{"id":16657,"date":"2021-05-10T19:40:16","date_gmt":"2021-05-10T17:40:16","guid":{"rendered":"http:\/\/agora.xtec.cat\/escestel\/?p=16657"},"modified":"2021-05-10T19:42:12","modified_gmt":"2021-05-10T17:42:12","slug":"joc-matematic-conjectura-de-collatz","status":"publish","type":"post","link":"https:\/\/agora.xtec.cat\/escestel\/general\/joc-matematic-conjectura-de-collatz\/","title":{"rendered":"JOC MATEM\u00c0TIC: CONJECTURA DE COLLATZ"},"content":{"rendered":"<p>En una formaci\u00f3 sobre matem\u00e0tiques, van proposar que els\/les mestres jugu\u00e9ssim a la Conjectura de Collatz i descobr\u00edssim qu\u00e8 hi passava quan s&#8217;arribava a l&#8217;1. Amb qualsevol nombre natural sempre s&#8217;arribar\u00e0 a l&#8217;1? Ens cridava l&#8217;atenci\u00f3 alguna cosa o patr\u00f3 mentre f\u00e8iem el c\u00e0lcul?<\/p>\n<p>Aquesta activitat \u00e9s for\u00e7a indicada per plantejar-la a l&#8217;alumnat de CM i CS. Doncs&#8230; Som-hi! Divendres passat l&#8217;alumnat de 4t van comen\u00e7ar a jugar-hi amb parella. Al principi, era una mica embolicat, hi havia errors de c\u00e0lcul o a l&#8217;hora de recon\u00e8ixer si alguns nombres eren parells o senars&#8230; per\u00f2, de mica en mica, cada parella va comen\u00e7ar a entendre millor en qu\u00e8 consistia el joc matem\u00e0tic.<\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000\"><span style=\"font-family: Georgia, serif\"><span style=\"font-size: xx-large\">Conjectura de Collatz<\/span><\/span><\/span><\/p>\n<p><span style=\"color: #202122\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\">La\u00a0<\/span><\/span><\/span><span style=\"color: #202122\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\"><b>Conjectura de Collatz<\/b><\/span><\/span><\/span><span style=\"color: #202122\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\">\u00a0\u00e9s una conjectura matem\u00e0tica aix\u00ed denominada perqu\u00e8 la va proposar per primer cop el matem\u00e0tic alemany Lothar Collatz l\u2019any 1937.<\/span><\/span><\/span><\/p>\n<h2 class=\"western\"><span style=\"color: #000000\"><span style=\"font-family: Georgia, serif\">Plantejament<\/span><\/span><\/h2>\n<p align=\"left\"><span style=\"color: #31849b\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\"><i><b>Considera la seg\u00fcent operaci\u00f3 sobre qualsevol nombre natural:<\/b><\/i><\/span><\/span><\/span><\/p>\n<ul>\n<li><span style=\"color: #31849b\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\"><i><b>Trieu un nombre natural, d&#8217;una xifra, de dues, etc<\/b><\/i><\/span><\/span><\/span><\/li>\n<li><span style=\"color: #31849b\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\"><i><b>Si el nombre \u00e9s parell, el dividim per dos.<\/b><\/i><\/span><\/span><\/span><\/li>\n<li><span style=\"color: #31849b\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\"><i><b>Si el nombre \u00e9s senar, el multipliquem (X3) i li afegim una unitat (+1). <\/b><\/i><\/span><\/span><\/span><\/li>\n<li><span style=\"color: #31849b\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\"><i><b>I anem seguint aquest proc\u00e9s.<\/b><\/i><\/span><\/span><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #31849b\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: large\"><i><b>La conjectura (=hip\u00f2tesi) diu que aquest proc\u00e9s arribar\u00e0 a obtenir el valor 1, independentment del nombre natural que escollim inicialment, per\u00f2&#8230;<\/b><\/i><\/span><\/span><\/span><\/p>\n<p align=\"center\"><span style=\"color: #00b050\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: xx-large\">VOLEU DESCOBRIR-HO?<\/span><\/span><\/span><\/p>\n<p><span style=\"color: #76923c\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: x-large\">US ANIMO A PASSAR UNA BONA ESTONA MATEM\u00c0TICA AMB EL VOSTRE FILL\/ VOSTRA FILLA PARTICIPANT \u201cAL JOC\u201d QUE PLANTEJA LA CONJECTURA DE COLLATZ.<\/span><\/span><\/span><\/p>\n<p><a name=\"_heading=h.gjdgxs\"><\/a><span style=\"color: #f79646\"><span style=\"font-family: Arial, serif\"><span style=\"font-size: xx-large\"><i>Ah! Una cosa&#8230; podeu fer \u00fas de la calculadora, perqu\u00e8 encara que sigui una activitat de c\u00e0lcul, el m\u00e9s divertit \u00e9s anar provant i provant, i provant&#8230; Aquesta \u00e9s la gr\u00e0cia!<\/i><\/span><\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>En una formaci\u00f3 sobre matem\u00e0tiques, van proposar que els\/les mestres jugu\u00e9ssim a la Conjectura de Collatz i descobr\u00edssim qu\u00e8 hi passava quan s&#8217;arribava a l&#8217;1. Amb qualsevol nombre natural sempre s&#8217;arribar\u00e0 a l&#8217;1? Ens cridava l&#8217;atenci\u00f3 alguna cosa o patr\u00f3 mentre f\u00e8iem el c\u00e0lcul?<br \/>\nAquesta activitat&hellip;  <a href=\"https:\/\/agora.xtec.cat\/escestel\/general\/joc-matematic-conjectura-de-collatz\/\" title=\"Read JOC MATEM\u00c0TIC: CONJECTURA DE COLLATZ\">Llegeix m\u00e9s\u00bb<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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":[13,1,4,5],"tags":[147,379,168,113,380,381],"class_list":["post-16657","post","type-post","status-publish","format-standard","hentry","category-4t","category-general","category-portada","category-primaria","tag-cm","tag-conjectura-de-collatz","tag-joc","tag-matematiques","tag-nombres-parells","tag-nombres-senars"],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/posts\/16657","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/comments?post=16657"}],"version-history":[{"count":1,"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/posts\/16657\/revisions"}],"predecessor-version":[{"id":16658,"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/posts\/16657\/revisions\/16658"}],"wp:attachment":[{"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/media?parent=16657"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/categories?post=16657"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/agora.xtec.cat\/escestel\/wp-json\/wp\/v2\/tags?post=16657"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}