{"id":2035,"date":"2016-09-24T22:24:01","date_gmt":"2016-09-24T21:24:01","guid":{"rendered":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/?p=2035"},"modified":"2018-02-17T02:05:33","modified_gmt":"2018-02-17T01:05:33","slug":"boite","status":"publish","type":"post","link":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/boite\/","title":{"rendered":"Bo\u00eete"},"content":{"rendered":"<h2>Objectifs<\/h2>\n<p>R\u00e9soudre un probl\u00e8me d&#8217;optimisation :<\/p>\n<ul>\n<li>\u00a0En 3<sup>\u00e8me<\/sup> ou en seconde\u00a0: Calcul litt\u00e9ral &#8211; Utilisation de la repr\u00e9sentation graphique d&#8217;une fonction pour conjecturer un maximum. \u00c9ventuellement un prolongement possible en utilisant un tableur pour encadrer la solution du probl\u00e8me.<\/li>\n<li>\u00a0En 1<sup>\u00e8re<\/sup>\u00a0: \u00c9tude d\u2019une fonction polyn\u00f4me de degr\u00e9 3.<\/li>\n<\/ul>\n<h2>Pr\u00e9requis<\/h2>\n<ul>\n<li>\u00a0Patron et volume du parall\u00e9l\u00e9pip\u00e8de rectangle.<\/li>\n<li>\u00a0Notion de fonction.<\/li>\n<\/ul>\n<h2>\u00c9nonc\u00e9<\/h2>\n<table>\n<tbody>\n<tr>\n<td width=\"392\">&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>On dispose d&#8217;une plaque rectangulaire cartonn\u00e9e de dimensions 120\u00a0cm sur 80\u00a0cm.<\/p>\n<p>&nbsp;<\/p>\n<p>Pour des raisons \u00e9conomiques, on veut d\u00e9couper dans ce carton le patron d&#8217;une bo\u00eete parall\u00e9l\u00e9pip\u00e9dique ayant un volume maximal.<\/p>\n<p>&nbsp;<\/td>\n<td width=\"260\">\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-2036\" src=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/Boite.jpg\" alt=\"boite\" width=\"192\" height=\"295\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>D\u00e9roulement de la s\u00e9quence<\/h2>\n<ul>\n<li>\u00a0Faire construire aux \u00e9l\u00e8ves le patron d&#8217;un parall\u00e9l\u00e9pip\u00e8de rectangle dans un cadre de dimensions 12\u00a0cm sur 8\u00a0cm. Indiquer les dimensions choisies puis calculer le volume du patron dessin\u00e9.<\/li>\n<\/ul>\n<ul>\n<li>\u00a0En classe: utilisation de GeoplanGeospace pour visualiser le patron, le pav\u00e9 droit et son volume \u00e0 l\u2019aide de figures communicantes ouvertes en mosa\u00efque verticale (on pilote la variable <em>x<\/em> dans le fichier \u00ab\u00a0boite_patron.g2w\u00a0\u00bb, on peut ouvrir le patron \u00e0 l\u2019aide des fl\u00e8ches du clavier dans le fichier \u00ab\u00a0boite.g3w\u00a0\u00bb et le placer en vue de face \u00e0 l\u2019aide la touche P).<br \/>\nOn peut ensuite ouvrir le fichier \u00ab\u00a0boite_courbe.g2w\u00a0\u00bb et le placer lui aussi en mosa\u00efque verticale afin de visualiser les variations du volume de la bo\u00eete<\/li>\n<\/ul>\n<h2>Documents<\/h2>\n<ul>\n<li><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/boite_patron.zip\">Fichier patron Boite<\/a>(geoplan)<\/li>\n<li><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/boite.zip\">Fichier Boite<\/a> (geospace)<\/li>\n<li><a href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-content\/uploads\/sites\/3\/2016\/09\/boite_courbe.zip\">Fichier courbe Boite<\/a> (geoplan)<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Objectifs R\u00e9soudre un probl\u00e8me d&#8217;optimisation : \u00a0En 3\u00e8me ou en seconde\u00a0: Calcul litt\u00e9ral &#8211; Utilisation de la repr\u00e9sentation graphique d&#8217;une fonction pour conjecturer un maximum. \u00c9ventuellement un prolongement possible en utilisant un tableur pour encadrer la solution du probl\u00e8me. \u00a0En 1\u00e8re\u00a0: \u00c9tude d\u2019une fonction polyn\u00f4me de degr\u00e9 3. Pr\u00e9requis \u00a0Patron et volume du parall\u00e9l\u00e9pip\u00e8de rectangle. &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/boite\/\">Lire la suite<\/a><\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[23,22,14,27],"tags":[],"class_list":["post-2035","post","type-post","status-publish","format-standard","hentry","category-seconde","category-lycee","category-numerique","category-voie-generale","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/2035","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/comments?post=2035"}],"version-history":[{"count":3,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/2035\/revisions"}],"predecessor-version":[{"id":2042,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/posts\/2035\/revisions\/2042"}],"wp:attachment":[{"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/media?parent=2035"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/categories?post=2035"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ent2d.ac-bordeaux.fr\/disciplines\/mathematiques\/wp-json\/wp\/v2\/tags?post=2035"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}