import work from year 2015-2016
This commit is contained in:
Benjamin Bertrand
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\parbox{0.65\linewidth}{Paul en visite à Paris admire la Pyramide, réalisée en verre feuilleté au centre de la cour intérieure du Louvre.
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Cette pyramide régulière a :
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\setlength\parindent{6mm}
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\begin{itemize}
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\item[$\bullet~~$] pour base un carré ABCD de côté 35 mètres ;
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\item[$\bullet~~$] pour hauteur le segment [SO] de longueur 22 mètres.
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\end{itemize}
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\setlength\parindent{0mm}}
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\hfill
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\parbox{0.3\linewidth}{
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\includegraphics[scale=0.2]{./fig/2014_CE_Exo4_pyramide}
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}
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\medskip
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Paul a tellement apprécié cette pyramide qu'il achète comme souvenir de sa visite une lampe à huile dont le réservoir en verre est une réduction à l'échelle $\dfrac{1}{500}$ de la vraie pyramide.
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Le mode d'emploi de la lampe précise que, une fois allumée, elle brûle 4 cm$^3$ d'huile par heure.
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Au bout de combien de temps ne restera-t-il plus d'huile dans le réservoir ? Arrondir à l'unité d'heures.
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\textbf{Rappel :} \emph{Volume d'une pyramide = un tiers du produit de l'aire de la base par la hauteur}
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\medskip
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\textbf{Faire apparaitre sur la copie la démarche utilisée. Toute trace de recherche sera prise en compte lors de l'évaluation même si le travail n'est pas complètement abouti.}
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Pour amortir les chocs contre les autres embarcations ou le quai, les péniches sont équipées de \og boudins \fg{} de protection.
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\parbox{0.48\linewidth}{
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\includegraphics[scale=0.2]{./fig/2014_juin_AN_Exo2}
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}\hfill
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\parbox{0.48\linewidth}{
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\begin{enumerate}
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\item Calculer le volume exact en cm$^3$ du \og boudin \fg de protection ci-contre, puis arrondir au centième.
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\item On veut réaliser une bouée deux fois plus grande. Quelle sera son volume?
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\item On veut réaliser une bouée qui serait réduite d'un rapport 0.4. Quelle sera son volume?
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\end{enumerate}
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}
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\textbf{Rappel}
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\textbf{Volume d'un cylindre de révolution} $V = \pi R^2 h$ où $h$ désigne la hauteur du cylindre et $R$ le rayon de la base.
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\textbf{Volume d'une boule} $V = \dfrac{4}{3}\pi R^3$ où $R$ désigne le rayon de la boule.
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\documentclass[a4paper,10pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
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% Title Page
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\titre{Agrandissement aire et volumes - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Troisième}
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\date{Mai 2016}
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\pagestyle{empty}
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\begin{document}
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\begin{Exo}
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\input{./2014_juin_AN_exo2.tex}
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\end{Exo}
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\begin{Exo}
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\input{./2014_CE_exo4.tex}
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\end{Exo}
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\pagebreak
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\setcounter{exo}{0}
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\begin{Exo}
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\input{./2014_juin_AN_exo2.tex}
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\end{Exo}
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\begin{Exo}
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\input{./2014_CE_exo4.tex}
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\end{Exo}
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\pagebreak
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\setcounter{exo}{0}
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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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26
3e/Unites_et_grandeurs/Agrandissement_aire_volume/index.rst
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3e/Unites_et_grandeurs/Agrandissement_aire_volume/index.rst
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|
||||
Notes sur le chapitre agrandissement des aires et des volumes pour les 3e
|
||||
#########################################################################
|
||||
|
||||
:date: 2016-05-30
|
||||
:modified: 2016-07-06
|
||||
:tags: Agrandissement, volume, aire
|
||||
:category: 3e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur les agrandissement et les réductions des aires et des volumes pour les 3e.
|
||||
|
||||
Objectifs
|
||||
=========
|
||||
|
||||
- Revoir les calculs d'aires et de volumes
|
||||
- Découvrir comment se comportent l'aire et le volumes lors d'un agrandissement.
|
||||
|
||||
Déroulement
|
||||
===========
|
||||
|
||||
- Séance 1-2: J'ai repris une activité de Sesamath. On veut faire un miniature d'un immeuble (un pavé droit) dont les dimensions sont données. J'ai partagé la classe en 4 parties, chaque partie devait calculer les dimensions de la miniature suivant différentes échelles. Une fois les dimensions calculées, on calculait la surface au sol ainsi que le volume du vrai immeuble et de la miniature.
|
||||
|
||||
On a ensuite tracé ces `graphiques <./graphs_echelles.pdf>`_ pour se rendre compte que l'évolution n'était pas toujours linéaire. *Ces graphiques en fait ne sont pas très révélateurs... Il faudrait faire le graphique en comparant les dimensions de plusieurs objets en fonction d'une seule échelle. Ce serait plus juste*.
|
||||
|
||||
On peut ensuite écrire le cours où on explique que quand on agrandit d'un facteur *k* l'aire est multipliée par k^2 et le volume par k^3.
|
||||
|
||||
- Les autres séances sont consacrées à cette `fiche d'exercices <./exo_agrandissement.pdf>`_.
|
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3817
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3e/Unites_et_grandeurs/Changement_unites/Exo/Exo_verres.tex
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|
||||
\documentclass[a5paper,12pt]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
|
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
|
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|
||||
% Title Page
|
||||
\titre{Changement d'unité - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Troisième}
|
||||
\date{Octobre 2015}
|
||||
|
||||
|
||||
\begin{document}
|
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|
||||
% inspiré de http://www.ilemaths.net/forum-sujet-496010.html
|
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|
||||
\vfill
|
||||
|
||||
Pour une soirée d'inauguration, les serveurs décident de préparer le cocktail suivant (la recette est donnée pour 4 verres)
|
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|
||||
\begin{itemize}
|
||||
\item $\frac{1}{3}$L de jus d'orange
|
||||
\item 1,6dL de jus d'abricot
|
||||
\item 8cL de jus de citron vert
|
||||
\item une banane (d'un volume d'environ $110cm^3$)
|
||||
\item 1 cuillère à café de miel (d'un volume d'environ $5cm^3$)
|
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\item 4mL de sirop de grenadine
|
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\end{itemize}
|
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\vfill
|
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\begin{enumerate}
|
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\item Quel est le volume d'un verre de ce cocktail? Donner le résultat en $cm^3$ arrondi à l'unité.
|
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\vfill
|
||||
\item Pour que les convives puissent apprécier leur cocktail, il doit être servi dans un beau verre ni trop rempli ni pas assez. Lequel de ces trois verres sera le plus approprier pour servir ce cocktail?
|
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\includegraphics[scale=0.4]{./fig/verres}
|
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\end{center}
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\vfill
|
||||
|
||||
On rappelle que le volume d'un cône est $V = \frac{1}{3} \pi \times r^2 \times h$
|
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\end{enumerate}
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\vfill
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After Width: | Height: | Size: 13 KiB |
BIN
3e/Unites_et_grandeurs/Changement_unites/Exo/planetes.pdf
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3e/Unites_et_grandeurs/Changement_unites/Exo/planetes.pdf
Normal file
Binary file not shown.
168
3e/Unites_et_grandeurs/Changement_unites/Exo/planetes.tex
Normal file
168
3e/Unites_et_grandeurs/Changement_unites/Exo/planetes.tex
Normal file
@@ -0,0 +1,168 @@
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\documentclass[a4paper,10pt,landscape, twocolumn]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
|
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\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
|
||||
|
||||
|
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% Title Page
|
||||
\titre{Changement d'unité notation scientifique - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
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\classe{Troisième}
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\date{Octobre 2015}
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\pagestyle{empty}
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\geometry{left=5mm,right=5mm, bottom= 5mm, top=5mm}
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\begin{document}
|
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|
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\begin{Exo}
|
||||
Voici les caractéristiques de plusieurs planètes du système solaire.
|
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\begin{multicols}{2}
|
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|
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\hspace{-0.5cm}
|
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\begin{tabular}{|c|p{2cm}|c|}
|
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\hline
|
||||
Planète & Rayon moyen (km) & Masse(kg) \\
|
||||
\hline
|
||||
Mercure & 2439,7 & $3,302\times 10^{23}$ \\
|
||||
\hline
|
||||
Terre & 6 371 & $5,9736 \times 10^{24}$ \\
|
||||
\hline
|
||||
Mars & 3390 & $6,4185 \times 10^{23}$ \\
|
||||
\hline
|
||||
Jupiter & 69 911 & $1,8986 \times 10^{27}$ \\
|
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\hline
|
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Neptune & 24 622 & $1,0243 \times 10^{26}$ \\
|
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\hline
|
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\end{tabular}
|
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\begin{enumerate}
|
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\item Classer ces planètes de la plus petite à la plus grande.
|
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\item Classer ces planète en fonction de leur masse.
|
||||
\item Classe les planètes selon leur masse volumique. La formule pour calculer la masse volumique est ($m$ représente la masse et $r$ le rayon).
|
||||
\begin{eqnarray*}
|
||||
\frac{3m}{4\pi\times r^3}
|
||||
\end{eqnarray*}
|
||||
\item Peut-on, à partir du calcul de la masse volumique faire deux groupes de planètes, les planètes gazeuses (planètes faites de gaz) et les planètes tellurique (planètes faites de roche)?
|
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\end{enumerate}
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\end{multicols}
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\end{Exo}
|
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\setcounter{exo}{0}
|
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\begin{Exo}
|
||||
Voici les caractéristiques de plusieurs planètes du système solaire.
|
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\begin{multicols}{2}
|
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|
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\hspace{-0.5cm}
|
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\begin{tabular}{|c|p{2cm}|c|}
|
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\hline
|
||||
Planète & Rayon moyen (km) & Masse(kg) \\
|
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\hline
|
||||
Mercure & 2439,7 & $3,302\times 10^{23}$ \\
|
||||
\hline
|
||||
Terre & 6 371 & $5,9736 \times 10^{24}$ \\
|
||||
\hline
|
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Mars & 3390 & $6,4185 \times 10^{23}$ \\
|
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\hline
|
||||
Jupiter & 69 911 & $1,8986 \times 10^{27}$ \\
|
||||
\hline
|
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Neptune & 24 622 & $1,0243 \times 10^{26}$ \\
|
||||
\hline
|
||||
\end{tabular}
|
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\begin{enumerate}
|
||||
\item Classer ces planètes de la plus petite à la plus grande.
|
||||
\item Classer ces planète en fonction de leur masse.
|
||||
\item Classe les planètes selon leur masse volumique. La formule pour calculer la masse volumique est ($m$ représente la masse et $r$ le rayon).
|
||||
\begin{eqnarray*}
|
||||
\frac{3m}{4\pi\times r^3}
|
||||
\end{eqnarray*}
|
||||
\item Peut-on, à partir du calcul de la masse volumique faire deux groupes de planètes, les planètes gazeuses (planètes faites de gaz) et les planètes tellurique (planètes faites de roche)?
|
||||
|
||||
\end{enumerate}
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\end{multicols}
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\end{Exo}
|
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\pagebreak
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\setcounter{exo}{0}
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||||
\begin{Exo}
|
||||
Voici les caractéristiques de plusieurs planètes du système solaire.
|
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\begin{multicols}{2}
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\hspace{-0.5cm}
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\hline
|
||||
Planète & Rayon moyen (km) & Masse(kg) \\
|
||||
\hline
|
||||
Mercure & 2439,7 & $3,302\times 10^{23}$ \\
|
||||
\hline
|
||||
Terre & 6 371 & $5,9736 \times 10^{24}$ \\
|
||||
\hline
|
||||
Mars & 3390 & $6,4185 \times 10^{23}$ \\
|
||||
\hline
|
||||
Jupiter & 69 911 & $1,8986 \times 10^{27}$ \\
|
||||
\hline
|
||||
Neptune & 24 622 & $1,0243 \times 10^{26}$ \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\begin{enumerate}
|
||||
\item Classer ces planètes de la plus petite à la plus grande.
|
||||
\item Classer ces planète en fonction de leur masse.
|
||||
\item Classe les planètes selon leur masse volumique. La formule pour calculer la masse volumique est ($m$ représente la masse et $r$ le rayon).
|
||||
\begin{eqnarray*}
|
||||
\frac{3m}{4\pi\times r^3}
|
||||
\end{eqnarray*}
|
||||
\item Peut-on, à partir du calcul de la masse volumique faire deux groupes de planètes, les planètes gazeuses (planètes faites de gaz) et les planètes tellurique (planètes faites de roche)?
|
||||
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
|
||||
\end{Exo}
|
||||
\setcounter{exo}{0}
|
||||
|
||||
\begin{Exo}
|
||||
Voici les caractéristiques de plusieurs planètes du système solaire.
|
||||
\begin{multicols}{2}
|
||||
|
||||
\hspace{-0.5cm}
|
||||
\begin{tabular}{|c|p{2cm}|c|}
|
||||
\hline
|
||||
Planète & Rayon moyen (km) & Masse(kg) \\
|
||||
\hline
|
||||
Mercure & 2439,7 & $3,302\times 10^{23}$ \\
|
||||
\hline
|
||||
Terre & 6 371 & $5,9736 \times 10^{24}$ \\
|
||||
\hline
|
||||
Mars & 3390 & $6,4185 \times 10^{23}$ \\
|
||||
\hline
|
||||
Jupiter & 69 911 & $1,8986 \times 10^{27}$ \\
|
||||
\hline
|
||||
Neptune & 24 622 & $1,0243 \times 10^{26}$ \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\begin{enumerate}
|
||||
\item Classer ces planètes de la plus petite à la plus grande.
|
||||
\item Classer ces planète en fonction de leur masse.
|
||||
\item Classe les planètes selon leur masse volumique. La formule pour calculer la masse volumique est ($m$ représente la masse et $r$ le rayon).
|
||||
\begin{eqnarray*}
|
||||
\frac{3m}{4\pi\times r^3}
|
||||
\end{eqnarray*}
|
||||
\item Peut-on, à partir du calcul de la masse volumique faire deux groupes de planètes, les planètes gazeuses (planètes faites de gaz) et les planètes tellurique (planètes faites de roche)?
|
||||
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
|
||||
\end{Exo}
|
||||
\pagebreak
|
||||
|
||||
|
||||
|
||||
\pagebreak
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
Binary file not shown.
@@ -0,0 +1,124 @@
|
||||
\documentclass[a4paper,12pt]{/media/documents/Cours/Prof/Enseignements/tools/style/classExo}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2015_2016}
|
||||
|
||||
% Title Page
|
||||
\titre{Changement d'unités et notation scientifique - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Troisième}
|
||||
\date{Octobre 2015}
|
||||
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{questions}
|
||||
\question
|
||||
Placer les éléments suivants sur des échelles de grandeurs.
|
||||
|
||||
\begin{itemize}
|
||||
\item Données de masses (en kg):
|
||||
\begin{multicols}{3}
|
||||
\begin{enumerate}
|
||||
\item Un litre d'eau
|
||||
\item Un virus
|
||||
\item La Voie Lactée
|
||||
\item Une cellule
|
||||
\item Un moustique
|
||||
\item Une feuille A4
|
||||
\item Un souris
|
||||
\item La Lune
|
||||
\item La population mondiale
|
||||
\item Un être humain
|
||||
\item Une baleine
|
||||
\item Le Titanic
|
||||
\item La Terre
|
||||
\item L'eau dans les océans
|
||||
\item Le Soleil
|
||||
\item Un atome d'hydrogène
|
||||
\item La production mondiale de pétrole annuelle
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\item Données de longueurs (en m):
|
||||
\begin{multicols}{3}
|
||||
\begin{enumerate}
|
||||
\item Distance à l'étoile la plus proche
|
||||
\item Un virus
|
||||
\item Une fourmi
|
||||
\item Distance de la Terre au Soleil
|
||||
\item Un immeuble
|
||||
\item Taille d'un stade
|
||||
\item L'Everest
|
||||
\item Un être humain
|
||||
\item Un marathon
|
||||
\item Diamètre de la Voie Lactée
|
||||
\item Rayon de la Terre
|
||||
\item Circonférence de la Terre
|
||||
\item Distance de la Terre à la Lune
|
||||
\item Distance au centre de la Voie Lactée
|
||||
\item Rayon d'un atome
|
||||
\item Diamètre d'un cheveux
|
||||
\item Distance à la galaxie d'Andromède
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{itemize}
|
||||
\vfill
|
||||
\setcounter{question}{0}
|
||||
\question
|
||||
Placer les éléments suivants sur des échelles de grandeurs.
|
||||
|
||||
\begin{itemize}
|
||||
\item Données de masses (en kg):
|
||||
\begin{multicols}{3}
|
||||
\begin{enumerate}
|
||||
\item Un litre d'eau
|
||||
\item Un virus
|
||||
\item La Voie Lactée
|
||||
\item Une cellule
|
||||
\item Un moustique
|
||||
\item Une feuille A4
|
||||
\item Un souris
|
||||
\item La Lune
|
||||
\item La population mondiale
|
||||
\item Un être humain
|
||||
\item Une baleine
|
||||
\item Le Titanic
|
||||
\item La Terre
|
||||
\item L'eau dans les océans
|
||||
\item Le Soleil
|
||||
\item Un atome d'hydrogène
|
||||
\item La production mondiale de pétrole annuelle
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\item Données de longueurs (en m):
|
||||
\begin{multicols}{3}
|
||||
\begin{enumerate}
|
||||
\item Distance à l'étoile la plus proche
|
||||
\item Un virus
|
||||
\item Une fourmi
|
||||
\item Distance de la Terre au Soleil
|
||||
\item Un immeuble
|
||||
\item Taille d'un stade
|
||||
\item L'Everest
|
||||
\item Un être humain
|
||||
\item Un marathon
|
||||
\item Diamètre de la Voie Lactée
|
||||
\item Rayon de la Terre
|
||||
\item Circonférence de la Terre
|
||||
\item Distance de la Terre à la Lune
|
||||
\item Distance au centre de la Voie Lactée
|
||||
\item Rayon d'un atome
|
||||
\item Diamètre d'un cheveux
|
||||
\item Distance à la galaxie d'Andromède
|
||||
\end{enumerate}
|
||||
\end{multicols}
|
||||
\end{itemize}
|
||||
\end{questions}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
52
3e/Unites_et_grandeurs/Changement_unites/index.rst
Normal file
52
3e/Unites_et_grandeurs/Changement_unites/index.rst
Normal file
@@ -0,0 +1,52 @@
|
||||
Notes sur le chapitre unité et notation scientifique
|
||||
####################################################
|
||||
|
||||
:date: 2015-10-20
|
||||
:modified: 2015-10-20
|
||||
:category: 3e
|
||||
:tags: Unites et grandeurs
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Notes sur le chapitre sur le changement d'unité et la notation scientifique.
|
||||
|
||||
Séquence 1
|
||||
==========
|
||||
|
||||
Cours: Changement d'unité (simples, surfacique, volumique)
|
||||
|
||||
Exercice: Exercice du cocktail et des verres.
|
||||
On donne l'exercice et on les laisse se démerder! Puis après un peu de temps, quand on commence à voir de bonnes choses émerger et d'autres bien galérer, on prend les bonnes idées que l'on reprend au tableau sans bien sûr terminer soit même. On les laisse finir.
|
||||
|
||||
Séquence 2
|
||||
==========
|
||||
|
||||
Objectifs: Écrire des chiffres à avec trop de 0 (pour laisser on espère surgir les puissances de 10 vues l'année dernière) et donner des exemples d'ordre de grandeur.
|
||||
|
||||
Cette activité se fait en groupe, il faut placer les éléments de grandeurs/nombres sur un axe gradué logarithmiquement (on explique le procédé de construction sans le faire entièrement au tableau). Pour la plénière, si aucun élève n'a utilisé les puissances de 10, on gradue avec des puissances de 10. Les valeurs des éléments seront alors données en notation scientifique, quelques uns pourront être mis en notation "classique", le reste sera à faire.
|
||||
|
||||
En bonus, on leurs demande par groupe de proposer quelque chose de plus grand que tout et quelque chose de plus petit que tout. Mis en commun en pleinière.
|
||||
|
||||
Séquence 3
|
||||
==========
|
||||
|
||||
Exercice sur la taille des planètes. On explique pas comment faire ces calculs, on les laisse revenir à la définition avec tous les 0!
|
||||
|
||||
Ce sera la moment aussi de parler de la réponse de la calculatrice pour la notation scientifique. Et de faire un peu de cours pour fixer ça.
|
||||
|
||||
Séquence 4
|
||||
==========
|
||||
|
||||
Cours sur le notation scientifique
|
||||
|
||||
Définition:
|
||||
Tous les nombres peuvent être écrit en *notation scientifique*. C'est à dire sous la forme
|
||||
|
||||
a*10^n avec a un nombre avec un seul chiffre non nul avant la virgule et n un entier.
|
||||
|
||||
Exemples:
|
||||
3,456*10^2 est l'écriture scientifique de 345,6
|
||||
3,456*10^{-4} est l'écriture scientifique de 0,0003456
|
||||
0,456*10^4 n'est pas un nombre en écriture scientifique.
|
||||
234,4565*10^4 n'est pas un nombre en écriture scientifique.
|
||||
|
||||
Exercices techniques sur la notation scientifique.
|
||||
|
||||
Reference in New Issue
Block a user