import work from year 2016-2017
This commit is contained in:
Benjamin Bertrand
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5e/Geometrie/Construction_figure/act_verification.pdf
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5e/Geometrie/Construction_figure/construction_n1.ggb
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5e/Geometrie/Construction_figure/construction_n1.ggb
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5e/Geometrie/Construction_figure/construction_n2.ggb
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65
5e/Geometrie/Construction_figure/index.rst
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5e/Geometrie/Construction_figure/index.rst
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|
||||
Notes sur le premier chapitre de géométrie pour les 5e
|
||||
######################################################
|
||||
|
||||
:date: 2016-08-28
|
||||
:modified: 2016-08-28
|
||||
:tags: geometrie, construction
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre de géométrie dessinée pour reprendre en main la construction de figure pour les 5e.
|
||||
|
||||
|
||||
Objectifs
|
||||
=========
|
||||
|
||||
- Coder une figure
|
||||
- Vocabulaire sur les figures de bases
|
||||
- Utiliser les outils de géométrie
|
||||
- Suivre une programme de construction
|
||||
|
||||
Déroulement
|
||||
===========
|
||||
|
||||
Au vu du découpage des heures, ce chapitre sera commencé dès le début de l'année en demi groupe. À ce moment la remédiation sera simplifiée.
|
||||
|
||||
Séance 1
|
||||
--------
|
||||
|
||||
`Activité de reproduction <./act_reproduction.pdf>`_ des carrés emboités. On demande aux élèves de reproduire la figure.
|
||||
|
||||
Une fois que quelques dessins ont été fait, on pose la question de comment vérifier si les dessins faits sont bien identiques au modèle. Ce qui devrait mener à une liste des caractéristiques du dessin.
|
||||
|
||||
C'est le moment où l'on rappelle comment coder une figure et le nom des formes que l'on voit sur le dessin.
|
||||
|
||||
Séance 2
|
||||
--------
|
||||
|
||||
`Activité de vérification <./act_verification.pdf>`_ d'un programme de construction.
|
||||
|
||||
Dans cette activité, on utilise les outils de géométrie pour vérifier des tracés. C'est aussi l'occasion de montrer le signe "appartient à" et de revoir le vocabulaire du cercle.
|
||||
|
||||
Séance 3
|
||||
--------
|
||||
|
||||
`Activité de transmission <./act_transmission.pdf>`_ le but est de faire un croquis tracé sans instruments de géométrie suffisamment bien codé pour qu'un camarade soit capable de reproduire la figure à l'identique.
|
||||
|
||||
Séance 4
|
||||
--------
|
||||
|
||||
Écriture d'un programme de construction avec Géogébra.
|
||||
|
||||
En plénière, on regarde une `première figure <./construction_n1.ggb>`_ à construire et on écrit une phrase pour décrire chaque étape. Chaque phrase sera discutée pour utiliser le bon vocabulaire.
|
||||
|
||||
Ensuite, on leur montre une `deuxième figure <./construction_n2.ggb>`_ à construire. Après quelques visionnages, on demande individuellement à chaque élève d'écrire une phrase par étape de construction en laissant la figure finale au tableau. On peut donner la `BD <./BD_construction.pdf>`_ pour rappeler les étapes.
|
||||
|
||||
Travail sur la durée
|
||||
--------------------
|
||||
|
||||
Des programmes de constructions à suivre.
|
||||
|
||||
Trace dans le cahier de bord
|
||||
----------------------------
|
||||
|
||||
- `carre et rectance <./carre_rectangle.pdf>`_
|
||||
- La définition du signe "appartient à"
|
||||
- La description de la construction de la deuxième figure
|
||||
BIN
5e/Geometrie/Construction_figure/lecon.pdf
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5e/Geometrie/Construction_figure/lecon.pdf
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62
5e/Geometrie/Construction_figure/pgm_contr_geogebra.tex
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62
5e/Geometrie/Construction_figure/pgm_contr_geogebra.tex
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|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
|
||||
|
||||
% Title Page
|
||||
\titre{Programme de construction - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Cinquième}
|
||||
\date{Octobre 2016}
|
||||
|
||||
|
||||
\newcommand{\lexo}{%
|
||||
\setcounter{exo}{0}
|
||||
\begin{Exo}
|
||||
Voici un programme de construction géométrique.
|
||||
\begin{center}
|
||||
\Ovalbox{%
|
||||
\begin{minipage}{0.3\textwidth}
|
||||
\begin{itemize}
|
||||
\item Placer 3 points A, B et C
|
||||
\item Tracer les demi-droites $[AB)$ et $[AC)$
|
||||
\item Tracer le segment $[BC]$
|
||||
\item Placer $D$ au mileu de $[AB]$
|
||||
\item Placer $E$ le milieu du segment $[AC]$
|
||||
\item Tracer le segment $[DE]$
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
}
|
||||
\end{center}
|
||||
\begin{enumerate}
|
||||
\item Executer ce programme avec Géogébra.
|
||||
\item Mesurer les segment $[BC]$ et $[DE]$. Quelle conjecture pouvez vous faire?
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\lexo
|
||||
|
||||
\vfill
|
||||
|
||||
\lexo
|
||||
|
||||
\pagebreak
|
||||
|
||||
\lexo
|
||||
|
||||
\vfill
|
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|
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\lexo
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
30
5e/Geometrie/Contruction_quadrilatere_triangle/index.rst
Normal file
30
5e/Geometrie/Contruction_quadrilatere_triangle/index.rst
Normal file
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|
||||
Notes sur la contruction des quadrilatères et des triangles pour les 5e
|
||||
#######################################################################
|
||||
|
||||
:date: 2017-01-08
|
||||
:modified: 2017-01-08
|
||||
:tags: geometrie
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur la construction au crayon des quadrilatères et des triangles.
|
||||
|
||||
Étape 1
|
||||
=======
|
||||
|
||||
On demande aux élèves de tracer
|
||||
|
||||
- Un rectangle de 3cm de longueur et de 5cm de largeur.
|
||||
- Le carré ABCD tel que AB=4cm
|
||||
|
||||
Les élèves essaie d'abord seul. Puis en plénière on insiste sur le fait de faire un croquis que l'on va coder. Ils continuent à construire leurs figures.
|
||||
|
||||
Pour ceux qui terminent rapidement, on peut ajouter un point ou une droite pour les faire travailler les symétries.
|
||||
|
||||
Cahier de bord: Croquis d'un carré et d'un triangle avec la définition d'un croquis.
|
||||
|
||||
Étape 2
|
||||
=======
|
||||
|
||||
On leurs demande de tracer un triangle avec 3 longueurs.
|
||||
|
||||
- Le triangle IJK tel que IJ=3cm, JK=4cm et IK=5cm
|
||||
BIN
5e/Geometrie/Parallelogramme/Quadrilateres.ggb
Normal file
BIN
5e/Geometrie/Parallelogramme/Quadrilateres.ggb
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BIN
5e/Geometrie/Parallelogramme/constr_paralllelogramme_geogeb.pdf
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5e/Geometrie/Parallelogramme/constr_paralllelogramme_geogeb.pdf
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|
||||
\documentclass[a5paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
|
||||
|
||||
% Title Page
|
||||
\titre{Découverte du parallélogramme - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Cinquième}
|
||||
\date{Mai 2017}
|
||||
|
||||
|
||||
\newcommand{\lexo}{%
|
||||
\setcounter{exo}{0}
|
||||
\begin{Exo}
|
||||
On veut découvrir une nouvelle figure géométrique avec Géogébra \includegraphics[scale=0.05]{./fig/geog_logo}. Pour cela, nous allons utiliser ce programme de construction.
|
||||
\begin{center}
|
||||
\Ovalbox{%
|
||||
\begin{minipage}{0.9\textwidth}
|
||||
\hspace{1cm}Construction d'un \textbf{parallélogramme}
|
||||
|
||||
\begin{itemize}
|
||||
\item Tracer deux segments $[AB]$ et $[BC]$.
|
||||
|
||||
\includegraphics[scale=0.5]{./fig/geog_seg}
|
||||
|
||||
\item Tracer la droite $(h)$ parallèle à $(AB)$ et qui passe par $C$.
|
||||
|
||||
\includegraphics[scale=0.5]{./fig/geog_para}
|
||||
|
||||
\item Tracer la droite $(i)$ parallèle à $(BC)$ et qui passe par $A$.
|
||||
\item Placer le point $D$ à l'intersection de $(h)$ et $(i)$.
|
||||
\end{itemize}
|
||||
\end{minipage}
|
||||
}
|
||||
\end{center}
|
||||
\begin{enumerate}
|
||||
\item Executer ce programme avec Géogébra.
|
||||
\item Déformer ce parallélogramme pour obtenir un rectangle, puis un carré.
|
||||
\item Tracer les diagonales $[AC]$ et $[BD]$ puis placer $E$ le point d'intersection.
|
||||
\item Mesurer $AE$ et $EC$. Que constatez vous quand vous déformez la figure?
|
||||
|
||||
\includegraphics[scale=0.5]{./fig/geog_mes}
|
||||
\end{enumerate}
|
||||
|
||||
\end{Exo}
|
||||
|
||||
}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\lexo
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
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5e/Geometrie/Parallelogramme/index.rst
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Notes sur la construction de parallelogramme pour les 5e
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########################################################
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:date: 2017-04-19
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:modified: 2017-05-29
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:tags: Geometrie, Parallelogramme
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:category: 5e
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:authors: Bertrand Benjamin
|
||||
:summary: Construction d'un parallelogramme pour les 5e
|
||||
|
||||
|
||||
Objectifs
|
||||
=========
|
||||
|
||||
- Tracer des droites parallèles et perpendiculaires
|
||||
- Tracer un parallelogramme
|
||||
- Initier la découverte des propriétés des parallelogrammes.
|
||||
|
||||
Étape 1
|
||||
=======
|
||||
|
||||
Découverte du parallélogramme avec Geogebra.
|
||||
|
||||
`Constrution d'un parallélogramme <./constr_paralllelogramme_geogeb.pdf>`_.
|
||||
|
||||
Étape 2
|
||||
=================
|
||||
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Reconnaître des parallelogrammes particuliers, les nommer puis trouver leurs propriétés.
|
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`Quadrilatères sur géogébra <./Quadrilateres.ggb>`_
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57
5e/Geometrie/Perimetre_aire/index.rst
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57
5e/Geometrie/Perimetre_aire/index.rst
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Notes sur la notion de périmètre et la géométrie mathématique pour les 5e
|
||||
#########################################################################
|
||||
|
||||
:date: 2017-02-20
|
||||
:modified: 2017-05-19
|
||||
:tags: Geometrie
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur la notion de périmètre et la géométrie mathématique pour les 5e
|
||||
|
||||
Étape 1
|
||||
=======
|
||||
|
||||
Quelques `exercices de construction <./longueur_tour.pdf>`_ où l'on de calculer la longueur du tour de la figure. Certain, à cause de leur taille, ne peuvent pas être dessinés. Les élèves sont forcés à utiliser le croquis et à faire des calculs.
|
||||
|
||||
Cahier de bord: Définition du périmètre d'une figure.
|
||||
|
||||
En calcul mental, on pourra ensuite s'autoriser à calculer le périmètre de figures.
|
||||
|
||||
Étape 2
|
||||
=======
|
||||
|
||||
Activité Curvica, il faut classer les figures en fonction de leur périmètre puis en fonction de leur aire.
|
||||
|
||||
- `Curvica triangulaire <./curvica.pdf>`_
|
||||
|
||||
|
||||
Étape 3
|
||||
=======
|
||||
|
||||
On va chercher à assimiler que la notion de découpage et recolage préserve l'aire. Et on commencera à élaborer des formules pour calculer ces aires.
|
||||
|
||||
- `Aire des polygones <./aire_polyognes.pdf>`_
|
||||
|
||||
Prolongation de l'activité (les vacances sont passées) avec d'autres polygones.
|
||||
|
||||
- `Classer les polygones <./classer_perim_aire.pdf>`_
|
||||
|
||||
|
||||
On peut conclure avec des questions bonus:
|
||||
|
||||
- Dessiner sur le quadrillage 2 figures avec le même périmètre mais pas la même aire.
|
||||
- Dessiner sur le quadrillage 2 figures avec la même aire mais pas le même périmètre.
|
||||
|
||||
Étape 4
|
||||
=======
|
||||
|
||||
On veut chercher des formules pour calculer les aires de certaines figures.
|
||||
|
||||
On dessine un rectangle au tableau et on demande de quoi a-t-on besoin pour calculer l'aire de cette figure.
|
||||
|
||||
Une fois la formule trouvée, on peut s'exercicer lors des calculs mentals.
|
||||
|
||||
Étape 5
|
||||
=======
|
||||
|
||||
On reproduit la même chose avec un triangle rectangle.
|
||||
BIN
5e/Geometrie/Perimetre_aire/longueur_tour.pdf
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5e/Geometrie/Perimetre_aire/longueur_tour.pdf
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54
5e/Geometrie/Perimetre_aire/longueur_tour.tex
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54
5e/Geometrie/Perimetre_aire/longueur_tour.tex
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|
||||
\documentclass[a4paper,12pt,landscape, twocolumn]{/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{Périmetre - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Cinquième}
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\date{Février 2017}
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\newcommand{\lexo}{%
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\setcounter{exo}{0}
|
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\begin{Exo}[Longueur du tour]
|
||||
\begin{enumerate}
|
||||
\item $ABC$ est un triangle tel que $AB = 4cm$ et $AC = CB = 6cm$.
|
||||
\begin{enumerate}
|
||||
\item Faire un croquis et dessinner ce triangle.
|
||||
\item \textbf{Mesurer} la longueur du tour de ce triangle.
|
||||
\item \textbf{Calculer} la longueur du tour de ce triangle.
|
||||
\end{enumerate}
|
||||
\item Abdou a un champ rectangulaire dont un côté mesure 5m et l'autre 3m. Il veut mettre du barrière autour. Quelle sera la longueur de cette barrière?
|
||||
\item $EFGH$ est un carré tel que $GF = 70cm$ et $FGI$ un triangle équilatéral. Quelle est la longueur du tour de la figure $AFIGH$?
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\end{enumerate}
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\end{Exo}
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}
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60
5e/Geometrie/Symetries/index.rst
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60
5e/Geometrie/Symetries/index.rst
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Notes sur la (re)découverte de symétries pour les 5e
|
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####################################################
|
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|
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:date: 2016-10-27
|
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:modified: 2017-03-31
|
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:tags: Geometrie, Symetrie
|
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:category: 5e
|
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:authors: Bertrand Benjamin
|
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:summary: Chapitre d'appropriation des symétries pour les 5e.
|
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|
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|
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Objectifs
|
||||
=========
|
||||
|
||||
- Reconnaitre des 2 types de symétries
|
||||
- Tracer le symétrique de figures
|
||||
|
||||
|
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Étape 1
|
||||
=======
|
||||
|
||||
Retrouver les transformations sur des `cocottes <./classer_symetries_A4.pdf>`_.
|
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|
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Sur la cahier de groupe, on range les cocottes qui ont subit les mêmes transformations et on écrit une phrase pour la décrire.
|
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|
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Étape 2
|
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=======
|
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|
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On s'intéresse à la famille *symétrie axiale*.
|
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|
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|
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|
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|
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Étape 3
|
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=======
|
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|
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On s'intéresse à la (nouvelle) famille *symétrie centrale*.
|
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|
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|
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|
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|
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On parle rapidement de la vignette restante.
|
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|
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Étape 4
|
||||
=======
|
||||
|
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`Premières symétries <./tracer_symetries1.pdf>`_ à tracer pour construire une technique de construction.
|
||||
|
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|
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Étape 5
|
||||
=======
|
||||
|
||||
Cette étape a été faite beaucoup plus tard dans l'année avec une classe plutôt faible. Il s'agit de reconstituer un vitrail cassé, le travail sur la symétrie facilite beaucoup la reproduction.
|
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|
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`Vitraux cassés <./TC_vitrail.pdf>`_
|
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|
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|
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After Width: | Height: | Size: 6.1 KiB |
BIN
5e/Geometrie/Symetries/tracer_symetries1_eleves.pdf
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5e/Geometrie/Symetries/tracer_symetries1_eleves.pdf
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36
5e/Geometrie/Symetries_math/index.rst
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36
5e/Geometrie/Symetries_math/index.rst
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|
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Notes sur les propriétés des symétries pour les 5e
|
||||
###################################################
|
||||
|
||||
:date: 2017-04-19
|
||||
:modified: 2017-04-19
|
||||
:tags: Geometrie, Symetrie
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Découvertes des propriétés des symétries pour les 5e
|
||||
|
||||
|
||||
Objectifs
|
||||
=========
|
||||
|
||||
- Revoir les symétries (constructions à la main)
|
||||
- Connaître les grandeurs convervées par ces tranformations
|
||||
|
||||
L'essentiel de cette séquence se fait avec Géogébra (donc en demi groupe).
|
||||
|
||||
Étape 1
|
||||
=======
|
||||
|
||||
Avec géogébra, on cherche à reconnaître les transformations puis de découvrir ce qu'elles concervent.
|
||||
|
||||
- `Transformations avec géogébra <./transformations.ggb>`_
|
||||
- `Tableau des transformations <./tbl_transformations.pdf>`_
|
||||
|
||||
Étape 2
|
||||
=======
|
||||
|
||||
Étude des transformations d'objets mathématiques et des propriétés qui en découlent (avec Géogébra). C'est un exercice à la fois d'autonomisation avec Géogébra et de recherche de propriétés géométriques.
|
||||
|
||||
Étape 3
|
||||
=======
|
||||
|
||||
Construction de figures avec des morceaux manquants. Les élèves auront besoin de réutiliser les propriétés pour les terminer.
|
||||
BIN
5e/Geometrie/Symetries_math/transformations.ggb
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BIN
5e/Geometrie/Symetries_math/transformations.ggb
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Reference in New Issue
Block a user