import work from year 2016-2017
This commit is contained in:
Benjamin Bertrand
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5e/Nombres_et_calculs/Divisibilite/corr_compete_hand.xlsx
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5e/Nombres_et_calculs/Divisibilite/corr_compete_hand.xlsx
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5e/Nombres_et_calculs/Divisibilite/definitions.pdf
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5e/Nombres_et_calculs/Divisibilite/definitions.tex
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5e/Nombres_et_calculs/Divisibilite/definitions.tex
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\documentclass[a5paper,12pt]{/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{Divisibilité - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Cinquième}
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\date{Septembre 2016}
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\renewcommand{\arraystretch}{1.3}
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\newcommand{\ladef}{%
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\section*{Définitions}
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\begin{itemize}
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\item Une \textbf{somme} est \makebox[4cm]{\dotfill} de plusieurs chiffres. \\
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\item Une \textbf{différence} est \makebox[4cm]{\dotfill} de deux chiffres. \\
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\item Un \textbf{produit} est \makebox[4cm]{\dotfill} de plusieurs chiffres. \\
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\item Un \textbf{quotient} est \makebox[4cm]{\dotfill} de deux chiffres.
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\end{itemize}
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}
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5e/Nombres_et_calculs/Divisibilite/definitions_a4.pdf
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5e/Nombres_et_calculs/Divisibilite/facture.ods
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5e/Nombres_et_calculs/Divisibilite/facture.pdf
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5e/Nombres_et_calculs/Divisibilite/facture.tex
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5e/Nombres_et_calculs/Divisibilite/facture.tex
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\documentclass[a4paper,10pt]{/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{Divisibilité - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Cinquième}
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\date{Septembre 2016}
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\renewcommand{\arraystretch}{1.3}
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\newcommand{\lexo}{%
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\setcounter{exo}{0}
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\begin{Exo}[Facture au camping]
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Voici les tarifs d'un camping pour l'été 2013
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\begin{center}
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\begin{tabular}{|*{3}{m{4cm}|}}
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\hline
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\multicolumn{3}{|c|}{\textbf{Par nuitée}} \\
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\hline
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Adulte: 8\euro (à partir de 7ans) & Voiture: 3\euro & Emplacement: 4\euro \\
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\hline
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\multicolumn{3}{|c|}{Les enfants de moins de 7 ans paient la moitié du tarif adulte.} \\
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\hline
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\end{tabular}
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\end{center}
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\begin{enumerate}
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\item Une famille composée de deux parents et de deux enfants de 3ans et de 8ans séjourne au camping avec une voiture du 6juillet au 15 juillet. Quel est le montant total à payer par cette famille?
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\item Le gérant du camping prépare un fichier de tableur pour pouoir donner rapidement des factures à ses clients au moment du paiement. Reproduit le tableau et complète-le pour que le monant à payer soit calculé automatiquement pour n'importe quelle famille.
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\end{enumerate}
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\end{Exo}
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}
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5e/Nombres_et_calculs/Divisibilite/facture_tableur.pdf
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5e/Nombres_et_calculs/Divisibilite/facture_tableur.pdf
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5e/Nombres_et_calculs/Divisibilite/index.rst
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5e/Nombres_et_calculs/Divisibilite/index.rst
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Notes sur le chapitre autour des diviseur pour les 5e
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#####################################################
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:date: 2016-08-27
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:modified: 2016-08-27
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:tags: Nombres et calculs, divisibilite
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:category: 5e
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:authors: Bertrand Benjamin
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:summary: Le chapitre autour du des 4 opérations et des diviseurs pour les 5e.
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Objectifs du chapitre
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=====================
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- Rédiger un réponse à problème de calcul
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- Utiliser correctement les 4 opérations
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- Vocabulaire somme, différence, produit, quotient, diviseur
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Progression
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===========
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Séance 1
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--------
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On distribue une `première liste de problème <./pb_4operations.pdf>`_. Chaque travail individuellement, puis en groupe. Un trace sur le cahier de groupe est rédigé pour chaque problème.
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Cette séance est mené en parallèle d'autres séance sur la durée.
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Séance 2
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--------
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On s'attaque maintenant à un `problème de partage <./pb_partage.pdf>` pour faire ressortir la notion de diviseur.
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On note une "correction" de l'exercice sur les équipes et on colle les `définitions à completer <./definitions.pdf`>_ sur la cahier de bord.
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Séance 3
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--------
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Problème de `division euclidienne <./pb_division_eucl.pdf>`_ quand les partages équitables sont impossibles.
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Séance 4
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--------
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Initiation aux `Kenken <www.kenken.com>`_ pour préparer du travail sur la durée.
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Travail sur cette `fiche kenken <./kenken.pdf>`_.
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Séance TICE
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-----------
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Introduction au tableur avec un `exercice de facture <./facture.pdf>`_
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Trace sur le cahier de bord
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===========================
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- Rédiger une réponse à une question
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- Vocabulaire somme, différence, produit, quotient, diviseur
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- La division euclidienne.
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5e/Nombres_et_calculs/Divisibilite/kenken.pdf
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5e/Nombres_et_calculs/Divisibilite/kenken.svg
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5e/Nombres_et_calculs/Divisibilite/kenken_a4.pdf
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5e/Nombres_et_calculs/Divisibilite/pb_4operations.pdf
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5e/Nombres_et_calculs/Divisibilite/pb_4operations.tex
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5e/Nombres_et_calculs/Divisibilite/pb_4operations.tex
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\documentclass[a4paper,10pt]{/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{Divisibilité - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Cinquième}
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\date{Septembre 2016}
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\newcommand{\lexo}{%
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\setcounter{exo}{0}
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\begin{Exo}
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Répond à la question tout seul, puis en groupe rédiger une réponse commune sur le cahier de groupe.
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\begin{enumerate}
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\item Dans une classe de sixième, il y a 16 garçons et 13 filles. L’élève le plus jeune est un garçon.
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Combien y a-t-il d'élèves dans la classe ?
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\item Au café, Thierry, Mathieu et Abdelkrim ont consommé chacun une limonade à 2,5 €. Thierry paie la note avec un billet de 20 €.
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Combien lui rend-on?
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\item Le cuisinier du collège a 17 litres de lait entier et 20 litres de lait écrémé dans sa réserve. Il utilise 11 litres de lait entier pour préparer une purée.
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Combien lui reste-t-il de lait entier ?
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\item Pour tapisser la salle à manger, un couple achète 8 rouleaux de papier à 7 € pièce et un pot de colle à 26,20 €.
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Combien dépensent-ils?
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\item Combien vaut la moitié de la moitié d’une heure?
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\item Un coureur fait 5 tours sur une piste d’athlétisme de 400m.
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Combien de kilomètres a-t-il parcourus?
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\end{enumerate}
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\end{Exo}
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}
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5e/Nombres_et_calculs/Divisibilite/pb_division_eucl.pdf
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5e/Nombres_et_calculs/Divisibilite/pb_division_eucl.tex
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\documentclass[a4paper,10pt]{/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{Divisibilité - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Cinquième}
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\date{Septembre 2016}
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\newcommand{\lexo}{%
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\setcounter{exo}{0}
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\begin{Exo}
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On organise une grande compétition de handball dans un college. Pour cela, il faut faire des équipes de 12 élèves. Voici le nombre d'élèves de chaque niveau:
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\begin{center}
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\begin{tabular}{|c|*{5}{c|}}
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\hline
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Niveau & 6e & 5e & 4e & 3e \\
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\hline
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Nombre d'élève & 354 & 366 & 298 & 410 \\
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\hline
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\end{tabular}
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\end{center}
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\begin{enumerate}
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\item Combien d'équipe peut-on faire avec les 6e? Combien d'élèves n'auront pas d'équipe?
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\item Même questions pour les autres classes.
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\item On mélange ensemble tous les élèves qui n'ont pas d'équipe. On veut faire des équipes d'arbitres. Combien d'équipes d'arbitres peut-on faire?
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\end{enumerate}
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\end{Exo}
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\begin{Exo}
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Une maîtresse d'école souhaite que ses 25 élèves l'aident à tailler ses 318 crayons.
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Elle prépare ainsi 25 tas de crayons, avec le même nombre de crayons dans chaque tas, et elle met le plus de crayons possibles dans chaque tas.
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\begin{enumerate}
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\item Combien de crayons la maîtresse doit-elle tailler elle-même ?
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\item Quand les élèves arrivent en classe, elle constate que Marie est absente et que seuls 24 élèves vont pouvoir tailler les crayons.
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Comment peut-elle modifier ses 25 tas pour en faire 24 tas avec le même nombre de crayons sans se fatiguer?
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\end{enumerate}
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\end{Exo}
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}
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5e/Nombres_et_calculs/Divisibilite/pb_partage.pdf
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5e/Nombres_et_calculs/Divisibilite/pb_partage.tex
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\documentclass[a4paper,12pt]{/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{Divisibilité - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Cinquième}
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\date{Septembre 2016}
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\newcommand{\lexo}{%
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\begin{Exo}
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Répond à la question tout seul, puis en groupe rédiger une réponse commune sur le cahier de groupe.
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\begin{enumerate}
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\item Mariama a 12 oeufs. Elle a mis 4 oeufs dans chaque panier. Combien de paniers a-t-elle?
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\item Dans un hôtel, on veut mettre 240 chambres réparties équitablement entre 7 étages. Combien y aura-t-il de chambre par étages?
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\item Dans une classe, il y a 28 élèves. Le professeur veut faire des équipes avec autant d'élèves. Quelles possibilités a-t-il pour faire ces équipes?
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\item Pour préparer une réunion en salle de permanence, le principal a 32 chaises. Il veut faire des rangées avec autant de chaises. Comment peut-il ranger ces chaises?
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\item Quand Mme Abdou prepare à manger pour ses enfants, elle prend soin que chacun ait autant de bananes et de mabawas et que rien ne soit jeté. Aujourd'hui pour le repas de ses enfants, elle a acheté 60 mabawas et 42 bananes.
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\begin{enumerate}
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\item Combien a-t-elle d'enfants?
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\item On donne un indice supplementaire, elle n'a eu que des jumeaux. Affiner votre réponse à la question précédente.
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\end{enumerate}
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\end{enumerate}
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\end{Exo}
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}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
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% Title Page
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\titre{Enchainement des opérations - Exercices}
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Cinquième}
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\date{Janvier 2017}
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\renewcommand{\arraystretch}{1.3}
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\newcommand{\lexo}{%
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\begin{Exo}[Grands calculs]
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Écris les calculs directement (sans calculatrice)
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\begin{tabular}{|*{4}{m{4cm}|}}
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\hline
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$A = 3 + 543 + 997 $ & $B = 25 \times 33\times 4 $ & $C = (3+4)\times8 $& $D = (3+4)\times(7-2) $ \\
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\hline
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$E = 43 - 9 + 1$ & $F = 18 - 2 - 9$ & $G = 4\times6 \div 2$& $H = 15 \div 3 \times 3$ \\
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\hline
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\end{tabular}
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\end{Exo}
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}
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\documentclass[a4paper,12pt]{/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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|
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% Title Page
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||||
\titre{Enchainement des opérations - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
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\classe{Cinquième}
|
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\date{Janvier 2017}
|
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|
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\renewcommand{\arraystretch}{1.3}
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\newcommand{\lexo}{%
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\setcounter{exo}{0}
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\begin{Exo}[D'autres priorités]
|
||||
Écris les calculs directement (sans calculatrice)
|
||||
|
||||
\begin{tabular}{|*{4}{m{4cm}|}}
|
||||
\hline
|
||||
$A = 3 \times 2 + 5$ & $B = 4 + 2 \times 5$ & $C = 10 - 2 \times 3$& $D = 2\times3 + 4\times5$ \\
|
||||
\hline
|
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\end{tabular}
|
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\end{Exo}
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}
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\pagestyle{empty}
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\begin{document}
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\lexo
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\vfill
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\lexo
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\vfill
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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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|
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44
5e/Nombres_et_calculs/Enchainement_operations/index.rst
Normal file
44
5e/Nombres_et_calculs/Enchainement_operations/index.rst
Normal file
@@ -0,0 +1,44 @@
|
||||
Notes sur l'enchainement des opérations pour les 5e
|
||||
###################################################
|
||||
|
||||
:date: 2017-01-19
|
||||
:modified: 2017-01-19
|
||||
:tags: Nombres et calculs
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur l'enchainement des opérations et sur les priorités de calculs.
|
||||
|
||||
|
||||
Nous avons déjà travaillé sur le sens du signe "=".
|
||||
|
||||
Étape 1
|
||||
-------
|
||||
|
||||
Prise de conscience de la nécessité de conventions de calculs.
|
||||
|
||||
On distribue `une série de calculs <./calculs_p_m_par.tex.pdf>`_ et on se concentre le ceux de la première ligne.
|
||||
|
||||
On constate que quand il n'y a que des additions et des opérations, on peut les faire dans l'ordre que l'on souhaite. Ce qui peut simplifier quelques calculs.
|
||||
|
||||
On établie une convention autour des parenthèses qu'il faut calculer en premier
|
||||
|
||||
Étape 2
|
||||
-------
|
||||
|
||||
On fait la même chose sur la 2e ligne. Pour constater que quand on + et - ou * et / sont mélangé, il faut conserver l'ordre.
|
||||
|
||||
Étape 3
|
||||
-------
|
||||
|
||||
Bilan de cours sur les priorités de calculs. Et on continue à en faire sur la durée lors du calcul mental.
|
||||
|
||||
On peut aussi faire des exercices où il faut ajouter les parenthèses au bon endroit pour trouver le résultat.
|
||||
|
||||
Étape 4
|
||||
-------
|
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|
||||
De la même façon qu'à l'étape 1, on donne des calculs mélangeant + et * .
|
||||
|
||||
`calculs des priorités du x sur + <./calculs_prio_p_m.pdf>`_
|
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|
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On établit les conventions autour des priorités de calculs.
|
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BIN
5e/Nombres_et_calculs/Enchainement_operations/priorite_503.pdf
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5e/Nombres_et_calculs/Enchainement_operations/priorite_503.svg
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BIN
5e/Nombres_et_calculs/Expression_litteral/distance_arret.pdf
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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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|
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% Title Page
|
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\titre{Expression litterale - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
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\classe{Cinquième}
|
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\date{Mars 2017}
|
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|
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\renewcommand{\lexo}{%
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\setcounter{exo}{0}
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\begin{Exo}
|
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\begin{center}
|
||||
{\Large\textbf{Distance d'arrêt}}
|
||||
\end{center}
|
||||
La distance d’arrêt pour un automobiliste est la distance qu'il parcourt entre le moment où il voit un obstacle et le moment où il s’arrête après avoir freiné.
|
||||
La distance d'arrêt, notée $D$, depend de la vitesse du conducteur $V$ et de son état:
|
||||
\begin{itemize}
|
||||
\item Pour un conducteur lucide:
|
||||
\[D = V\div 6 + 0,007\times V^2\]
|
||||
\item Pour un conducteur peu lucide:
|
||||
\[D = V\div 2 + 0,007\times V^2\]
|
||||
\end{itemize}
|
||||
\begin{enumerate}
|
||||
\item Complète le tableau suivant en écrivant les calculs sur ton cahier.
|
||||
|
||||
\hspace{-0.7cm}
|
||||
\begin{tabular}{|m{3.5cm}|*{5}{p{1.3cm}|}}
|
||||
\hline
|
||||
Vitesse $V$ en km/h & 50 & 90 & 100 & 110 & 130 \\
|
||||
\hline
|
||||
Distance $D$ d'arrêt pour le conducteur lucide & & & & & \\
|
||||
\hline
|
||||
Distance $D$ d'arrêt pour le conducteur peu lucide & & & & & \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\item Un conducteur roule à 100 km/h. Un obstacle surgit à 100 m de lui. Pourra-t-il s’arrêter à temps ?
|
||||
\item Un conducteur lucide veut pouvoir s’arrêter en 10 mètres au maximum. Détermine la vitesse qu’il ne doit pas dépasser.
|
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\end{enumerate}
|
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\end{Exo}
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}
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\pagestyle{empty}
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\lexo
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\pagebreak
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\lexo
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\pagebreak
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%%% Local Variables:
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%%% TeX-master: "master"
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%%% End:
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|
||||
34
5e/Nombres_et_calculs/Expression_litteral/index.rst
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34
5e/Nombres_et_calculs/Expression_litteral/index.rst
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|
||||
Notes sur le calcul littéral en 5e
|
||||
##################################
|
||||
|
||||
:date: 2017-02-02
|
||||
:modified: 2017-03-27
|
||||
:tags: Nombres et calculs, Expression littérale
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre d'initiation au calcul littéral en 5e
|
||||
|
||||
|
||||
Nous avons déjà travaillé sur le `sens du signe "=" <../Sens_de_egal_programme_calculs/>`_ et sur `l'enchainement des opérations <../Enchainement_operations>`_.
|
||||
|
||||
Étape 1
|
||||
-------
|
||||
|
||||
Problème ouvert où il faut trouver une façon de compter des carrés de pierre dans un mosaïque.
|
||||
|
||||
`Carré de pierres <./carre_pierres.pdf>`_.
|
||||
|
||||
Les élèves commencent à compter un par un les mozaiques pour chaque carré de pierre. On laisse une trace dans le cahier de bord ce qui permet de quitter la notion du "petit/moyen/grand" carré de pierres.
|
||||
|
||||
On suggère que pour répondre à la question, il faut faire d'autres carrés de pierres (avec remédiation pour les "rectangles" de pierres). On laisse un trace dans le cahier de bord sur d'éventuelles erreurs sur les rectangles.
|
||||
|
||||
Il faut ensuite réussir à faire émerger la notion de formule pour calculer le nombre de mozaiques pour n'importe quel carré de pierre.
|
||||
|
||||
|
||||
Étape 2
|
||||
-------
|
||||
|
||||
Manipulation d'une formule, avec la calculatrice et le tableur, de distance d'arrêt.
|
||||
|
||||
`Distance d'arret <./distance_arret.pdf>`_
|
||||
|
||||
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5e/Nombres_et_calculs/Fraction_decimaux/division17par7.tex
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|
||||
\documentclass[a5paper,12pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classExo}
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\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
|
||||
|
||||
% Title Page
|
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\titre{Fraction et forme décimale - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
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\classe{Cinquième}
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\date{Mai 2017}
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\begin{Exo}[Problèmes qui se ressemblent]
|
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Sans calculatrice répondre aux problèmes suivants.
|
||||
\begin{enumerate}
|
||||
\item Bob partage de manière équitable ses 17 billes entre ses 7 amis. Quelle est la part de chacun ?
|
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\item Abdou peut porter 7litres d'eau par voyage. Combien de voyage devra-t-il faire pour transporter 17litres?
|
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\item Bill partage de manière équitable 17 euros entre 7 personnes. Quelle est la part de chacun ?
|
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\item Un segment $[AB]$ de longueur 17 unités est partagé en 7 segments de même longueur.
|
||||
|
||||
\includegraphics[scale=0.9]{./fig/segmentAB}
|
||||
|
||||
Quelle est la longueur de chacun des 7 segments ?
|
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\end{enumerate}
|
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|
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\end{Exo}
|
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}
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32
5e/Nombres_et_calculs/Fraction_decimaux/index.rst
Normal file
32
5e/Nombres_et_calculs/Fraction_decimaux/index.rst
Normal file
@@ -0,0 +1,32 @@
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Notes sur la construction et l'égalité entre fractions pour les 5e
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#####################################################################
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:date: 2017-04-28
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:modified: 2017-04-28
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:tags: Nombres et calculs, Fraction
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:category: 5e
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:authors: Bertrand Benjamin
|
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:summary: Le chapitre la construction de fraction et de l'égalité entre fractions.
|
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|
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Étape 1
|
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-------
|
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|
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À partir de `dessins <./surface partagee.pdf>`_, on retrouve les fractions associées. C'est le moment de voir quelques égalités entre les fractions.
|
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|
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On les laisse toutes les chercher puis on commence à corriger la première (réajustement pour les plus faibles).
|
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Défis pour les 4 dernières:
|
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|
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- Figure 4: Trouver une fraction avec dénominateur 80
|
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- Figure 5: Trouver une fraction avec le plus grand dénominateur
|
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- Figure 6 et 7: fraction avec le plus petit dénominateur.
|
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|
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Les vacances sont arrivées un peu vite. Il faut donc reprendre après! C'est l'occasion d'ajouter les fractions de longueurs.
|
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|
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- `Surfaces et longueurs partagées présentation <./surface_longueurs_partagees.pdf>`_
|
||||
- `Surfaces et longueurs partagées élèves <./surface_longueurs_partagees_eleves.pdf>`_
|
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|
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Étape 2
|
||||
-------
|
||||
|
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La séquence 1 a été l'occasion d'écrire des égalités a/b = ca/cb. On cherche à remplir les pointillés dans a/b = .../cb
|
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32
5e/Nombres_et_calculs/Fractions/index.rst
Normal file
32
5e/Nombres_et_calculs/Fractions/index.rst
Normal file
@@ -0,0 +1,32 @@
|
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Notes sur la construction et l'égalité entre fractions pour les 5e
|
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#####################################################################
|
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:date: 2016-11-24
|
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:modified: 2017-01-13
|
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:tags: Nombres et calculs, Fraction
|
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:category: 5e
|
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:authors: Bertrand Benjamin
|
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:summary: Le chapitre la construction de fraction et de l'égalité entre fractions.
|
||||
|
||||
|
||||
Étape 1
|
||||
-------
|
||||
|
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À partir de `dessins <./surface partagee.pdf>`_, on retrouve les fractions associées. C'est le moment de voir quelques égalités entre les fractions.
|
||||
|
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On les laisse toutes les chercher puis on commence à corriger la première (réajustement pour les plus faibles).
|
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Défis pour les 4 dernières:
|
||||
|
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- Figure 4: Trouver une fraction avec dénominateur 80
|
||||
- Figure 5: Trouver une fraction avec le plus grand dénominateur
|
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- Figure 6 et 7: fraction avec le plus petit dénominateur.
|
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|
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Les vacances sont arrivées un peu vite. Il faut donc reprendre après! C'est l'occasion d'ajouter les fractions de longueurs.
|
||||
|
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- `Surfaces et longueurs partagées présentation <./surface_longueurs_partagees.pdf>`_
|
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- `Surfaces et longueurs partagées élèves <./surface_longueurs_partagees_eleves.pdf>`_
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Étape 2
|
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-------
|
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La séquence 1 a été l'occasion d'écrire des égalités a/b = ca/cb. On cherche à remplir les pointillés dans a/b = .../cb
|
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BIN
5e/Nombres_et_calculs/Fractions/surface partagee.pdf
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|
After Width: | Height: | Size: 9.6 KiB |
BIN
5e/Nombres_et_calculs/Nombres_relatifs/bilan_nbr_relatifs.pdf
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5e/Nombres_et_calculs/Nombres_relatifs/bilan_nbr_relatifs.pdf
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|
||||
\documentclass[a4paper,10pt]{/media/documents/Cours/Prof/Enseignements/2016-2017/tools/style/classCours}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2016-2017/theme}
|
||||
|
||||
% Title Page
|
||||
\titre{Cours nombres relatifs}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Cinquième}
|
||||
\date{Octobre 2016}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\newcommand{\bilan}{%
|
||||
Les mathématiciens ont inventé les nombres négatifs pour que la soustraction soit toujours possible.
|
||||
|
||||
-15 est le résultat de la soustraction 0 - 15
|
||||
|
||||
\begin{itemize}
|
||||
\item -15 et -6,3 sont des nombres \textbf{négatifs}.
|
||||
\item 85 et 3,7 sont des nombres \textbf{positifs}.
|
||||
\end{itemize}
|
||||
|
||||
\begin{center}
|
||||
\Ovalbox{
|
||||
\makebox{Un nombre relatif est un nombre négatif ou positif}
|
||||
}
|
||||
\end{center}
|
||||
|
||||
Attention, le "-" de "-15" n'est pas une soustraction: c'est la marque qui permet de dire que le nombre est négatif.
|
||||
|
||||
Dans la vie courante on peut dire:
|
||||
\begin{multicols}{2}
|
||||
\icon[scale=0.3]{thermometer_snow} La température est de $-7^{o}$C.
|
||||
|
||||
\icon[scale=0.3]{diving} Le plongeur est descendu à -50m.
|
||||
|
||||
\icon[scale=0.3]{coins} Le solde de votre compte est de -400\euro.
|
||||
|
||||
\icon[scale=0.3]{elevator} L'ascenseur s'est arrêté à l'étage -2.
|
||||
|
||||
\icon[scale=0.3]{papers} L'écriture à été inventé en -3000.
|
||||
\end{multicols}
|
||||
|
||||
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\bilan
|
||||
|
||||
\vfill
|
||||
|
||||
\bilan
|
||||
|
||||
\vfill
|
||||
|
||||
\bilan
|
||||
|
||||
\vfill
|
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\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
28
5e/Nombres_et_calculs/Nombres_relatifs/index.rst
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28
5e/Nombres_et_calculs/Nombres_relatifs/index.rst
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|
||||
Notes sur le chapitre d'introduction des nombres relatifs pour les 5e
|
||||
#####################################################################
|
||||
|
||||
:date: 2016-10-24
|
||||
:modified: 2017-01-08
|
||||
:tags: Nombres et calculs
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre d'introduction des nombres relatifs pour les 5e de l'année 2016-2017
|
||||
|
||||
|
||||
Étape 1
|
||||
-------
|
||||
|
||||
Des soustractions (avec à la fin des soustractions dites impossibles) sont écrites au tableau.
|
||||
Les élèves travaillent individuellement pour donner des réponses. Puis plénière de mise en commun.
|
||||
|
||||
On écrit des problèmes où l'on aurait besoin de faire les calculs pour discuter des résultats.
|
||||
|
||||
Un `bilan sur les nombres relatifs <./bilan_nbr_relatifs.pdf>`_ est donné.
|
||||
|
||||
Étape 2
|
||||
-------
|
||||
|
||||
Comparaison des nombres relatifs et placement sur un axe (insister sur le fait que pour comparer des nombres, on peut les placer sur un axe).
|
||||
|
||||
Entrainement sur la durée pour faire ces soustractions et comparer les nombres relatifs.
|
||||
|
||||
BIN
5e/Nombres_et_calculs/Operations_relatifs/comparer_relatifs.pdf
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5e/Nombres_et_calculs/Operations_relatifs/comparer_relatifs.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{Opérations sur les relatifs - Exercices}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{Cinquième}
|
||||
\date{Mars 2017}
|
||||
|
||||
\renewcommand{\arraystretch}{1.3}
|
||||
|
||||
|
||||
\newcommand{\lexo}{%
|
||||
\setcounter{exo}{0}
|
||||
\begin{Exo}[Comparaisons]
|
||||
\begin{enumerate}
|
||||
\item Trier ces nombres dans l'ordre croissant
|
||||
\begin{eqnarray*}
|
||||
1 \qquad 4,2 \qquad -2 \qquad -5 \qquad 0,5 \qquad -3
|
||||
\end{eqnarray*}
|
||||
\item Trier ces nombres dans l'ordre décroissant
|
||||
\begin{eqnarray*}
|
||||
3 \qquad -2 \qquad -2,5 \qquad -1 \qquad -3 \qquad -3,1
|
||||
\end{eqnarray*}
|
||||
\end{enumerate}
|
||||
\end{Exo}
|
||||
|
||||
\begin{Exo}[Pointillés]
|
||||
Compléter quand c'est possible les pointillés pour que les inégalités soient vraies.
|
||||
\begin{multicols}{3}
|
||||
\begin{itemize}
|
||||
\item $3 < ..... < 4$
|
||||
\item $-5 < ..... < 0$
|
||||
\item $-1 < ..... < 1$
|
||||
\item $ 3 < ..... < 4$
|
||||
\item $-2 < ..... < -1$
|
||||
\item $-5 < ..... < -4$
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\end{multicols}
|
||||
|
||||
\end{Exo}
|
||||
}
|
||||
|
||||
\pagestyle{empty}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\lexo
|
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|
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\vfill
|
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|
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\lexo
|
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|
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\vfill
|
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\end{document}
|
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|
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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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32
5e/Nombres_et_calculs/Operations_relatifs/index.rst
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32
5e/Nombres_et_calculs/Operations_relatifs/index.rst
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|
||||
Notes sur les opérations sur les relatifs pour les 5e
|
||||
#####################################################
|
||||
|
||||
:date: 2017-03-13
|
||||
:modified: 2017-03-16
|
||||
:tags: Nombres et calculs, relatifs
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur les opérations avec les relatifs pour les 5e de l'année 2016-2017
|
||||
|
||||
|
||||
Étape 1
|
||||
-------
|
||||
|
||||
Les soustractions donnant à des nombres négatifs a été travaillé depuis un bon moment (calcul mental). Les élèves ont perdu l'habitude d'utiliser un axe pour raisonner. Cette étape est là pour réintroduire cet outil.
|
||||
|
||||
Étape 2 à 6
|
||||
-----------
|
||||
|
||||
L'élaboration des techniques de calculs va se faire sur au moins 4 séances avec la progression du suivante:
|
||||
|
||||
- Somme du type :math: `4+(-4)` (somme nulle)
|
||||
- Somme du type :math: `4+(-3)` et :math: `(-4) + 6` (somme positive)
|
||||
- Somme du type :math: `(-3)+(-4)` (somme de deux négatifs)
|
||||
- Somme du type :math: `2+(-4)` (somme négative)
|
||||
|
||||
Des calculs sont donnés au tableau. Après une courte réfléction seul et un travail de groupe, on met en commun.
|
||||
|
||||
Étape 7
|
||||
-------
|
||||
|
||||
Exercices techniques sur la durée
|
||||
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58
5e/Nombres_et_calculs/Reperage_plan/index.rst
Normal file
58
5e/Nombres_et_calculs/Reperage_plan/index.rst
Normal file
@@ -0,0 +1,58 @@
|
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Notes sur la formalisation du reperage dans le plan pour les 5e
|
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###############################################################
|
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|
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:date: 2017-01-08
|
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:modified: 2017-01-08
|
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:tags: Reperage
|
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:category: 5e
|
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:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur le repérage dans le plan pour les 5e.
|
||||
|
||||
Étape 0: Bataille Navale classique
|
||||
----------------------------------
|
||||
|
||||
Activité récréative autour de la bataille navale.
|
||||
|
||||
`Grille de jeu classique <./bataille_navale_recreatif.pdf>`_
|
||||
|
||||
À Mayotte, les enfants ne connaissent pas ce jeu, il est donc nécessaire de prendre son temps pour expliquer les règles.
|
||||
|
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C'est l'occasion de revoir comment lire un tableau et de prendre l'habitude de donner en premier la coordonnée horizontale puis celle verticale.
|
||||
|
||||
Étape 1: Bataille Navale
|
||||
------------------------
|
||||
|
||||
Encore une activité récréative qui se place bien avant les vacances.
|
||||
|
||||
`Grille de jeu repérage <./bataille_navale_reperage.pdf>`_.
|
||||
|
||||
- Prof vs élèves: chaque équipe et le prof place ces bateaux. À chaque début de cours, le prof tire une fois sur toutes les grilles de la classe et chaque équipe tire une fois contre le prof. Cette étape permet de prendre le temps pour que tout le monde puisse comprendre les mécanismes.
|
||||
|
||||
- Élèves vs élèves: comme la bataille naval sur un quadrillage mais sur un repère (les bateaux sont placés sur les noeuds).
|
||||
|
||||
Étape 2: Le repère
|
||||
------------------
|
||||
|
||||
Repère où il faut retrouver les coordonnées de points, en placer d'autres puis les relier pour faire apparaitre un message.
|
||||
|
||||
`Fiche d'exercice <./reperage_exo.pdf>`_
|
||||
|
||||
`Repère vide <./fig/repere.pdf>`_
|
||||
|
||||
|
||||
Étape 3
|
||||
-------
|
||||
|
||||
Formalisation sur le cahier de bord avec le vocabulaire
|
||||
|
||||
Exercices techniques autour du vocabulaire.
|
||||
|
||||
Étape sur le durée
|
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------------------
|
||||
|
||||
Dessins à faire à partir d'une liste de coordonnées
|
||||
|
||||
- `Site pour faire des fiches <https://www.worksheetworks.com/math/geometry/graphing/coordinate-pictures.html>`_
|
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|
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|
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BIN
5e/Nombres_et_calculs/Reperage_plan/reperage_exo.pdf
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5e/Nombres_et_calculs/Reperage_plan/reperage_exo.pdf
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68
5e/Nombres_et_calculs/Reperage_plan/reperage_exo.tex
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5e/Nombres_et_calculs/Reperage_plan/reperage_exo.tex
Normal file
@@ -0,0 +1,68 @@
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\documentclass[a4paper,12pt]{/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{Reperage dans le plan- Exercices}
|
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% \seconde \premiereS \PSTMG \TSTMG
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\classe{Cinquième}
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\date{Janvier 2017}
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\renewcommand{\arraystretch}{1.3}
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\newcommand{\lexo}{%
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\setcounter{exo}{0}
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\begin{Exo}[Reperage!]
|
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Voici un repère où l'on a placé des points.
|
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|
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\begin{minipage}{0.4\textwidth}
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\includegraphics[scale=0.7]{./fig/repere_lettres}
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\end{minipage}
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\begin{minipage}{0.55\textwidth}
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\begin{enumerate}
|
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\item Retrouve comment décrire précisement la position des points
|
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|
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\begin{tabular}{*{3}{p{3cm}}}
|
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A \dotfill & B \dotfill & C \dotfill \\
|
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C \dotfill & D \dotfill &E \dotfill\\
|
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F \dotfill& G\dotfill &
|
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\end{tabular}
|
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\item Placer les points suivants
|
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|
||||
\begin{tabular}{*{3}{p{3cm}}}
|
||||
Z (4;4) & Y (3;4) & X (1; -4) \\
|
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W (-1; -4) & V (-4;4) & T(-2:-4) \\
|
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S (-1;0) & &
|
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\end{tabular}
|
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|
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\item Relier les points pour dévoiler le message.
|
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\begin{itemize}
|
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\item F - V - G - E - T
|
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\item W - C - A - X
|
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\item S - H
|
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\item D - Y - B - Z
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\end{itemize}
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\end{enumerate}
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\end{minipage}
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\end{Exo}
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}
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\pagestyle{empty}
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\begin{document}
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\lexo
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\vfill
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\lexo
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\vfill
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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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@@ -0,0 +1,31 @@
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Notes sur le chapitre sur le sens du signe "=" et les programmes de calculs pour les 5e
|
||||
#######################################################################################
|
||||
|
||||
:date: 2016-11-03
|
||||
:modified: 2016-11-03
|
||||
:tags: Nombres et calculs, Programme de calculs
|
||||
:category: 5e
|
||||
:authors: Bertrand Benjamin
|
||||
:summary: Chapitre sur le signe "=" et les programmes de calculs
|
||||
|
||||
|
||||
Étape 1
|
||||
-------
|
||||
|
||||
On commence par redéfinir le sens du signe "=" à travers des exercices du type:
|
||||
|
||||
Écris le nombre 36:
|
||||
- sous la forme de la somme de 2 nombres
|
||||
- sous la forme d'un produit de 2 nombres
|
||||
- sous la forme du double d'un nombre
|
||||
|
||||
On en profite pour insister sur le fait que "=" ne signifie pas "donne" comme avec une calculatrice.
|
||||
|
||||
Dans la durée on peut faire chercher le plus de calculs donnant 42 et de les écrire comme une grande égalité.
|
||||
|
||||
Étape 2
|
||||
-------
|
||||
|
||||
Programmes de calculs.
|
||||
|
||||
|
||||
Reference in New Issue
Block a user