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ztsrIZH^toGFq@)#K^YPe!Q>1v7UfTj*q1;Q%fjP&y8dyC-bECgJd!}-og?=RQVT|SlK{i9X;qW`peK?WZ9o)K=jye;*s$$ zt^WkVSpPad|2wD$bPfC+>Cu#3GV`NH@)%bh*}B!esBU)T_3K^nL2Q$0!OsMJImZ%! zf&cu}7p7v;Il#uWH)23aUZS3t>%ZO|)+z*>rtou}c?^{3b6&hR8^dqgk^gmbec8eyB9HGY~9XfeQ!E@Wh78{KXfX5|)4p25FwHU{0um z1)Oi)uwSgPv37XU^p&w4EgZ=WM;7Rg!g>&pW2z8IjkrSb#mlxpr?98PS**BzYc2d@ zfh++xz*ePnAH_9x`J*g#o{E}ltS09W`IYB|BA{c%!UrJBvrQarkYm8VRE z{?CE`H=^pVasQj{{4a*|f5y8090vcVY}fBWC-+ab>-Ty7+qiVLGcr2nX3W7HOX^) sVCdwmtsQ<-ynoye|Dc3H&i`@h>>YIN9R4_Q%m4rj6ATH7ptR8c0*-P`_ +- `TP version Excel <./TP_ajustement_affine_esperances_vie.xlsx>`_ + +Capacités travaillées : + + - Représenter un nuage de points. + - Déterminer et utiliser un ajustement affine pour interpoler ou extrapoler des valeurs inconnues. + +Objectifs : + +- Dans un contexte réel, s'entraîner à utiliser le tableur, à tracer des graphiques à partir d’un tableur. +- Comprendre l’intérêt de l’ajustement affine pour interpoler ou extrapoler des valeurs. Comprendre certaines limites de l’ajustement affine. +- Voir tableurs “TP ajustement affine” + + +Etape 2 - Sur PAPIER (2 séances) +================================ + +EN AMONT : Cours à distribuer et compléter - I série stat à deux variables et II - nuage de points + +.. image:: ./1B_Serie_nuage_points.pdf + :height: 200px + :alt: Cours sur la série statistique à 2 variables et les nuages de points + +Capacités travaillées : + +- Représenter un nuage de points. +- Déterminer et utiliser un ajustement affine pour interpoler ou extrapoler des valeurs inconnues. + +Objectifs : + +- S’entrainer à tracer à la main des nuages de points +- Réaliser un ajustement affine “au jugé” +- Comparer les différents tracés réalisés “au jugé” par les élèves (utiliser la caméra pour projeter les différentes productions) - quelle est la meilleure et pourquoi ? +- Formuler une méthode pour trouver la meilleure droite (constructif) +- Comparer d’autres candidats (à créer par le professeur) pour expliquer pourquoi elles sont moins bien + +Mise en oeuvre : + +PARTIE A de l’Exercice “World Happiness” + +.. image:: ./2E_World_Happiness.pdf + :height: 200px + :alt: Mesure du bonheur + +- À partir de la série de données fournies et d’un repère orthonormé imprimé, les élèves réalisent un nuage de points. Chacun tracera ensuite un ajustement affine “au jugé” (prévoir plusieurs repères par élève afin que chacun puisse recommencer pour s’améliorer au fure et à mesure des discussions) +- Retrouver l’équation de la droite à partir du tracé +- Deux par deux, comparaison des ajustements affines réalisés, choix du meilleur ou création d’un meilleur ajustement et élaboration d’une argumentation pour soutenir son ajustement +- 3 présentations d’élèves à la classe + 2 présentations mauvaises par le professeur : participation de la classe pour élaborer des critiques des différentes droites +- Présentation par le professeur de la méthode des moindre carrés pour comparer plusieurs couples (a,b) +- Chacun calcule $\sum (yi - (axi+b))^2$ avec le couple (a,b) qu’il aura trouvé pour comparer les différents + +Etape 3 - Avec la CALCULATRICE (1 séance) +========================================= + +Capacités travaillées + +- Représenter un nuage de points. +- Déterminer et utiliser un ajustement affine pour interpoler ou extrapoler des valeurs inconnues. + + +Objectifs : + +- Utiliser la calculatrice pour obtenir l’équation d’un ajustement affine + +Mise en oeuvre de la séance : + +PARTIE B de l’Exercice “World Happiness” + +- Présentation par le professeur de situations pour lesquels un ajustement affine n’est pas adapté +- Reprendre les données et le nuage de points réalisés à la séance précédente pour réaliser la + +PARTIE B de l’Exercice “World Happiness” (méthode p106-107 du livre) +- Pour les plus rapides : 51 p 114 du livre + +EN AVAL : Cours à distribuer et compléter - III ajustement affine + +Etape 4 - PYTHON OU TABLEUR - au choix (1 séance ensemble, puis en DM) +====================================================================== + + +Capacités travaillées + +- Représenter un nuage de points. +- Déterminer et utiliser un ajustement affine pour interpoler ou extrapoler des valeurs inconnues. + +Objectif : + +Constituer un petit dossier autour de séries statistiques à 2 variables (data set fournis par le professeur) dans lequel vous devrez interpoler / extrapoler des valeurs à l’aide d’un ajustement affine + +Sujet : Parmi les “data set” proposés, vous choisirez une situation à étudier. A l’aide d’un tableur ou de Python, vous devrez produire une analyse de la situation, se reposant sur un nuage de points, un ajustement affine et des interpolations ou extrapolations. Vous vous efforcerez : + +- de rendre le tracer de votre nuage et points et votre ajustement affine dans votre dossier +- de faire des phrases complètes d’analyse de la série statistique +- d’utiliser le vocabulaire du cours dans votre analyse +- de bien faire apparaître les valeurs que vous avez estimé +- de rendre un ou des fichiers propres et bien organisés + +Pour aller plus loin, pour ceux qui le souhaitent : Vous pourrez chercher à automatiser le calcul de $\sum (yi - (axi+b))^2$, à partir d’une série statistique diff --git a/TST/index.rst b/TST/index.rst index 62ec0b6..8a63cd7 100644 --- a/TST/index.rst +++ b/TST/index.rst @@ -2,7 +2,7 @@ Terminale technologique ####################### :date: 2020-08-21 -:modified: 2021-03-18 +:modified: 2021-04-25 :authors: Bertrand Benjamin :category: TST :tags: Progression @@ -58,13 +58,13 @@ Période 4 (Février mars avril - 7 semaines) - `Somme des termes d'une suite <./09_Somme_suites>`_ - `Probabilités conditionnelles <./10_Probabilites_conditionnelles>`_ -- Ajustement affine `Questions flashs de la période 4 <./Questions_Flash/P4>`_ Période 5 (Mai juin - 7 semaines) ================================== +- `Ajustement affine <./11_Ajustement_affine>`_ - Ordre de grandeur et échelle logarithmique - Étude de la fonction inverse - Étude de fonctions