite cette méthode: l'imprécision.
|
||||||
|
|
||||||
|
Quelques valeurs de triplets de Pythagore primitifs (`source <http://villemin.gerard.free.fr/Wwwgvmm/Addition/TripProp.htm>`_):
|
||||||
|
|
||||||
|
::
|
||||||
|
|
||||||
|
a, b, c
|
||||||
|
3, 4, 5
|
||||||
|
5, 12, 13
|
||||||
|
8, 15, 17
|
||||||
|
7, 24, 25
|
||||||
|
20, 21, 29
|
||||||
|
12, 35, 37
|
||||||
|
9, 40, 41
|
||||||
|
28, 45, 53
|
||||||
|
11, 60, 61
|
||||||
|
16, 63, 65
|
||||||
|
33, 56, 65
|
||||||
|
48, 55, 73
|
||||||
|
13, 84, 85
|
||||||
|
36, 77, 85
|
||||||
|
39, 80, 89
|
||||||
|
65, 72, 97
|
||||||
|
20, 99, 101
|
||||||
|
60, 91, 109
|
||||||
|
|
||||||
|
Étape 2: Animation pour induites le théorème
|
||||||
|
============================================
|
||||||
|
|
||||||
|
On présente l'animation `puzzle <./puzzle.ggb>`_ (ou sous `la version mepc <./puzzle_bis.ggb>`_) en leur expliquant que ce découpage a permis aux mathématiciens de **calculer** la longueur manquante.
|
||||||
|
|
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|
On leur demande d'exploiter cette découverte pour calculer la longueur pour le triangle 5-12. Après un travail de groupe, si l'idée n'a pas émergée, on peut faire un croquis pour y calculer l'aire des carrés.
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Cahier de bord: une note sur l'écriture a*a qui peut être réécrite avec un carré.
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Étape 3: Pratique du proto-théorème
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===================================
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Réutilisation de ce qui a été fait l'étape 2 sur 3 exemples (sans utilisation de la racine carré). Chaque groupe produit un début de rédaction afin de garder une trace pour le cahier de bord.
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Cahier de bord: On colle de `puzzle deplié <./B1_Puzzle_Pythagore.pdf>`_, on écrit l'égalité des aires.
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Étape 4: cette égalité des aires est-elle vraie pour tous les triangles?
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========================================================================
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On pose cette question aux élèves. Ils doivent y répondre en illustrant. Cette étape va permettre de continuer à habituer les élèves à ces calculs d'aires.
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Cahier de bord: On écrit que ce n'est le cas que pour les triangles rectangles.
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4e/03_Pythagore/puzzle.ggb
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4e/03_Pythagore/puzzle.ggb
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4e/03_Pythagore/puzzle_bis.ggb
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4e/03_Pythagore/puzzle_bis.ggb
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Reference in New Issue
Block a user