import work from year 2016-2017
This commit is contained in:
Benjamin Bertrand
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3e/Geometrie/Aire_perim/TC_carrelage.pdf
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3e/Geometrie/Aire_perim/TC_carrelage.pdf
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3e/Geometrie/Aire_perim/TC_carrelage.tex
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3e/Geometrie/Aire_perim/TC_carrelage.tex
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\documentclass[a5paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
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% Title Page
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\titre{Aire et périmètre- Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Mai 2017}
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\pagestyle{empty}
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\newcommand{\lexo}{%
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\setcounter{exo}{0}
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\begin{Exo}[Carrelage]
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Voici le plan de l'appartement des parents de Chloé.
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\vfill
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\hspace{-1.5cm}
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\includegraphics[scale=0.7]{./fig/plan_maison}
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\vfill
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Les parents de Chloé souhaitent changer le carrelage du sol de sa chambre. Ils doivent acheter de la colle pour carrelage. Voici les indications marquées sur un seau de colle:
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\vfill
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\begin{center}
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\Ovalbox{%
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\begin{minipage}{0.7\textwidth}
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\begin{itemize}
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\item \textbf{Destination} Sol - intérieur / extérieur.
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\item \textbf{Surface couverte} $5m^2$
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\item \textbf{Couleur} Gris
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\item \textbf{Contenance} 20kg
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\end{itemize}
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\end{minipage}
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}
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\end{center}
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\vfill
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Quel est le nombre minimum de seaux de colle, les parents doivent acheter pour poser le carrrelage dans la chambre de Choé?
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\vfill
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\end{Exo}
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}
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\begin{document}
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\lexo
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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/Aire_perim/TC_carrelage_a4.pdf
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3e/Geometrie/Aire_perim/TC_carrelage_a4.pdf
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3e/Geometrie/Aire_perim/fig/plan_maison.pdf
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3e/Geometrie/Aire_perim/fig/plan_maison.pdf
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3e/Geometrie/Aire_perim/fig/plan_maison.svg
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3e/Geometrie/Aire_perim/fig/plan_maison.svg
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19
3e/Geometrie/Aire_perim/index.rst
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Notes autour des grandeurs (périmètre, aire) d'une figure puur les 3e pro
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#########################################################################
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:date: 2017-04-18
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:modified: 2017-04-18
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:tags: Géométrie, Périmètre, Aire
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:category: 3e
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:authors: Bertrand Benjamin
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:summary: Révision (?) des grandeurs mesurables d'une figure pour les 3e prépa pro.
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Étape 1
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=======
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Sans formule, on s'approprie la notion d'aire et de périmètre.
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`Aire et périmètre d'un polygone <./perim_aire_polyognes.pdf>`_
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Le travail sur le calcul du périmètre force les élèves à réutiliser le théorème de Pythagore.
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BIN
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id="flowPara7263">Quelle est le périmètre et l'aire des polygones ci-dessous ?</flowPara></flowRoot></g></g></svg>
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After Width: | Height: | Size: 18 KiB |
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3e/Geometrie/Reciproques/index.rst
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|
||||
Notes autour des réciproques des théorèmes de géométries pour les 3e
|
||||
####################################################################
|
||||
|
||||
:date: 2017-03-21
|
||||
:modified: 2017-04-18
|
||||
:tags: Géométrie, Pythagore, Thalès
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Découverte des réciproques des théorèmes de géométrie pour les 3e.
|
||||
|
||||
|
||||
On aurait pu faire ça en prenant le temps comme il est expliqué en dessous mais par manque de temps, on se contentera de la méthode bourrin!
|
||||
|
||||
Méthode bourin
|
||||
==============
|
||||
|
||||
Cette méthode pourrait rappeler ce qu'on fait en enseignement explicite.
|
||||
|
||||
Étape 1
|
||||
-------
|
||||
|
||||
Après avoir un peu parlé du sens du mot réciproque, on montre à travers un exemple comment on démontre que 2 droites sont parallèles.
|
||||
|
||||
Ils s'exercent sur des exemples simples.
|
||||
|
||||
Étape 2
|
||||
-------
|
||||
|
||||
Des exercices type brevet.
|
||||
|
||||
|
||||
Méthode douce(?)
|
||||
================
|
||||
|
||||
Les 2 réciproques peuvent se faire de façon indépendante.
|
||||
|
||||
Étape 1 (Pythagore)
|
||||
-------------------
|
||||
|
||||
Activité Géogébra pour remarquer que le triangle est rectangle uniquement quand on a l'égalité des aires.
|
||||
|
||||
Cahier de bord: Le théorème de Pythagore peut être utilisé pour démontrer que 2 droites sont perpendiculaires.
|
||||
|
||||
Étape 2 (Thalès)
|
||||
----------------
|
||||
|
||||
Comment déterminer que 2 triangles sont semblables (un agrandissement l'un de l'autre)?
|
||||
|
||||
Est-il possible de les placer d'une certaine façon pour que les 2 côtés soient parallèles? Et sans que les triangles se superposent?
|
||||
|
||||
Cahier de bord: Le théorème de Thalès peut être utilisé pour démontrer que 2 droites sont parallèles.
|
||||
|
||||
Étape 3 (exercices sur la durée)
|
||||
--------------------------------
|
||||
|
||||
Exercices type brevet.
|
||||
|
||||
Étape 4 (tache complexe)
|
||||
------------------------
|
||||
|
||||
|
||||
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41
3e/Geometrie/Reperage_espace/index.rst
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3e/Geometrie/Reperage_espace/index.rst
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|
||||
Notes autour du chapitre sur les coordonnées dans l'espace pour les 3e
|
||||
######################################################################
|
||||
|
||||
:date: 2016-10-05
|
||||
:modified: 2016-10-05
|
||||
:tags: Probabilités
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Notes sur le chapitre autour du repérage dans l'espace pour les 3e pour l'année 2015/2016
|
||||
|
||||
Étape 1
|
||||
-------
|
||||
|
||||
`Découverte <./E1_decouverte_reperage.pdf>`_ de la notion de coordonnées dans l'espace.
|
||||
|
||||
On se met d'accord que pour aller d'un sommet (rappelle du vocabulaire vu avec les prismes) on doit passer par les arrêtes. Et on constate qu'il y a pleins de chemin différents et qu'on peut en choisir un plus "sympathique" que les autres ce qui donne naissance aux coordonnées.
|
||||
|
||||
|
||||
Étape 2
|
||||
-------
|
||||
|
||||
`Approfondissement <./E2_entrainement_coord.pdf>`_ de la notion en cherchant plus systématiquement les coordonnées des points et en plaçant des points.
|
||||
|
||||
Cahier de bord: On colle la première fiche et on donne la définition du repère et des coordonnées des points.
|
||||
|
||||
Étape 3
|
||||
-------
|
||||
|
||||
`Renforcement <./E3_coordonnees_complexes.pdf>`_ de la notion. Le travail est plus technique.
|
||||
|
||||
Ètape 3(bis)
|
||||
------------
|
||||
|
||||
Pour varier la forme des énoncés de ce chapitre, on peut reprendre l'`exercice de Sésamath <./exo_sesamath.pdf>`_ qui propose un point de vu légèrement différent.
|
||||
|
||||
Étape 4
|
||||
-------
|
||||
|
||||
`Complexification <./E4_coordonnees_complexes_suite.pdf>`_ des exercices avec des fractions et des points géométriques particuliers à trouver.
|
||||
|
||||
|
||||
BIN
3e/Geometrie/Thales_agrandissement/TC_tipi.pdf
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51
3e/Geometrie/Thales_agrandissement/TC_tipi.tex
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|
||||
\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
|
||||
|
||||
% Title Page
|
||||
\titre{Thalès et agrandissement - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Troisième}
|
||||
\date{Avril 2017}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
|
||||
\newcommand{\lexo}{%
|
||||
\setcounter{exo}{0}
|
||||
\begin{Exo}[Tipi]
|
||||
L’habitation traditionnelle des Indiens des plaines d’Amérique du Nord est le tipi.
|
||||
|
||||
Un tipi est constitué de longues tiges de bois appuyées les unes aux autres, d’une enveloppe extérieure faite de peaux d’animaux et d’une porte toujours orientée vers l’Est.
|
||||
|
||||
Chaque perche en bois mesure 21 pieds et dépasse de 3 pieds. Le rayon du cercle tracé au sol mesure 7,5 pieds.
|
||||
|
||||
Le grand chef indien veut coiffer le cercle formé par le haut des perches de son tipi d’un chapeau de plumes.
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Quel doit être le diamètre de son chapeau?
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\titre{Thalès et agrandissement - Exercices}
|
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% \seconde \premiereS \PSTMG \TSTMG
|
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\classe{Troisième}
|
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\date{Novembre 2016}
|
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\newcommand{\ombreChinoise}{%
|
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|
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Pour sa pièce de théâtre, le metteur en scène a besoin d'un grand arbre de 4m de haut en ombre chinoise. Pour cela, il possède une miniature de cet arbre mesurant 55cm qu'il va éclairé avec une lampe. Cet arbre miniature est fixé à 5m de la toile.
|
||||
|
||||
Explique au metteur en scène ou il doit mettre la lampe pour que l'ombre du sapin ait la bonne taille.
|
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\end{Exo}
|
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}
|
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\newcommand{\tourPise}{%
|
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\begin{Exo}
|
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Inspiré par l'expérience de Thalès, Tom en voyage à Pise veut mesurer la tour penchée grâce à son ombre. Il se renseigne et apprend qu'elle est penchée de $4,19^o$ comme sur le dessin suivant:
|
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|
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\hspace{-1cm}
|
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\begin{minipage}{0.3\textwidth}
|
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\includegraphics[scale=0.3]{./fig/ombre_pise}
|
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\end{minipage}
|
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|
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Une fois le bâton installé, il mesure les distances suivantes:
|
||||
\begin{itemize}
|
||||
\item Diamètre de la tour: 15.5m.
|
||||
\item Taille du baton 1,5m.
|
||||
\item Taille de l'ombre du baton: 2m
|
||||
\item Taille de l'ombre de la tour: 66,95m
|
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\end{itemize}
|
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\end{minipage}
|
||||
|
||||
\begin{enumerate}
|
||||
\item Comment doit-il placer son bâton pour pouvoir appliquer le théorème de Thalès? Dessiner le baton sur le dessin.
|
||||
|
||||
\item Reporter les mesures sur le dessin.
|
||||
\item Calculer la hauteur de la tour de Pise.
|
||||
\end{enumerate}
|
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\end{Exo}
|
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|
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}
|
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\tourPise
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33
3e/Geometrie/Thales_agrandissement/index.rst
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33
3e/Geometrie/Thales_agrandissement/index.rst
Normal file
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|
||||
Notes autour du chapitre sur Thalès et l'agrandissement pour les 3e
|
||||
###################################################################
|
||||
|
||||
:date: 2016-08-11
|
||||
:modified: 2016-08-11
|
||||
:tags: Geometrie, Thales, Agrandissement
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Notes sur le chapitre sur l'agrandissement et le théorème de Thalès pour les 3e
|
||||
|
||||
Séance 1
|
||||
--------
|
||||
|
||||
Activité de découpage du `puzzle <./puzzle.pdf>`_.
|
||||
|
||||
On ramasse les productions et on fait une photocopie des différents agrandissements. Trace écrite sur l'agrandissement et la proportion des longueurs.
|
||||
|
||||
Séance 2
|
||||
--------
|
||||
|
||||
Situations des "Thalès" (sans le nommer) pour calculer une longueur du triangle et présentation de deux situations pathologiques (non alignement et non parallélisme) pour mettre en lumière les hypothèses du théorème de Thalès (`decouverte de thales <./decouverte_de_thales.pdf>`_)
|
||||
|
||||
Cours théorème de Thalès.
|
||||
|
||||
Séance 3
|
||||
--------
|
||||
|
||||
Exercices techniques sur Thalès (à écrire au tableau). Possibilité de faire avec l'égalité des rapports
|
||||
|
||||
Problème autour de Thalès dans la durée (Un en lien avec l'éclipse de soleil du 1septembre 2016?)
|
||||
|
||||
|
||||
|
||||
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34
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|
||||
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|
||||
\classe{Troisième}
|
||||
\date{Septembre 2016}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{Exo}
|
||||
La figure ci-dessous est un puzzle de 5 pièces inscrite dans dans un carré de côté 16cm. Reproduire le puzzle de sorte qu'il soit inscrit dans un carré dont le côté est une des valeurs suivantes:
|
||||
|
||||
\begin{center}
|
||||
\hfill 18 cm \hfill 17cm \hfill 12cm \hfill 10cm
|
||||
\end{center}
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||||
\vfill
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|
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\begin{center}
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\includegraphics[scale=1]{./fig/puzzle}
|
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\end{center}
|
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|
||||
\vfill
|
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|
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|
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|
||||
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%%% End:
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La figure ci-dessous est un puzzle de 3 pièces inscrite dans dans un carré de côté 16cm. Reproduire le puzzle de sorte qu'il soit inscrit dans un carré dont le côté mesure 8cm.
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\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
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% Title Page
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\titre{Définition du cosinus}
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\classe{Troisième}
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\date{Janvier 2017}
|
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\pagestyle{empty}
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\newcommand{\lexo}{%
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\begin{Exo}[Reproduction de triangles]
|
||||
\begin{enumerate}
|
||||
\item Tracer les agrandissements ou les réductions des triangles suivants pour que les hypothénuses mesurent:
|
||||
\begin{center}
|
||||
5cm \qquad 8cm \qquad 12cm \qquad 15cm
|
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\end{center}
|
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|
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\includegraphics[scale=0.7]{./fig/triangle_repro}
|
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|
||||
\item Mesurer la longueur du côté adjacents pour compléter le tableau.
|
||||
|
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\begin{tabular}{|*{6}{p{2.5cm}|}}
|
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\hline
|
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Hypothénuse & 5 & 8 & 10 & 12 & 15 \\
|
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\hline
|
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Adjacent & & & & & \\
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\hline
|
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\end{tabular}
|
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|
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\item Ce tableau est-il un tableau de proportionnalité?
|
||||
|
||||
\item Comment peut-on calculer la longueur du côté adjacent quand l'hypothénuse mesure 10cm?
|
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54
3e/Geometrie/Triangle_rectange/index.rst
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54
3e/Geometrie/Triangle_rectange/index.rst
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|
||||
Notes autour du chapitre sur les triangles rectangles
|
||||
#####################################################
|
||||
|
||||
:date: 2016-11-26
|
||||
:modified: 2017-01-20
|
||||
:tags: Geometrie, Trigonometrie, Pythagore
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Notes sur le chapitre sur les outils pour calculer des éléments dans un triangle rectangle.
|
||||
|
||||
Étape 1: Théorème de Pythagore
|
||||
------------------------------
|
||||
|
||||
À la fin d'un cours, pendant 10min, seul puis en groupe, on écrit tout ce que l'on se rappelle sur le théorème de Pythagore.
|
||||
|
||||
Cahier de bord: On rédige le théorème de Pythagore en précisant le vocabulaire.
|
||||
|
||||
On fait quelques exercices techniques pour apprendre à rédiger et utiliser ce théorème.
|
||||
|
||||
`Pythagore sur la durée <./pb_duree_triangle_rectangle.pdf>`_
|
||||
|
||||
Étape 2: Découverte du Cosinus
|
||||
------------------------------
|
||||
|
||||
On trace des copies agrandies ou réduites de triangles rectangles et on complète un tableau avec les mesures de l'hypoténuse et du côté adjacents pour remarquer que c'est un tableau de proportionnalité. Le rapport ne dépend que de l'angle, on l'appellera le cosinus de l'angle.
|
||||
|
||||
`Reproduction de triangles pour définir le cosinus <./definition_cos.pdf>`_
|
||||
|
||||
Ce travail est fait en équipe et on partage la classe en 3. Chaque partie s'occupera d'un seul angle.
|
||||
|
||||
On laisse une trace sur le cahier de bord pour donner la définition du cosinus d'un angle.
|
||||
|
||||
Voici un exemple de production d'élèves: `production d'élèves <./prod_eleves_cos.pdf>`_
|
||||
|
||||
Étape 3: Calculer des longueurs avec le cosinus
|
||||
-----------------------------------------------
|
||||
|
||||
On donne un exercice de calcul de longueur. Les élèves doivent exploiter la trace laissée dans le cahier de bord pour produire une réponse. Le travail se fait seul puis en groupe. Une mise en commun en plénière permet d'améliorer les rédactions et d'en produire une de référence que l'on inscrit dans le cahier de bord.
|
||||
|
||||
On reproduit ce genre d'exercices, sur plusieurs cours.
|
||||
|
||||
Étape 4: Calculer un angle avec le cosinus
|
||||
------------------------------------------
|
||||
|
||||
De la même manière, on pose la question de retrouver la mesure de l'angle. Si la question n'est pas soulevée par les élèves, on pose la question de l'inversion du cosinus et on explique la fonction *arccos* en prenant bien soin de s'assurer que les élèves sachent l'utiliser sur leur calculatrice.
|
||||
|
||||
On reproduit ce genre d'exercices, sur plusieurs cours.
|
||||
|
||||
Étape 5 et suivantes: pour aller plus loin
|
||||
------------------------------------------
|
||||
|
||||
`Problèmes autour des angles <./Etape 1 problème et retour sur cosinus.odt>`_
|
||||
|
||||
Une `activité autour de l'escargot de Pythagore <./escargot_pythagore.odt>`_ avec une ouverture sur le tableur.
|
||||
BIN
3e/Geometrie/Triangle_rectange/intro_trigo.pdf
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44
3e/Geometrie/Triangle_rectange/intro_trigo.tex
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|
||||
\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
|
||||
|
||||
% Title Page
|
||||
\titre{Introduction à la trigonométrie}
|
||||
\classe{Troisième}
|
||||
\date{Janvier 2017}
|
||||
|
||||
\pagestyle{empty}
|
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\geometry{left=5mm,right=5mm, bottom= 10mm, top=10mm}
|
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|
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\begin{document}
|
||||
|
||||
|
||||
Compléter le tableau suivant en fonction des triangles.
|
||||
|
||||
\begin{tabular}{|c|*{6}{c|}}
|
||||
\hline
|
||||
Triangle & Hypoténuse & coté adjacent & coté opposé & angle & $\frac{\mbox{coté adjacent}}{\mbox{Hypoténuse}}$ & $\frac{\mbox{coté opposé}}{\mbox{Hypoténuse}}$ \\
|
||||
\hline
|
||||
ABC & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
DEF & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
GHI & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
JKL & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
MNP & ...... = ...... & ...... = ...... & ...... = ...... & ...... = ...... & $\frac{......}{......} = ......$ & $\frac{......}{......} = ......$ \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.55]{./fig/triangles}
|
||||
\end{center}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
3e/Geometrie/Triangle_rectange/pb_duree_triangle_rectangle.pdf
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9357
3e/Geometrie/Triangle_rectange/pb_duree_triangle_rectangle.svg
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3e/Geometrie/Triangle_rectange/prod_eleves_cos.pdf
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3e/Geometrie/Triangle_rectange/prod_eleves_cos.pdf
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11395
3e/Geometrie/Triangle_rectange/prod_eleves_cos.svg
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40
3e/Geometrie/Trigonometrie/index.rst
Normal file
40
3e/Geometrie/Trigonometrie/index.rst
Normal file
@@ -0,0 +1,40 @@
|
||||
Notes autour des formules trigonométries pour les 3e
|
||||
####################################################
|
||||
|
||||
:date: 2017-03-21
|
||||
:modified: 2017-03-21
|
||||
:tags: Géométrie, Trigonométrie
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Toutes les formules trigonométries pour les 3e.
|
||||
|
||||
|
||||
Les 2 réciproques peuvent se faire de façon indépendante.
|
||||
|
||||
Étape 1 (Pythagore)
|
||||
-------------------
|
||||
|
||||
Activité géogébra
|
||||
|
||||
Cahier de bord: Le théorème de Pythagore peut être utilisé pour démontrer que 2 droites sont perpendiculaires.
|
||||
|
||||
Étape 2 (Thalès)
|
||||
----------------
|
||||
|
||||
Comment déterminer que 2 triangles sont semblables?
|
||||
|
||||
Est-il possible de les placer d'une certaine façon pour que les 2 côtés soient parallèles? Et sans que les triangles se superposent?
|
||||
|
||||
Cahier de bord: Le théorème de Thalès peut être utilisé pour démontrer que 2 droites sont parallèles.
|
||||
|
||||
Étape 3 (exercices sur la durée)
|
||||
--------------------------------
|
||||
|
||||
Étape 4 (tache complexe)
|
||||
------------------------
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user