diff --git a/1ST/02_Generalites_sur_les_fonctions/1B_representations.pdf b/1ST/02_Generalites_sur_les_fonctions/1B_representations.pdf index 49b0581..4c4d472 100644 Binary files a/1ST/02_Generalites_sur_les_fonctions/1B_representations.pdf and b/1ST/02_Generalites_sur_les_fonctions/1B_representations.pdf differ diff --git a/2nd/01_Proportion_et_fractions/1B_proportion.pdf b/2nd/01_Proportion_et_fractions/1B_proportion.pdf index ce73284..6363cf9 100644 Binary files a/2nd/01_Proportion_et_fractions/1B_proportion.pdf and b/2nd/01_Proportion_et_fractions/1B_proportion.pdf differ diff --git a/2nd/01_Proportion_et_fractions/1B_proportion.tex b/2nd/01_Proportion_et_fractions/1B_proportion.tex index aa8807a..9efab74 100644 --- a/2nd/01_Proportion_et_fractions/1B_proportion.tex +++ b/2nd/01_Proportion_et_fractions/1B_proportion.tex @@ -2,7 +2,7 @@ \usepackage{myXsim} \author{Benjamin Bertrand} -\title{Proportion et fréquence - Cours} +\title{Proportion et fractions - Cours} \date{Septembre 2022} \pagestyle{empty} @@ -31,12 +31,12 @@ circle, minimum size =3cm, fill=blue!50, - label={45:$B$}] (circleB) at (0,0.5){}; + label={45:$A$}] (circleB) at (0,0.5){}; \node[draw, circle, minimum size =2cm, fill=orange!80, - label={135:$A$}] (circleA) at (0,0.2){}; + label={135:$B$}] (circleA) at (0,0.2){}; \end{tikzpicture} diff --git a/2nd/01_Proportion_et_fractions/1E_proportion.pdf b/2nd/01_Proportion_et_fractions/1E_proportion.pdf index d259848..364eead 100644 Binary files a/2nd/01_Proportion_et_fractions/1E_proportion.pdf and b/2nd/01_Proportion_et_fractions/1E_proportion.pdf differ diff --git a/2nd/01_Proportion_et_fractions/2B_proportion_quantite.pdf b/2nd/01_Proportion_et_fractions/2B_proportion_quantite.pdf index d0c815f..2244e43 100644 Binary files a/2nd/01_Proportion_et_fractions/2B_proportion_quantite.pdf and b/2nd/01_Proportion_et_fractions/2B_proportion_quantite.pdf differ diff --git a/2nd/01_Proportion_et_fractions/2B_proportion_quantite.tex b/2nd/01_Proportion_et_fractions/2B_proportion_quantite.tex index 055da5a..8bda0e2 100644 --- a/2nd/01_Proportion_et_fractions/2B_proportion_quantite.tex +++ b/2nd/01_Proportion_et_fractions/2B_proportion_quantite.tex @@ -2,7 +2,7 @@ \usepackage{myXsim} \author{Benjamin Bertrand} -\title{Proportion et fréquence - Cours} +\title{Proportion et fractions - Cours} \date{Septembre 2022} \pagestyle{empty} diff --git a/2nd/01_Proportion_et_fractions/3B_proportion_de_proportion.pdf b/2nd/01_Proportion_et_fractions/3B_proportion_de_proportion.pdf new file mode 100644 index 0000000..cbd5dfa Binary files /dev/null and b/2nd/01_Proportion_et_fractions/3B_proportion_de_proportion.pdf differ diff --git a/2nd/01_Proportion_et_fractions/3B_proportion_de_proportion.tex b/2nd/01_Proportion_et_fractions/3B_proportion_de_proportion.tex new file mode 100644 index 0000000..c2738fa --- /dev/null +++ b/2nd/01_Proportion_et_fractions/3B_proportion_de_proportion.tex @@ -0,0 +1,65 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Proportion et fractions - Cours} +\date{Septembre 2022} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\setcounter{section}{2} +\section{Proportion d'une proportion} + +\begin{propriete}[ Proportion d'une quantité] + \begin{minipage}{0.7\linewidth} + Soient $A$, $B$ et $C$ trois ensembles tels que $C \subset B \subset A$. + + On note + \begin{itemize} + \item $p$ la proportion de $B$ dans $A$. + \item $p'$ la proportion de $C$ dans $B$. + \end{itemize} + + Alors la proportion de $C$ dans $A$ est + \[ + p \times p' + \] + \end{minipage} + \hfill + \begin{minipage}{0.3\linewidth} + \begin{tikzpicture} + \node[draw, + circle, + minimum size =3cm, + fill=blue!50, + label={45:$C$}] (circleB) at (0,0.5){}; + \node[draw, + circle, + minimum size =2cm, + fill=orange!80, + label={135:$B$}] (circleA) at (0,0.2){}; + \node[draw, + circle, + minimum size =1.2cm, + fill=green!80, + label={-80:$C$}] (circleA) at (0,0.3){}; + + \end{tikzpicture} + \end{minipage} +\end{propriete} + +\paragraph{Exemple:} + +\begin{enumerate} + \item Dans un lycée, il y a 40\% des élèves qui sont en filières technologiques. Dans les filières technologiques, 35\% sont des garçons. Quel est la proportion de garçon en filières technologiques dans le lycée? + + \afaire{ + \vspace{2cm} + } +\end{enumerate} + +\end{document} diff --git a/2nd/01_Proportion_et_fractions/4E_fraction_egyptiennes.odp b/2nd/01_Proportion_et_fractions/4E_fraction_egyptiennes.odp deleted file mode 100644 index b40ce51..0000000 Binary files a/2nd/01_Proportion_et_fractions/4E_fraction_egyptiennes.odp and /dev/null differ diff --git a/2nd/01_Proportion_et_fractions/4E_fraction_egyptiennes.pdf b/2nd/01_Proportion_et_fractions/4E_fraction_egyptiennes.pdf deleted file mode 100644 index ec450ec..0000000 Binary files a/2nd/01_Proportion_et_fractions/4E_fraction_egyptiennes.pdf and /dev/null differ diff --git a/2nd/01_Proportion_et_fractions/4P_fraction_egyptiennes.pdf b/2nd/01_Proportion_et_fractions/4P_fraction_egyptiennes.pdf new file mode 100644 index 0000000..2aeed21 Binary files /dev/null and b/2nd/01_Proportion_et_fractions/4P_fraction_egyptiennes.pdf differ diff --git a/2nd/01_Proportion_et_fractions/all_exercises.pdf b/2nd/01_Proportion_et_fractions/all_exercises.pdf index 98267dd..b51fd00 100644 Binary files a/2nd/01_Proportion_et_fractions/all_exercises.pdf and b/2nd/01_Proportion_et_fractions/all_exercises.pdf differ diff --git a/2nd/01_Proportion_et_fractions/exercises.tex b/2nd/01_Proportion_et_fractions/exercises.tex index a868d2f..f206caf 100644 --- a/2nd/01_Proportion_et_fractions/exercises.tex +++ b/2nd/01_Proportion_et_fractions/exercises.tex @@ -173,3 +173,55 @@ \end{itemize} Sur l'ensemble de ces quatre mois, quel a été le pourcentage de photos réussies? \end{exercise} + +% ---------------- +% 2E proportion de proportions +\begin{exercise}[subtitle={Proportions emboités}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] +\end{exercise} + +% ---------------- +% 3E Fractions égyptiennes +\begin{exercise}[subtitle={Fraction égyptienne}, step={3}, origin={???}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] + \begin{enumerate} + \item Est-il possible de trouver deux nombres entiers distincts $a$ et $b$ tels que: + \[ + \frac{1}{a} + \frac{1}{b} = 1 + \] + \item Est-il possible de trouver deux nombres entiers distincts $a$, $b$ et $c$ tels que: + \[ + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 1 + \] + \item Avec 4 nombres? 5? Et plus? + \end{enumerate} +\end{exercise} + +\begin{hint} + \begin{enumerate} + \item Pliez les disques en parties égale de + \begin{multicols}{6} + 2 morceaux + + 3 morceaux + + 4 morceaux + + 8 morceaux + + 12 morceaux + \end{multicols} + \item Indiquez sur les disques les fractions correspondantes + \[ + \frac{1}{2} \qquad + \frac{1}{3} \qquad + \frac{1}{4} \qquad + \frac{1}{8} \qquad + \frac{1}{12} \qquad + \] + \item Reconstituez un disque complet à l'aide de 3 portions. + \item Reconstituez un disque complet à l'aide de 4 portions. + \item Utilisez votre matériel pour répondre au problème initial. + \end{enumerate} +\end{hint} + +\begin{exercise}[subtitle={Technique}, step={3}, origin={Création}, topics={ Proportion et fractions }, tags={ Statistiques, Fractions }, mode={\searchMode}] +\end{exercise} diff --git a/2nd/01_Proportion_et_fractions/index.rst b/2nd/01_Proportion_et_fractions/index.rst index 964459b..717b8b7 100644 --- a/2nd/01_Proportion_et_fractions/index.rst +++ b/2nd/01_Proportion_et_fractions/index.rst @@ -111,5 +111,18 @@ Le livre MEpC propose des automatismes reprenant le principe de démonstration. Étape 3: Proportion de proportion et multiplication des fractions ----------------------------------------------------------------- +Bilan sur les proportions de proportions + +.. image:: ./3B_proportion_de_proportion.pdf + :height: 200px + :alt: Bilan sur les proportions de proportions + + Étape 4: Addition/soustraction de fractions ------------------------------------------- + +Activité des fractions égyptiennes + +.. image:: ./4P_fraction_egyptiennes.pdf + :height: 200px + :alt: Document de présentation des fractions égyptiennes diff --git a/2nd/01_Proportion_et_fractions/solutions.pdf b/2nd/01_Proportion_et_fractions/solutions.pdf index 6e81374..5d18ea9 100644 Binary files a/2nd/01_Proportion_et_fractions/solutions.pdf and b/2nd/01_Proportion_et_fractions/solutions.pdf differ