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0000000..edaf821 --- /dev/null +++ b/Clg_Mouthe/4e/Calcul_litteral/Modelisation/E1_pgm_calc.tex @@ -0,0 +1,48 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +\author{} +\date{Novembre 2018} +\title{Programme de calculs} +\tribe{Quatrième} + +\pagestyle{empty} + +\begin{document} + +\begin{exercise}[subtitle={Programme n°1}] +Voici le programme de calcul n°1. On peut l’appliquer à n'importe quel nombre. + +\begin{itemize} + \item Triple + \item Ajoute 4 + \item Double + \item Retire 4 +\end{itemize} + +Appliquer le programme n°1 aux nombres 5, – 5 et 2/3. +\end{exercise} + +\begin{exercise}[subtitle={Programme n°2}] + Voici le programme de calcul n°2. On peut l’appliquer à n'importe quel nombre. + + \begin{itemize} + \item Prends l’opposé du double + \item Ajoute 3 + \item Multiplie par 5 + \item Retire 2 + \end{itemize} + + Appliquer le programme n°2 aux nombres 4, – 4 et 5/2. +\end{exercise} + +\printexercise{exercise}{1} +\printexercise{exercise}{2} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/Clg_Mouthe/4e/Calcul_litteral/Modelisation/E4_carre_mystere.pdf b/Clg_Mouthe/4e/Calcul_litteral/Modelisation/E4_carre_mystere.pdf new file mode 100644 index 0000000000000000000000000000000000000000..abf7380bef5353100688e6afcc0db753a9601d10 GIT binary patch literal 37431 zcma(2Q;aT7(Dn=8gEgKtwr$(CZQHi(nKia;+qP}n_RRjjU-pyinG`t4IicgPkXJ`q<%?(8-ZDMQYY>v-B&%lBI|65RWq88T9 zCXV=YqSgk^Cc-90cE%=9yu46O&Wy z*3nc3mkio9XEN;AXxwgX#K4VExotN2>^Rd^%S*L-WV2hTI+-{a00nDXIY!E>PO#U$ z&YvW`#vq@VXEYHel{M^5irOL>4k%31of1u89L5qAg!x(I>;K;8~P9S 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l'allure. + + Pour savoir combien il lui faut de mosaïques pour un carré mystérieux, il utilise la formule : $c \times 8 - 16$ où $c$ désigne le nombre de mosaïques sur un côté. + + Peut-il aussi utiliser les formules suivantes ? + + \begin{itemize} + \item Formule 1 : $(c \times 4 - 4) + (c \times 4 - 12)$ + \item Formule 2 : $c \times 4 + (c - 2) \times 4 - 8$ + \item Formule 3 : $c \times 4 + (c - 4) \times 4$ + \item Formule 4 : $(c - 4) \times 8 + 16 $ + \item Formule 5 : $(c - 2) \times 2 \times 4 $ + \item Formule 6 : $c + c + (c - 4) \times 2 + c + c + (c - 4) \times 2$ + \end{itemize} +\end{exercise} + +\printexercise{exercise}{1} + + + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: diff --git a/Clg_Mouthe/4e/Calcul_litteral/Modelisation/index.rst b/Clg_Mouthe/4e/Calcul_litteral/Modelisation/index.rst new file mode 100644 index 0000000..13e8351 --- /dev/null +++ b/Clg_Mouthe/4e/Calcul_litteral/Modelisation/index.rst @@ -0,0 +1,52 @@ +Modélisation et calcul littéral avec les 4e de Mouthe 2018 +########################################################## + +:date: 2018-11-07 +:modified: 2018-11-07 +:tags: Calcul littéral, Modélisation +:category: 4e +:authors: Bertrand Benjamin +:summary: Utilisation du calcul littéral pour calculer du "n'importe quel" avec les 4e de Mouthe en 2018. + + +Étape 1: Programme de calculs +============================= + +Rapide tour des `programmes de calculs <./E1_pgm_calc.pdf>`_. + +On insistera sur la façon d'écrire les calculs avec une attention particulière au signe = ! + +Pour les élèves qui avancent bien, on leurs posera une question où ils devront renverser le programme ou tâtonner. + +Cahier de bord: Un exemple de rédaction de l'exécution d'un programme de calculs. + +Étape 2: Carré de Pierre +======================== + +`Exercice du carré de pierres <./carre_pierres.pdf>`_ pour redécouvrir l'utilité de la lettre et découvrir les premières manipulations littérales. + +Les élèves vont pouvoir commencer par reproduire d'autres carrés de pierres pour compter le nombre de mosaïques. On se posera la question du sens de "n'importe quel carré de pierre". + +Le but c'est qu'à la fin les élèves construise des formules/programme de calculs pour dénombrer le nombre de mosaïques. Les élèves pourront venir au tableau pour expliquer à la classe leur formule. + +Cahier de bord: les formules et les explications qui les démontrent. On dira que toutes ces formules sont égales. + +Étape 3: Carré de Pierre double côté +==================================== + +Cette fois ci, des formules sont proposées il faut trouver lesquelles calculent le nombre de mosaïques pour faire `un carré de pierres à double côté <./E3_carre_pierres_choix_formule.pdf>`_ + +On attend 3 méthodes: +- Un dessin qui explique la validité de la formule +- Un calcul pour relier 2 formules +- Un calcul qui démontre qu'un formule ne calcule pas la bonne chose. + +Cahier de bord: Un résumé de ce qui a été trouvé. + +Étape 4: Carré de Pierre inconnu +================================ + +`Le type de carré de pierre est inconnu <./E4_carre_mystere.pdf>`_ mais on connait une formule qui permet de calculer le nombre de mosaïques nécessaires pour le construire. Il faut trouver les autres formules qui le permettent aussi. + +Cahier de bord: Les techniques trouvées pour transformer les expressions. +