{"id":2578,"date":"2023-02-08T16:49:34","date_gmt":"2023-02-08T15:49:34","guid":{"rendered":"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=2578"},"modified":"2025-12-05T11:31:53","modified_gmt":"2025-12-05T10:31:53","slug":"la-somme-de-dix-entiers-consecutifs","status":"publish","type":"post","link":"https:\/\/math.univ-lyon1.fr\/dream\/?p=2578","title":{"rendered":"La somme de dix entiers cons\u00e9cutifs"},"content":{"rendered":"\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/\">Accueil<\/a> \u00bb <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=3328\">Ressources p\u00e9dagogiques<\/a> \u00bb <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=79\">Le panier \u00e0 probl\u00e8mes<\/a> \u00bb La somme de dix entiers cons\u00e9cutifs<\/p>\r\n<h2>\u00c9nonc\u00e9 du probl\u00e8me<\/h2>\r\n<p>Trouver le plus rapidement possible la somme de 10 nombres entiers cons\u00e9cutifs.<\/p>\r\n<p>Par exemple la somme de 17, 18, 19, 20, 21, 22, 23, 24, 25, 26.<\/p>\r\n<p><em>Ce probl\u00e8me provient des travaux de Barallobres (Barallobres, 2007 ; Barallobres &amp; Giroux, 2008).<\/em><br \/><em>On peut aussi trouver une analyse dans Durand-Guerrier (2010).<\/em><\/p>\r\n<h3>Objets potentiellement travaill\u00e9s \/ Connaissances en jeu<\/h3>\r\n<p>Les objectifs d&rsquo;apprentissage d\u00e9pendent du niveau de la classe et peuvent \u00eatre multiples<\/p>\r\n<h3>Cycle 3<\/h3>\r\n<p>Calcul mental et le calcul r\u00e9fl\u00e9chi<br \/>Num\u00e9ration d\u00e9cimale<br \/>Apprendre \u00e0 d\u00e9gager des \u00ab r\u00e8gles g\u00e9n\u00e9rales \u00bb \u00e0 partir d&rsquo;exemples en situation de recherche<\/p>\r\n<h3>Cycle 4<\/h3>\r\n<p>Calcul litt\u00e9ral<\/p>\r\n<h3>Lyc\u00e9e<\/h3>\r\n<p>R\u00e9activer la relation entre \u00e9critures alg\u00e9briques et programmes de calcul<br \/>Chercher \u00e0 d\u00e9terminer plusieurs proc\u00e9dures de r\u00e9solution possibles (moyenne, m\u00e9diane, somme de Gauss, suite arithm\u00e9tique, etc.) <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/03\/La-somme-des-10-entiers-consecutifs.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charcher le document complet <\/a><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Trouver le plus rapidement possible la somme de 10 nombres entiers cons\u00e9cutifs.<\/p>\n","protected":false},"author":3,"featured_media":2846,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107],"tags":[],"niveau":[112,113,114],"type_situation":[116],"theme_maths":[118],"probleme_associe":[137],"type-expe":[],"class_list":{"0":"post-2578","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":"niveau-lycee","11":"type_situation-situation-probleme","12":"theme_maths-nombres-et-calculs","13":"probleme_associe-la-somme-de-dix-entiers-consecutifs","14":"czr-hentry"},"rttpg_featured_image_url":{"full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"landscape":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"portraits":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"thumbnail":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS-150x150.png",150,150,true],"medium":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS-300x96.png",300,96,true],"large":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"1536x1536":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"2048x2048":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"tc-grid-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"tc-grid":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS-570x194.png",570,194,true],"tc-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS-270x194.png",270,194,true],"slider-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"slider":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"tc-sq-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS-510x194.png",510,194,true],"tc-ws-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS.png",605,194,false],"tc-ws-small-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS-528x194.png",528,194,true],"tc-slider-small":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/SOMME10ENTIERS-517x141.png",517,141,true]},"rttpg_author":{"display_name":"St\u00e9phanie CROQUELOIS","author_link":"https:\/\/math.univ-lyon1.fr\/dream\/?author=3"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?cat=107\" rel=\"category\">Situation Probl\u00e8me<\/a>","rttpg_excerpt":"Trouver le plus rapidement possible la somme de 10 nombres entiers 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