{"id":3186,"date":"2023-11-28T19:33:22","date_gmt":"2023-11-28T18:33:22","guid":{"rendered":"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=3186"},"modified":"2026-04-27T12:46:42","modified_gmt":"2026-04-27T10:46:42","slug":"les-deux-tours","status":"publish","type":"post","link":"https:\/\/math.univ-lyon1.fr\/dream\/?p=3186","title":{"rendered":"Les deux tours"},"content":{"rendered":"\n<h2>\n\t\t\t\u00c9nonc\u00e9 du probl\u00e8me\t<\/h2>\n\tDeux tours, hautes de 30 m et de 40 m, sont distantes l&rsquo;une de l&rsquo;autre de 50 m.\u00a0Un puits est\u00a0situ\u00e9 entre les deux tours.<br \/>\nDeux oiseaux volants \u00e0 la m\u00eame vitesse s&rsquo;envolent en m\u00eame temps, chacun du sommet de chaque\u00a0tour, pour se poser au m\u00eame moment sur le puits.<br \/>\nComment pourrais-tu faire pour d\u00e9terminer la position de ce puits entre les deux tours ?\n\t\t\t<a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=79\" target=\"_self\">\n\t\t\t\t\t\tRetour Panier \u00e0 probl\u00e8mes\n\t\t\t\t\t<\/a>\n\t<h3>Comp\u00e9tences transversales<\/h3>\nCe probl\u00e8me de mod\u00e9lisation d&rsquo;une situation concr\u00e8te est tr\u00e8s riche car il permet de :<br \/>\n\u2666 Travailler sur la notion d&rsquo;hypoth\u00e8se (en math\u00e9matiques et en sciences).<br \/>\n\u2666 Mobiliser des proc\u00e9dures de r\u00e9solution multiples.<br \/>\n\u2666 Travailler la notion d&rsquo;\u00e9chelle et la proportionnalit\u00e9.\n\t<h3>Connaissances math\u00e9matiques<\/h3>\n\u2666 Construction de m\u00e9diatrice et utilisation des propri\u00e9t\u00e9s de la m\u00e9diatrice.<br \/>\n\u2666 Th\u00e9or\u00e8me de Pythagore.<br \/>\n\u2666 D\u00e9veloppement et r\u00e9duction d&rsquo;expressions litt\u00e9rales.<br \/>\n\u2666 Mise en \u00e9quation d&rsquo;un probl\u00e8me.\n\t\t\t<a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/12\/DREAM_NarrationRecherche_Deux_tours.pdf\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t\tT\u00e9l\u00e9charcher le document complet\n\t\t\t<\/a>\n\n","protected":false},"excerpt":{"rendered":"<p>Deux tours de 30\u202fm et 40\u202fm, distantes de 50\u202fm, et un puits entre elles. Comment d\u00e9terminer sa position si deux oiseaux partent des sommets et arrivent simultan\u00e9ment\u202f?<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107],"tags":[],"niveau":[113],"type_situation":[116],"theme_maths":[120],"probleme_associe":[],"type-expe":[],"class_list":{"0":"post-3186","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-situation-probleme","7":"niveau-cycle-4","8":"type_situation-situation-probleme","9":"theme_maths-espace-et-geometrie","10":"czr-hentry"},"rttpg_featured_image_url":null,"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":"Deux tours de 30\u202fm et 40\u202fm, distantes de 50\u202fm, et un puits entre elles. Comment d\u00e9terminer sa position si deux oiseaux partent des sommets et arrivent simultan\u00e9ment\u202f?","_links":{"self":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/3186","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3186"}],"version-history":[{"count":6,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/3186\/revisions"}],"predecessor-version":[{"id":3808,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/3186\/revisions\/3808"}],"wp:attachment":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3186"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3186"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3186"},{"taxonomy":"niveau","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fniveau&post=3186"},{"taxonomy":"type_situation","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype_situation&post=3186"},{"taxonomy":"theme_maths","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftheme_maths&post=3186"},{"taxonomy":"probleme_associe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fprobleme_associe&post=3186"},{"taxonomy":"type-expe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype-expe&post=3186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}