{"id":2887,"date":"2023-12-06T21:20:09","date_gmt":"2023-12-06T20:20:09","guid":{"rendered":"https:\/\/math.univ-lyon1.fr\/dream\/?p=2887"},"modified":"2025-12-05T11:20:42","modified_gmt":"2025-12-05T10:20:42","slug":"le-chateau-de-cartes","status":"publish","type":"post","link":"https:\/\/math.univ-lyon1.fr\/dream\/?p=2887","title":{"rendered":"Le ch\u00e2teau de cartes"},"content":{"rendered":"\r\n

Accueil<\/a> \u00bb Ressources p\u00e9dagogiques<\/a> \u00bb Le panier \u00e0 probl\u00e8mes<\/a> \u00bb Le ch\u00e2teau de cartes<\/p>\r\n

\u00c9nonc\u00e9 du probl\u00e8me<\/h2>\r\n

\"ChateauCartesIllustration\" Un ch\u00e2teau de cartes \u00e0 un \u00e9tage est compos\u00e9 de deux cartes.
Un ch\u00e2teau de cartes \u00e0 deux \u00e9tages est compos\u00e9 de sept cartes.
Pour r\u00e9aliser trois \u00e9tages, il faut quinze cartes.
Combien faut-il de cartes pour r\u00e9aliser un ch\u00e2teau de sept \u00e9tages ? Trente \u00e9tages ? Cent \u00e9tages ?<\/p>\r\n

Au cycle 3<\/h3>\r\n

Le\u00a0ch\u00e2teau de cartes<\/strong>\u00a0est un probl\u00e8me de pr\u00e9-alg\u00e9brisme o\u00f9 l’\u00e9l\u00e8ve devra rep\u00e9r\u00e9 un motif qui d\u00e9crit les constructions successives.<\/p>\r\n

Un sujet simple \u00e0 comprendre et pour lequel les \u00e9l\u00e8ves peuvent se lancer facilement dans la recherche : ils peuvent faire des dessins pour comprendre le m\u00e9canisme de construction des ch\u00e2teaux et d\u00e9terminer rapidement le nombre de cartes n\u00e9cessaires pour obtenir des ch\u00e2teaux ayant un petit nombre d’\u00e9tages.<\/p>\r\n

Comp\u00e9tences transversales<\/h3>\r\n

\u2666 Mettre en place une strat\u00e9gie pour compter le nombre de cartes.
\u2666 Organiser sa recherche, ses id\u00e9es de mani\u00e8re claire.
\u2666 Transmettre sous forme de textes, sch\u00e9mas, figures, codages. . .sa d\u00e9marche de recherche \u00e0 une personne ext\u00e9rieure.
\u2666 \u00catre capable de raisonner avec logique et rigueur et donc savoir :
– Identifier un probl\u00e8me et mettre au point une d\u00e9marche de r\u00e9solution
– Identifier, expliquer, rectifier une erreur
– Distinguer ce dont on est s\u00fbr de ce qu’il faut prouver
– Mettre \u00e0 l’essai plusieurs pistes de solution
\u2666 Communiquer, \u00e0 l’\u00e9crit, en utilisant un langage math\u00e9matique adapt\u00e9<\/p>\r\n

Connaissances math\u00e9matiques<\/h3>\r\n

\u2666 Utilisation \u00e9ventuelle de la notion de suite.
\u2666 Utilisation de la formule permettant de calculer la somme des n premiers entiers :\"\"<\/a><\/p>\r\n

\u2666 Ce sujet peut \u00eatre trait\u00e9 sans faire appel \u00e0 des aspects du programme de math\u00e9matiques du coll\u00e8ge ce qui peut avoir comme objectif d’int\u00e9resser des \u00e9l\u00e8ves plut\u00f4t d\u00e9crocheurs face aux math\u00e9matiques.<\/p>\r\n

T\u00e9l\u00e9charcher le document complet <\/a><\/p>\r\n","protected":false},"excerpt":{"rendered":"

Un ch\u00e2teau de cartes grandit vite : 2 cartes pour 1 \u00e9tage, 7 pour 2, 15 pour 3\u2026 Combien en faut-il pour 7, 30 ou m\u00eame 100 \u00e9tages ?<\/p>\n","protected":false},"author":3,"featured_media":2520,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107],"tags":[],"niveau":[112,113],"type_situation":[116],"theme_maths":[118,119],"probleme_associe":[134],"type-expe":[],"class_list":{"0":"post-2887","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-situation-probleme","8":"niveau-cycle_3","9":"niveau-cycle-4","10":"type_situation-situation-probleme","11":"theme_maths-nombres-et-calculs","12":"theme_maths-ogd-fonctions","13":"probleme_associe-le-chateau-de-cartes","14":"czr-hentry"},"rttpg_featured_image_url":{"full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration.png",849,264,false],"landscape":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration.png",849,264,false],"portraits":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration.png",849,264,false],"thumbnail":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-150x150.png",150,150,true],"medium":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-300x93.png",300,93,true],"large":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration.png",849,264,false],"1536x1536":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration.png",849,264,false],"2048x2048":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration.png",849,264,false],"tc-grid-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration.png",849,264,false],"tc-grid":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-570x264.png",570,264,true],"tc-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-270x250.png",270,250,true],"slider-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-849x200.png",849,200,true],"slider":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-849x200.png",849,200,true],"tc-sq-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-510x264.png",510,264,true],"tc-ws-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration.png",849,264,false],"tc-ws-small-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-528x264.png",528,264,true],"tc-slider-small":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/ChateauCartesIllustration-517x94.png",517,94,true]},"rttpg_author":{"display_name":"St\u00e9phanie 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