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\end{enumerate}
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\end{enumerate}
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\end{multicols}
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\end{multicols}
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\end{exercise}
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\end{exercise}
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\begin{exercise}[subtitle={Techniques}, step={4}, origin={Les maths ensemble et pour chacun 4e}, topics={ Multiplication nombre relatif }, tags={ }]
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Faire les calculs suivants
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\begin{multicols}{3}
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\begin{enumerate}[label=(\alph*)]
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\item $7 + (-6) =$
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\item $7 - (-6) =$
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\item $7 \times (-6) =$
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\item $(-5) + (-5) =$
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\item $(-5) - (-5) =$
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\item $(-5) \times (-5) =$
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\item $(-2) + (-4) + (-3)=$
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\item $(-2) - (-4) - (-3)=$
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\item $(-2) \times (-4) \times (-3) =$
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\end{enumerate}
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\end{multicols}
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\end{exercise}
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65
4e/03_Pythagore/index.rst
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4e/03_Pythagore/index.rst
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|||||||
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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.
|
||||||
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Quelques valeurs de triplets de Pythagore primitifs (`source <http://villemin.gerard.free.fr/Wwwgvmm/Addition/TripProp.htm>`_):
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::
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a, b, c
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3, 4, 5
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5, 12, 13
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8, 15, 17
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7, 24, 25
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20, 21, 29
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12, 35, 37
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9, 40, 41
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28, 45, 53
|
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11, 60, 61
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16, 63, 65
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33, 56, 65
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48, 55, 73
|
||||||
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13, 84, 85
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36, 77, 85
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39, 80, 89
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65, 72, 97
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||||||
|
20, 99, 101
|
||||||
|
60, 91, 109
|
||||||
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|
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|
Étape 2: Animation pour induites le théorème
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|
============================================
|
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|
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.
|
||||||
|
|
||||||
|
Étape 3: Pratique du proto-théorème
|
||||||
|
===================================
|
||||||
|
|
||||||
|
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.
|
||||||
|
|
||||||
|
Cahier de bord: On colle de `puzzle deplié <./B1_Puzzle_Pythagore.pdf>`_, on écrit l'égalité des aires.
|
||||||
|
|
||||||
|
Étape 4: cette égalité des aires est-elle vraie pour tous les triangles?
|
||||||
|
========================================================================
|
||||||
|
|
||||||
|
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.
|
||||||
|
|
||||||
|
Cahier de bord: On écrit que ce n'est le cas que pour les triangles rectangles.
|
||||||
|
|
||||||
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|
||||||
|
|
||||||
BIN
4e/03_Pythagore/puzzle.ggb
Normal file
BIN
4e/03_Pythagore/puzzle.ggb
Normal file
Binary file not shown.
BIN
4e/03_Pythagore/puzzle_bis.ggb
Normal file
BIN
4e/03_Pythagore/puzzle_bis.ggb
Normal file
Binary file not shown.
Loading…
Reference in New Issue
Block a user