On avance sur la p5 avec les 601

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Bertrand Benjamin 2018-05-07 09:06:13 +03:00
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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\author{}
\date{Mai 2018}
\title{Géométrie dessinée vs géométrie mathématique}
\tribe{Sixième}
\pagestyle{empty}
\renewcommand{\arraystretch}{2}
\newcommand{\content}{%
Les mathématiciens n'étudient pas les dessins géométriques car sur un dessin, il y a forcément des défauts de tracé et les mesures ne peuvent pas être exactes.
Pour mieux comprendre le monde qui nous entoure, les mathématiciens ont décidé d'étudier des objets géométriques entièrement \textbf{imaginaires, parfaits, avec des mesures exactes} : un cercle parfaitement rond, sans épaisseur ; un segment parfaitement droit d'exactement 3,8 cm etc.
Il y a donc deux types de géométrie plane.
\bigskip
\hspace{-1cm}
\begin{tabular}{|*{2}{p{0.5\textwidth}|}}
\hline
\parbox[m]{0.4\textwidth}{\textbf{Géométrie dessinée} \\ Étudiée à l'école primaire et au collège} &
\parbox[m]{0.4\textwidth}{\textbf{Géométrie mathématique} \\ Étudiée au collège, au lycée, ...} \\
\hline
On étudie et on fait des dessins: segments dessinés, carrés dessinés ... &
On étudie des objets géométriques imaginaires et "parfait": segment mathématiques, carrés mathématiques ... \\
\hline
La mesure d'un segment dessiné ne peut pas être infiniment précise ni exacte &
La longueur d'un segment imaginaire est infiniment précise et exacte \\
\hline
Une droite dessinée n'est pas parfaitement droite et elle a une épaisseur et une couleur &
Une droite mathématique est parfaitement droite et elle n'a pas d'épaisseur ni de couleur. \\
\hline
Une figure doit être dessinée avec la plus grande précision &
Un croquis à main levé suffit, par contre il faut coder la figure.\\
\hline
\end{tabular}
}
\begin{document}
\content
\vfill
\content
\vfill
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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\author{}
\date{Mars 2018}
\title{Vrais/Faux sur les quadrilatères}
\tribe{Sixième}
\pagestyle{empty}
\begin{document}
\begin{exercise}[subtitle={Vrai ou faux?}]
En t'aidant des figures que tu peux déformer sur la tablette, dit si les phrases suivantes sont vraies ou fausses. Tu peux faire un dessin pour expliquer ta réponse.
\begin{enumerate}
\item Tous les carrés sont des quadrilatères.
\item Tous les rectangles ont les quatre côtés de la même longueur.
\item Tous les carrés sont des losanges.
\item Il existe des rectangles qui sont aussi des carrés.
\item Tous les losanges ont leurs diagonales qui se coupent en angle droit.
\end{enumerate}
\end{exercise}
\vfill
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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\author{}
\date{Mars 2018}
\title{Double carré}
\tribe{Sixième}
\pagestyle{empty}
\begin{document}
\begin{exercise}[subtitle={Double carré}]
ABEF est un carré mathématique tel que : AB = 5 cm.
BCDE est un autre carré mathématique.
\begin{enumerate}
\item Faire un croquis à main levé de la figure.
\item Tracer le plus précisément la figure.
\item Quel est le périmètre du rectangle mathématique ACDF ? Quelle est son aire ?
\item Quel est le périmètre du triangle mathématique ADF ? Quelle est son aire ?
\end{enumerate}
\end{exercise}
\vfill
\printexercise{exercise}{1}
\vfill
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\printexercise{exercise}{1}
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\printexercise{exercise}{1}
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@ -2,7 +2,7 @@ De la géométrie dessinée à la géométrie mathématiques avec les 6e pour l'
######################################################################################## ########################################################################################
:date: 2018-05-01 :date: 2018-05-01
:modified: 2018-05-01 :modified: 2018-05-07
:authors: Bertrand Benjamin :authors: Bertrand Benjamin
:category: 6e :category: 6e
:tags: Geométrie :tags: Geométrie
@ -18,10 +18,12 @@ Série de Vrai/faux sur des phrases nécessitants la déformation des figures
-> Tous les carrés sont des quadrilatères. -> Tous les carrés sont des quadrilatères.
Cahier de bord: Dessins des quadrilatères avec les phrases justes sur chaque quadrilatères.
Étape 2: Tracer des quadrilatères Étape 2: Tracer des quadrilatères
================================= =================================
On demande à tous les élèves de nous tracer un quadrilatère et un carré sur une feuille blanche. On demande à tous les élèves de nous tracer un quadrilatère et un carré sur une feuille blanche (en précisant qu'ils doivent coder leurs figures)
En plénière, on demande que doit-on vérifier pour valider ou pas les dessins. En plénière, on demande que doit-on vérifier pour valider ou pas les dessins.
@ -33,14 +35,14 @@ On ouvre sur la différence entre la géométrie dessinée et la géométrie mat
Étape 3 Étape 3
======= =======
Avec les productions des élèves, les disques..., les élèves nomment les figures puis cherchent exhaustivement les defauts. Avec les productions des élèves, les disques..., les élèves nomment les figures puis cherchent exhaustivement les défauts.
Cahier de bord: Bilan p 340. Cahier de bord: `différences entre géométrie dessinée et géométrie mathématique <./B2_dessin_math.pdf>`_
Étape 4 Étape 4
======= =======
Calcul de l'aire et du périmètre avec 2 carrés (cfp351) Calcul de l'aire et du périmètre avec `2 carrés <./E4_double_carre.pdf>`_
Étape 5 Étape 5
======= =======

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\documentclass[a4paper,12pt]{article}
\usepackage{myXsim}
\date{Mai 2018}
\title{Calculer le volume}
\tribe{Sixième}
\pagestyle{empty}
%\geometry{left=10mm,right=10mm, top=5mm}
\begin{document}
\begin{exercise}[subtitle={Calculer les volumes \Rep}]
\begin{enumerate}
\item Calculer le volume des 3 objets suivants
\hspace{-1.2cm}
\includegraphics[scale=0.8]{./fig/volumes_cubes}
\item Calculer le volume des 2 objets suivants
\hspace{-1cm}
\includegraphics[scale=0.8]{./fig/volumes_nocubes}
\end{enumerate}
\end{exercise}
\begin{exercise}[subtitle={Empillement des cubes \Rep}]
Quel est le volume de chacun de ces empilements?
\includegraphics[scale=0.4]{./fig/empilements}
\end{exercise}
\end{document}
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@ -2,7 +2,7 @@ Volumes avec les 6e pour l'année 2017-2018
########################################## ##########################################
:date: 2018-05-02 :date: 2018-05-02
:modified: 2018-05-02 :modified: 2018-05-07
:authors: Bertrand Benjamin :authors: Bertrand Benjamin
:category: 6e :category: 6e
:tags: Géométrie, Volumes :tags: Géométrie, Volumes
@ -29,22 +29,22 @@ Puis en groupe, on cherche à décrire en une phrase comment on peut reconnaîtr
Cahier de bord: Les phrases produites par les élèves. Cahier de bord: Les phrases produites par les élèves.
Étape 2 Étape 3
======= =======
Mesure de tout ce qui est possible de mesurer sur des volumes physiques. Mesure de tout ce qui est possible de mesurer sur des volumes physiques.
Cahier de bord: introduction du volume et de l'unité de volume. Cahier de bord: `introduction du volume et de l'unité de volume <./B3_volumes.pdf>`_
Étape 3
=======
Empilement de cubes où l'on calcule les volumes
Cahier de bord: Formule du volume d'un pavé droit
Étape 4 Étape 4
======= =======
`Empilements de cubes <./E4_calculer_volume.pdf>`_ où l'on calcule les volumes
Cahier de bord: Formule du volume d'un pavé droit
Étape 5
=======
Tache complexe avec un calcul de volume. Tache complexe avec un calcul de volume.