{"id":1133,"date":"2023-06-05T13:51:21","date_gmt":"2023-06-05T11:51:21","guid":{"rendered":"https:\/\/matematika.otroci.org\/?p=1133"},"modified":"2023-06-13T11:23:46","modified_gmt":"2023-06-13T09:23:46","slug":"kombinatorika","status":"publish","type":"post","link":"https:\/\/matematika.otroci.org\/index.php\/2023\/06\/05\/kombinatorika\/","title":{"rendered":"3.R. Kombinatorika"},"content":{"rendered":"\n<p>Dobrodo\u0161li u zanimljiv svijet kombinatorike! U tre\u0107em razredu matematike, upustit \u0107emo se u putovanje kroz razli\u010dite na\u010dine brojanja, raspore\u0111ivanja i kombiniranja objekata. Kroz igre, aktivnosti i zadatke, nau\u010dit \u0107emo o osnovama kombinatorike i njenom utjecaju na matematiku i svakodnevni \u017eivot.<\/p>\n\n\n\n<p>Kombinatorika je grana matematike koja prou\u010dava na\u010dine kako brojati, raspore\u0111ivati i kombinirati objekte. Nau\u010dit \u0107emo kako brojati objekte koriste\u0107i razli\u010dite strategije, poput postupka &#8220;jedan po jedan&#8221; ili &#8220;brojanja u skupinama&#8221;. Otkrit \u0107emo kako ova jednostavna pravila mogu pomo\u0107i u brojanju ve\u0107ih skupova objekata.<\/p>\n\n\n\n<p>Kroz kombinatoriku, razvit \u0107emo vje\u0161tinu kombiniranja objekata na razli\u010dite na\u010dine. Nau\u010dit \u0107emo kako razli\u010diti redoslijed i raspored mogu utjecati na broj mogu\u0107nosti. Istra\u017eit \u0107emo koncepte permutacija (razli\u010diti redoslijedi) i kombinacija (bez obzira na redoslijed) te kako ih primijeniti u prakti\u010dnim situacijama.<\/p>\n\n\n\n<p>Tako\u0111er \u0107emo se baviti brojanjem skupova objekata kori\u0161tenjem dijagrama Vennovih krugova i dijagrama stabla. Nau\u010dit \u0107emo kako koristiti ove dijagrame za organiziranje informacija i izra\u010dunavanje broja mogu\u0107nosti. Primijenit \u0107emo ove vje\u0161tine u rje\u0161avanju matemati\u010dkih problema, poput brojanja kombinacija boja, predmeta ili timova.<\/p>\n\n\n\n<p>Na ovoj stranici prona\u0107i \u0107ete mnogo primjera, ilustracija i vje\u017ebi koje \u0107e vam pomo\u0107i da bolje razumijete kombinatoriku. Kroz interaktivne aktivnosti, igre i zadatke, razvit \u0107emo vje\u0161tine brojanja, logi\u010dkog razmi\u0161ljanja i analize.<\/p>\n\n\n\n<p>Jeste li spremni za putovanje kroz svijet kombinatorike? Krenimo zajedno na ovo matemati\u010dko putovanje, istra\u017eujmo na\u010dine brojanja, raspore\u0111ivanja i kombiniranja objekata te primijenimo ove vje\u0161tine u rje\u0161avanju razli\u010ditih matemati\u010dkih problema!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Radni listovi<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/matematika.otroci.org\/pdf\/3.r\/Kombinatorika_01.pdf\"><img loading=\"lazy\" decoding=\"async\" width=\"724\" height=\"1024\" src=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_01-724x1024.png\" alt=\"\" class=\"wp-image-984\" srcset=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_01-724x1024.png 724w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_01-212x300.png 212w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_01-768x1086.png 768w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_01-1086x1536.png 1086w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_01-1448x2048.png 1448w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_01-600x848.png 600w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_01.png 1654w\" sizes=\"auto, (max-width: 724px) 100vw, 724px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/matematika.otroci.org\/pdf\/3.r\/Kombinatorika_02.pdf\"><img loading=\"lazy\" decoding=\"async\" width=\"724\" height=\"1024\" src=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_02-1-724x1024.png\" alt=\"\" class=\"wp-image-1418\" srcset=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_02-1-724x1024.png 724w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_02-1-212x300.png 212w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_02-1-768x1086.png 768w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_02-1-1086x1536.png 1086w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_02-1-1448x2048.png 1448w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_02-1-600x848.png 600w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_02-1.png 1654w\" sizes=\"auto, (max-width: 724px) 100vw, 724px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/matematika.otroci.org\/pdf\/3.r\/Kombinatorika_03.pdf\"><img loading=\"lazy\" decoding=\"async\" width=\"724\" height=\"1024\" src=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_03-1-724x1024.png\" alt=\"\" class=\"wp-image-1419\" srcset=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_03-1-724x1024.png 724w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_03-1-212x300.png 212w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_03-1-768x1086.png 768w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_03-1-1086x1536.png 1086w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_03-1-1448x2048.png 1448w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_03-1-600x848.png 600w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_03-1.png 1654w\" sizes=\"auto, (max-width: 724px) 100vw, 724px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Rje\u0161enje<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/matematika.otroci.org\/pdf\/3.r\/Kombinatorika_res_01.pdf\"><img loading=\"lazy\" decoding=\"async\" width=\"724\" height=\"1024\" src=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_01-724x1024.png\" alt=\"\" class=\"wp-image-987\" srcset=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_01-724x1024.png 724w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_01-212x300.png 212w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_01-768x1086.png 768w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_01-1086x1536.png 1086w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_01-1448x2048.png 1448w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_01-600x848.png 600w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_01.png 1654w\" sizes=\"auto, (max-width: 724px) 100vw, 724px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/matematika.otroci.org\/pdf\/3.r\/Kombinatorika_res_02.pdf\"><img loading=\"lazy\" decoding=\"async\" width=\"724\" height=\"1024\" src=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_02-1-724x1024.png\" alt=\"\" class=\"wp-image-1421\" srcset=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_02-1-724x1024.png 724w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_02-1-212x300.png 212w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_02-1-768x1086.png 768w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_02-1-1086x1536.png 1086w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_02-1-1448x2048.png 1448w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_02-1-600x848.png 600w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_02-1.png 1654w\" sizes=\"auto, (max-width: 724px) 100vw, 724px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/matematika.otroci.org\/pdf\/3.r\/Kombinatorika_res_03.pdf\"><img loading=\"lazy\" decoding=\"async\" width=\"724\" height=\"1024\" src=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_03-1-724x1024.png\" alt=\"\" class=\"wp-image-1422\" srcset=\"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_03-1-724x1024.png 724w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_03-1-212x300.png 212w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_03-1-768x1086.png 768w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_03-1-1086x1536.png 1086w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_03-1-1448x2048.png 1448w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_03-1-600x848.png 600w, https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/06\/Kombinatorika_res_03-1.png 1654w\" sizes=\"auto, (max-width: 724px) 100vw, 724px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Dobrodo\u0161li u zanimljiv svijet kombinatorike! U tre\u0107em razredu matematike, upustit \u0107emo se u putovanje kroz razli\u010dite na\u010dine brojanja, raspore\u0111ivanja i<\/p>\n","protected":false},"author":1,"featured_media":307,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[7],"tags":[],"class_list":["post-1133","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-3-razred"],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/matematika.otroci.org\/wp-content\/uploads\/2023\/05\/10_06_matematika.jpg","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/posts\/1133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/comments?post=1133"}],"version-history":[{"count":7,"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/posts\/1133\/revisions"}],"predecessor-version":[{"id":1440,"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/posts\/1133\/revisions\/1440"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/media\/307"}],"wp:attachment":[{"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/media?parent=1133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/categories?post=1133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/matematika.otroci.org\/index.php\/wp-json\/wp\/v2\/tags?post=1133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}