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index 0000000..0227d02 --- /dev/null +++ b/3e/Nombres_Calculs/Nombres_premiers_fractions/E1_partages_equitables.tex @@ -0,0 +1,51 @@ +\documentclass[a4paper,12pt]{article} +\usepackage{myXsim} + +\title{Nombre premiers - Exercices} +\tribe{Troisième} +\date{Mars 2018} + +\pagestyle{empty} + +\begin{document} + +\begin{exercise}[subtitle={Partages équitables \Cal \Rai}] + Abdou a 24 fleurs, Mariam a 16 fleurs et Roubouanti en a 29. Chacun veut partager ses fleurs. + + Abdou anonce: + \begin{quote} + \textit{Si on est 6 ou 8, je peux partager mes fleurs équitablement} + \end{quote} + + Mariam continue + \begin{quote} + \textit{Il faut forcement que l'on soit 4 ou 8 pour pouvoir partager les miennes équitablement. C'est la seule solution.} + \end{quote} + + Roubouanti conclut + \begin{quote} + \textit{Quelque soit le nombre de personnes, je ne pourrai jamais partager mes fleurs équitablement.} + \end{quote} + + Que pensez vous de ces affirmations? + +\end{exercise} + +\begin{exercise}[subtitle={Aucun reste! }] + Au supermarché, le jambon est vendu par paquets de 6 tranches et le pain de mie par paquets de 20 tranches. J'aime me faire des sandwichs avec une tranche de jambon et 2 tranches de pain de mie. + + Je n'aime pas gaspiller et je ne veux donc pas de reste. Combien de paquet de chaque dois-je acheter? Combien de sandwichs vais-je pouvoir me faire? +\end{exercise} + +\vfill +\printexercise{exercise}{1} +\printexercise{exercise}{2} +\vfill + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/3e/Nombres_Calculs/Nombres_premiers_fractions/E2_crible_eratostene.pdf b/3e/Nombres_Calculs/Nombres_premiers_fractions/E2_crible_eratostene.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c4ce6540311e1b67eb38d657be2592a2980ca453 GIT binary patch literal 34860 zcmcG$W0)n~vNgKOwr$(CtGaA;b=kIU8(p?-8(p?-+xmLHXYYHz=bZcF{JHDb%vd>R zW~_)9IY*3q7MX&mI2{u`8#LL>!q5sdCm|!Dt$_tJFE2F14`UlsCo@78c20J}e?HI* z;^tOP#twuG;#T@j#-hfCwnoO#{QS_4P7cQU*3fQiRasJwI1*B@wnED%6Q;uT9j zW13A0F(o*04e!a{0P%4_kakFdQzysrYU(BpFrd(=-Sr57I-|#D>WYe-RzX!gYE|!6 zh4+>wm#+Hc@~-;~8*am{s^*7_UDK}@yW8=@q4np7ID6;yruOy^9dq^bCADUA%VRHR zcV+L)uJvjGYqk4e^T&&$$>c?kj?9*Zk+z)8Yy4xa$?8gV*NRuY)SjOo=XU|ax!=x* z-rCA}bt{jTLoJbOaMO2_H*wdN=PEqBj9v2b-Jj1@)nD$uw*+tBTxGU6%ZhQs7VA+h 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a/3e/Nombres_Calculs/Nombres_premiers_fractions/E2_crible_eratostene.tex b/3e/Nombres_Calculs/Nombres_premiers_fractions/E2_crible_eratostene.tex new file mode 100644 index 0000000..52027c5 --- /dev/null +++ b/3e/Nombres_Calculs/Nombres_premiers_fractions/E2_crible_eratostene.tex @@ -0,0 +1,88 @@ +\documentclass[a5paper,12pt, landscape]{article} +\usepackage{myXsim} + +\title{Crible d'Ératostène \hfill \icon{abstract-002}} +\tribe{Troisième} +\date{Mars 2018} + +\pagestyle{empty} +\geometry{left=5mm,right=5mm, bottom= 10mm, top=10mm} + +% Construction du tableau avec les nombre de 1 à 100 +\newcommand{\numInBox}[1]{% + \framebox{\parbox[][14pt][b]{1.2em}{% + \centering% + #1% + }}% +} + +\newcounter{clig} +\newcounter{ccol} +\newcounter{cligmax} +\newcounter{ccolmax} +\newcounter{csym} +\newcommand{\range}[3]{% + % #1 min, #3 nbr ligne, #4 nbr col + \setcounter{clig}{0}% Mise à zéro des compteurs de ligne + \setcounter{ccol}{0}% et de colonne + \setcounter{cligmax}{#2}% arguments 3 et 4 pour fixer + \setcounter{ccolmax}{#3}% le nombre max de colonnes et de lignes + \whiledo{\value{clig}<\value{cligmax}}{% + \setcounter{ccol}{0}% remise à zéro du compteur de colonne + \whiledo{\value{ccol}<\value{ccolmax}}{% + % on calcule le numéro du symbole + \setcounter{csym}{% + \value{clig}*\value{ccolmax}+\value{ccol}+#1} + \numInBox{\thecsym} + \stepcounter{ccol}% + }% on passe à la colonne suivante + \stepcounter{clig}% on passe à la ligne suivante + % on saute une ligne , sauf à la fin + \ifthenelse{\value{clig}<\value{cligmax}}{\\}{}% +}} + + +\begin{document} + +\maketitle + +On cherche à découvrir une famille de nombres aux propriétés très particulières, \textbf{les nombres premiers}. + +\begin{multicols}{2} + + \begin{center} + \range{1}{10}{10} + \end{center} + + + \columnbreak + + \Ovalbox{% + \begin{minipage}{0.42\textwidth} + \hspace{0.2cm} + \textbf{Algorithme du Crible} + \begin{itemize} + \item Sélectionner un nombre. + \item S'il n'est pas barré, l'entourer. + \item Barrer tous les multiples de ce nombre. + \end{itemize} + \end{minipage} + } + +\begin{enumerate} + \item Appliquer cet algorithme à 2. + \item Appliquer cet algorithme à 3. + \item Appliquer cet algorithme à 4. + \item Appliquer cet algorithme aux autres nombres dans l'ordre croissant. + \item Faire la liste de tous les nombres entourés. Ce sont tous les nombres premiers inférieur à 100. + \item Écrire une phrase expliquant ce qui lie tous ces nombres. +\end{enumerate} +\end{multicols} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/3e/Nombres_Calculs/Nombres_premiers_fractions/exercises/E1_partages_equitables-exercise-1-exercise-body.tex b/3e/Nombres_Calculs/Nombres_premiers_fractions/exercises/E1_partages_equitables-exercise-1-exercise-body.tex new file mode 100644 index 0000000..65f3e76 --- /dev/null +++ b/3e/Nombres_Calculs/Nombres_premiers_fractions/exercises/E1_partages_equitables-exercise-1-exercise-body.tex @@ -0,0 +1,29 @@ +% ------------------------------------------------------------------------ +% file `E1_partages_equitables-exercise-1-exercise-body.tex' +% in folder `exercises/' +% +% exercise of type `exercise' with id `1' +% +% generated by the `exercise' environment of the +% `xsim' package v0.11 (2018/02/12) +% from source `E1_partages_equitables' on 2018/03/15 on line 12 +% ------------------------------------------------------------------------ + Abdou a 24 fleurs, Mariam a 16 fleurs et Roubouanti en a 29. Chacun veut partager ses fleurs. + + Abdou anonce: + \begin{quote} + \textit{Si on est 6 ou 8, je peux partager mes fleurs équitablement} + \end{quote} + + Mariam continue + \begin{quote} + \textit{Il faut forcement que l'on soit 4 ou 8 pour pouvoir partager les miennes équitablement. C'est la seule solution.} + \end{quote} + + Roubouanti conclut + \begin{quote} + \textit{Quelque soit le nombre de personnes, je ne pourrai jamais partager mes fleurs équitablement.} + \end{quote} + + Que pensez vous de ces affirmations? + diff --git a/3e/Nombres_Calculs/Nombres_premiers_fractions/exercises/E1_partages_equitables-exercise-2-exercise-body.tex b/3e/Nombres_Calculs/Nombres_premiers_fractions/exercises/E1_partages_equitables-exercise-2-exercise-body.tex new file mode 100644 index 0000000..ff2ca60 --- /dev/null +++ b/3e/Nombres_Calculs/Nombres_premiers_fractions/exercises/E1_partages_equitables-exercise-2-exercise-body.tex @@ -0,0 +1,13 @@ +% ------------------------------------------------------------------------ +% file `E1_partages_equitables-exercise-2-exercise-body.tex' +% in folder `exercises/' +% +% exercise of type `exercise' with id `2' +% +% generated by the `exercise' environment of the +% `xsim' package v0.11 (2018/02/12) +% from source `E1_partages_equitables' on 2018/03/15 on line 34 +% ------------------------------------------------------------------------ + Au supermarché, le jambon est vendu par paquets de 6 tranches et le pain de mie par paquets de 20 tranches. J'aime me faire des sandwichs avec une tranche de jambon et 2 tranches de pain de mie. + + Je n'aime pas gaspiller et je ne veux donc pas de reste. Combien de paquet de chaque dois-je acheter? Combien de sandwichs vais-je pouvoir me faire? diff --git a/3e/Nombres_Calculs/Nombres_premiers_fractions/index.rst b/3e/Nombres_Calculs/Nombres_premiers_fractions/index.rst new file mode 100644 index 0000000..a642bb0 --- /dev/null +++ b/3e/Nombres_Calculs/Nombres_premiers_fractions/index.rst @@ -0,0 +1,34 @@ +Nombres premiers et fractions irreductibles avec les 3e pour l'année 2017-2018 +############################################################################## + +:date: 2018-03-15 +:modified: 2018-03-15 +:tags: Nombres et opérations, Fraction, Nombre premier +:category: 3e +:authors: Bertrand Benjamin +:summary: Notes sur le chapitre autour des fractions irréductibles et des nombres premiers pour les 3e pour l'année 2017-2018 + +Étape 1 +======= + +`Problèmes de partages <./E1_partages_equitables.pdf>`_ pour rappeler le vocabulaire "diviseur", "multiple". + +Les commentaires autour du commentaire de Roubouanti mène à la définition des nombres premiers. + +Étape 2 +======= + +Recherche des nombres premiers par un algorithme: `Crible d'Ératostène <./crible_eratostene.pdf>`_. + +Étape 3 +======= + +Découverte de la réduction des fractions. On donne une fraction (30/35 ou 85/180) au tableau et on demande de trouver d'autres fractions avec le plus petit dénominateur possible et d'expliquer la démarche. + +Dans le cahier de bord, on laisse un trace en parlant de diviseur et une justification de la méthode où on barre. L'intérêt de décomposer en produit de facteur est aussi mis en valeur. + +Étape 4 (sur la durée) +====================== + +Décomposition en produit de facteurs et réduction de fraction (à balancer au tableau). +