Réciproques et fonctions affines pour les 302
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3e/Geometrie/Reciproques/B3_scratch.pdf
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3e/Geometrie/Reciproques/B3_scratch.pdf
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3e/Geometrie/Reciproques/B3_scratch.tex
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3e/Geometrie/Reciproques/B3_scratch.tex
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\title{Réciproque du théorème de Pythagore avec Scratch}
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\tribe{Troisième}
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\date{Avril 2018}
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\pagestyle{empty}
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\geometry{left=10mm,right=10mm,top=10mm,bottom=10mm}
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\setscratch{print=true}
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\begin{document}
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On a écrit un programme avec Scratch qui dit quand un triangle est rectangle ou non.
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\begin{minipage}{0.5\textwidth}
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\begin{scratch}
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\blockinit{Quand \greenflag est cliqué}
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\blocksensing{demander \txtbox{Longueur de l'hypothénuse?} et attendre}
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\blockvariable{mettre \selectmenu{IK} à \ovalsensing{réponse}}
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\blocksensing{demander \txtbox{Longueur d'un petit côté?} et attendre}
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\blockvariable{mettre \selectmenu{IJ} à \ovalsensing{réponse}}
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\blocksensing{demander \txtbox{Longueur du dernier côté?} et attendre}
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\blockvariable{mettre \selectmenu{JK} à \ovalsensing{réponse}}
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\blockvariable{mettre \selectmenu{$IK^2$} à \ovaloperator{\ovalvariable{IK} * \ovalvariable{IK}}}
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\blockvariable{mettre \selectmenu{$IJ^2$} à \ovaloperator{\ovalvariable{IJ} * \ovalvariable{IJ}}}
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\blockvariable{mettre \selectmenu{$JK^2$} à \ovaloperator{\ovalvariable{JK} * \ovalvariable{JK}}}
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\blockvariable{mettre \selectmenu{$JK^2+IJ^2$} à \ovaloperator{\ovalvariable{$JK^2$} + \ovalvariable{$IJ^2$}}}
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\blockifelse{Si \ovaloperator{\ovalvariable{$IK^2$} = \ovalvariable{$JK^2+IJ^2$}} alors}%
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{
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\blocklook{dire \txtbox{Le triangle est rectangle}}
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}
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{
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\blocklook{dire \txtbox{Le triangle n'est pas rectangle}}
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}
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\end{scratch}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\includegraphics[scale=0.9]{./fig/triangleIJK}
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\begin{scratch}
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\blockinit{Quand \greenflag est cliqué}
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\blocksensing{demander \txtbox{Longueur de l'hypothénuse?} et attendre}
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\blockvariable{mettre \selectmenu{IK} à \ovalsensing{réponse}}
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\blocksensing{demander \txtbox{Longueur d'un petit côté?} et attendre}
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\blockvariable{mettre \selectmenu{IJ} à \ovalsensing{réponse}}
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\blocksensing{demander \txtbox{Longueur du dernier côté?} et attendre}
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\blockvariable{mettre \selectmenu{JK} à \ovalsensing{réponse}}
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\blockifelse{Si \ovaloperator{
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\ovaloperator{\ovalvariable{IK} * \ovalvariable{IK}}
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=
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\ovaloperator{
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\ovaloperator{\ovalvariable{IJ} * \ovalvariable{IJ}}
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+
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\ovaloperator{\ovalvariable{JK} * \ovalvariable{JK}}
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}
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} alors}%
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{
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\blocklook{dire \txtbox{Le triangle est rectangle}}
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}
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{
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\blocklook{dire \txtbox{Le triangle n'est pas rectangle}}
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}
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\end{scratch}
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\end{minipage}
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\vfill
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On a écrit un programme avec Scratch qui dit quand un triangle est rectangle ou non.
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\begin{minipage}{0.5\textwidth}
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\begin{scratch}
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\blockinit{Quand \greenflag est cliqué}
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\blocksensing{demander \txtbox{Longueur de l'hypothénuse?} et attendre}
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\blockvariable{mettre \selectmenu{IK} à \ovalsensing{réponse}}
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\blocksensing{demander \txtbox{Longueur d'un petit côté?} et attendre}
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\blockvariable{mettre \selectmenu{IJ} à \ovalsensing{réponse}}
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\blocksensing{demander \txtbox{Longueur du dernier côté?} et attendre}
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\blockvariable{mettre \selectmenu{JK} à \ovalsensing{réponse}}
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\blockvariable{mettre \selectmenu{$IK^2$} à \ovaloperator{\ovalvariable{IK} * \ovalvariable{IK}}}
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\blockvariable{mettre \selectmenu{$IJ^2$} à \ovaloperator{\ovalvariable{IJ} * \ovalvariable{IJ}}}
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\blockvariable{mettre \selectmenu{$JK^2$} à \ovaloperator{\ovalvariable{JK} * \ovalvariable{JK}}}
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\blockvariable{mettre \selectmenu{$JK^2+IJ^2$} à \ovaloperator{\ovalvariable{$JK^2$} + \ovalvariable{$IJ^2$}}}
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\blockifelse{Si \ovaloperator{\ovalvariable{$IK^2$} = \ovalvariable{$JK^2+IJ^2$}} alors}%
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{
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\blocklook{dire \txtbox{Le triangle est rectangle}}
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}
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{
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\blocklook{dire \txtbox{Le triangle n'est pas rectangle}}
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}
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\end{scratch}
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\end{minipage}
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\begin{minipage}{0.5\textwidth}
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\includegraphics[scale=0.9]{./fig/triangleIJK}
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\begin{scratch}
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\blockinit{Quand \greenflag est cliqué}
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\blocksensing{demander \txtbox{Longueur de l'hypothénuse?} et attendre}
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\blockvariable{mettre \selectmenu{IK} à \ovalsensing{réponse}}
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\blocksensing{demander \txtbox{Longueur d'un petit côté?} et attendre}
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\blockvariable{mettre \selectmenu{IJ} à \ovalsensing{réponse}}
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\blocksensing{demander \txtbox{Longueur du dernier côté?} et attendre}
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\blockvariable{mettre \selectmenu{JK} à \ovalsensing{réponse}}
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\blockifelse{Si \ovaloperator{
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\ovaloperator{\ovalvariable{IK} * \ovalvariable{IK}}
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=
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\ovaloperator{
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\ovaloperator{\ovalvariable{IJ} * \ovalvariable{IJ}}
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+
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\ovaloperator{\ovalvariable{JK} * \ovalvariable{JK}}
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}
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} alors}%
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{
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\blocklook{dire \txtbox{Le triangle est rectangle}}
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}
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{
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\blocklook{dire \txtbox{Le triangle n'est pas rectangle}}
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}
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\end{scratch}
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\end{minipage}
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\vfill
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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3e/Geometrie/Reciproques/fig/triangleIJK.pdf
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After Width: | Height: | Size: 4.2 KiB |
@ -2,7 +2,7 @@ Réciproques en géométrie avec les 3e pour l'année 2017-2018
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###########################################################
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:date: 2018-03-13
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:modified: 2018-03-13
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:modified: 2018-04-10
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:tags: Geometrie, Thales, Pythagore
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:category: 3e
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:authors: Bertrand Benjamin
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@ -56,6 +56,8 @@ Exercices techniques pour vérifier qu'un triangle est rectangle.
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Programmer Scratch pour qu'il nous dise si un triangle est rectangle ou non.
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Cahier de bord: On colle `les propositions <./B3_scratch.pdf>`_ qui sont sorties
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Étape 4
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-------
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@ -65,9 +67,11 @@ On peut espérer une première forme comme ceci:
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Tableau de proportionnalité -> parallèles et alignés
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On leur demande de trouver (et de tracer) un contre exemple où on a le tableau de proportionnalité mais pas les droites parallèles et pas les points alignés.
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On leur donne un tableau de proportionnalité et on leur demande de tracer une situation où les longueurs sont respectées mais où au moins une des conclusions est fausse. C'est l'occasion de parler de contre-exemple.
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On en conclut qu'il faut les points alignés. Puis on écrit la réciproque.
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On débat sur ce que l'on veut laisser dans les conclusions et ce que l'on doit passer dans les hypothèses pour arriver à la version finale de la réciproque.
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Cahier de bord: La réciproque du théorème de Thalès et le contre exemple trouvé.
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Étape 5
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-------
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BIN
3e/Gestion_donnees/Fonctions_affines/Duree_exo.pdf
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3e/Gestion_donnees/Fonctions_affines/Duree_exo.pdf
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50
3e/Gestion_donnees/Fonctions_affines/Duree_exo.tex
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3e/Gestion_donnees/Fonctions_affines/Duree_exo.tex
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\documentclass[a4paper,12pt]{article}
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\usepackage{myXsim}
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\title{Exercices sur la durée}
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\tribe{Troisième}
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\date{Avril 2018}
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\pagestyle{empty}
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\begin{document}
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\begin{exercise}[subtitle={Un peu de géométrie? \Mod \Cal}]
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On veut comparer l'aire des deux figures ci-dessous en faisant varierla valeur de $x$.
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\hspace{-1cm}
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\includegraphics[scale=0.7]{./fig/rect_trapeze}
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\begin{enumerate}
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\item Quelle figure à la plus grande surface quand $x$ vaut 4?
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\item Quelle figure à la plus grande surface quand $x$ vaut 1?
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\item Pour chaque figure, proposer une fonction permettant de tranformer x en l'aire.
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\item Proposer à l'aide du tableur, une façon de savoir à partir de quel valeur de $x$ la première figure a une plus grande aire que la deuxième.
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\end{enumerate}
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\end{exercise}
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\begin{exercise}[subtitle={Salaires \Mod \Rai}]
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Jean, Faïza et Bob fabriquent tous les 3 des jouets mais ne sont pas payé de la même façons.
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\begin{itemize}
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\item Jean a un salaire fixe de 1500\euro par mois.
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\item Faïza a un salaire de 1000\euro augmenté d'une prime de 4\euro par jouet qu'il a frabriqué.
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\item Bob a un salaire de 500\euro mais a une prime de 7\euro par jouet.
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\end{itemize}
|
||||
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Qui est le mieux payé des 3?
|
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\end{exercise}
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After Width: | Height: | Size: 22 KiB |
@ -11,14 +11,34 @@ Situations linéaires et affines avec les 3e pour l'année 2017-2018
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Étape 1
|
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-------
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|
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Étape 2
|
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-------
|
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Travail autour de 3 `forfaits téléphonique <./E1_abonnement.pdf>`_. Il sera à faire au départ seul puis en groupe pour saisir les nuances des 3 forfaits. La question 2 pourra être fait après un premier bilan de plénière.
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Les questions, 1 et 3, seront à rédiger rédiger dans le cahier de groupe.
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Cahier de bord: à partir des phrases construites dans la question 3, on découvrira un nouveau type de fonction: les fonctions affines.
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Étape 2 (TICE)
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--------------
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On répond à la question 4. L'outil adapté pour cette question est le tableur, on laisse les élèves choisir la méthode de leur choix pour y répondre. Si l'idée de sort pas, on leur propose de calculer les prix des forfaits entre 0 textos envoyés et 500 textos et ensuite de tracer les graphiques.
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Cahier de bord: Le tableau avec les formules étirables et les graphiques. On analyse comment reconnaitre le graphique d'une fonction affine.
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`Problèmes sur la durée <./Duree_exo.pdf>`_
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Étape 3
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-------
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On commence à entrer dans des situations plus abstraites où l'on étudie des fonctions sans liens avec une situation.
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Travail pour reconnaître les fonctions sous différentes formes (non modélisée, formule, tableau et graphique).
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Cahier de bord: Lire le coefficient directeur pour une 'fonction linéaire', retrouver l'ordonnée à l'origine et la coefficient directeur d'une fonction affine.
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Étape 4
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-------
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Représenter les formules de fonctions à partir d'un tableau, d'un graphique.
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Loading…
Reference in New Issue
Block a user