From 63794f761c0218e677a53be0740f090d39fa07fc Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 8 Nov 2018 20:03:48 +0100 Subject: [PATCH] =?UTF-8?q?Feat(4e):=20D=C3=A9but=20du=20chapitre=20sur=20?= =?UTF-8?q?Pythagore?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Clg_Mouthe/4e/Geometrie/Pythagore/index.rst | 61 ++++++++++++++++++ Clg_Mouthe/4e/Geometrie/Pythagore/puzzle.ggb | Bin 0 -> 7487 bytes .../4e/Geometrie/Pythagore/puzzle_bis.ggb | Bin 0 -> 6494 bytes 3 files changed, 61 insertions(+) create mode 100644 Clg_Mouthe/4e/Geometrie/Pythagore/index.rst create mode 100644 Clg_Mouthe/4e/Geometrie/Pythagore/puzzle.ggb create mode 100644 Clg_Mouthe/4e/Geometrie/Pythagore/puzzle_bis.ggb diff --git a/Clg_Mouthe/4e/Geometrie/Pythagore/index.rst b/Clg_Mouthe/4e/Geometrie/Pythagore/index.rst new file mode 100644 index 0000000..2425a93 --- /dev/null +++ b/Clg_Mouthe/4e/Geometrie/Pythagore/index.rst @@ -0,0 +1,61 @@ +Découverte du théorème de Pythagore avec les 4e de Mouthe +######################################################### + +:date: 2018-11-08 +:modified: 2018-11-08 +:tags: Geométrie, Pythagore +:category: 4e +:authors: Bertrand Benjamin +:summary: Découverte du théorème Pythagore, du carré et de la racine carré avec les 4e de Mouthe. + + +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 `_): + +:: + + 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. + +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. + +Cahier de bord: une note sur l'écriture axa 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. + +Étape 4: Technique et intro de la racine carré +============================================== + +On donne un triangle qui a besoin de la racine carré pour être calculé. Par tâtonnement les élèves essaient d'approcher une valeur. 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