{"id":1706,"date":"2022-12-05T11:03:22","date_gmt":"2022-12-05T09:03:22","guid":{"rendered":"https:\/\/lumatikka.luma.fi\/sv\/?page_id=1706"},"modified":"2025-06-27T14:20:24","modified_gmt":"2025-06-27T11:20:24","slug":"materialsamlingar","status":"publish","type":"page","link":"https:\/\/lumatikka.luma.fi\/sv\/material\/materialsamlingar\/","title":{"rendered":"Materialsamlingar"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">Materialsamlingar<\/h1>\n\n\n\n<p>Av allt utbildningsmaterial p\u00e5 LUMATIKKA och LUMATIKKA+ -kurserna har det sammanst\u00e4llts olika tematiska samlingar i Biblioteket f\u00f6r \u00f6ppna l\u00e4rresurser (AOE). Det har ocks\u00e5 gjorts en \u00f6versikt \u00f6ver samlingarna, som du hittar lite l\u00e4ngre ner p\u00e5 den h\u00e4r sidan. Man kan ocks\u00e5 leta fram samlingarna direkt p\u00e5 AOE-tj\u00e4nsten utifr\u00e5n ett tema eller en m\u00e5lgrupp eller till exempel genom att skriva ordet LUMATIKKA i s\u00f6kf\u00e4ltet. Det svenska materialet hittar du genom att byta spr\u00e5ket p\u00e5 webbplatsen till svenska l\u00e4ngst upp p\u00e5 sidan till h\u00f6ger. Det finska materialet hittar du i sin tur p\u00e5 den finskspr\u00e5kiga versionen av webbplatsen. Observera att en stor del av v\u00e5rt videomaterial har svensk textning, \u00e4ven om titeln p\u00e5 videon \u00e4r p\u00e5 finska.<\/p>\n\n\n\n<p>LUMATIKKA och LUMATIKKA+ -materialet som lagts ut p\u00e5 AOE-tj\u00e4nsten har den \u00f6ppna licensen CC BY-SA 4.0 (Erk\u00e4nnande-DelaLika 4.0 Internationell). Licensen g\u00f6r det m\u00f6jligt att kopiera, sprida och omarbeta materialet utifr\u00e5n egna behov. D\u00e4rf\u00f6r f\u00e5r materialet fritt anv\u00e4ndas i undervisningen, och vid behov kan det ocks\u00e5 skr\u00e4ddarsys utifr\u00e5n kontext, situation, m\u00e5lgrupp och behov.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"323\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-6-1024x323.png\" alt=\"Ing\u00e5ngssidan till Biblioteket f\u00f6r \u00f6ppna l\u00e4rresurser (AOE) och s\u00f6krutan d\u00e4r det stor S\u00f6kord \/ Utbildninsstadium \/ Undervisnings\u00e4mne \/ Typ av l\u00e4romaterial.\" class=\"wp-image-1712\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-6-1024x323.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-6-300x95.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-6-768x242.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-6-1536x485.png 1536w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-6.png 1607w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><em>Ing\u00e5ngssidan till Biblioteket f\u00f6r \u00f6ppna l\u00e4rresurser (AOE) och s\u00f6krutan.<\/em><\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Tematisk indelning av materialsamlingar<\/h2>\n\n\n\n<p>Listan nedan ger en tematisk \u00f6versikt \u00f6ver v\u00e5ra materialsamlingar. Genom att klicka p\u00e5 namnet p\u00e5 samlingen f\u00e5r du fram en direktl\u00e4nk till materialet och information om utbildningsstadierna materialet l\u00e4mpar sig b\u00e4st f\u00f6r. Materialsamlingarna har sammanst\u00e4llts av utbildningsmaterial p\u00e5 LUMATIKKA eller LUMATIKKA+ -kurserna. N\u00e5gra samlingar har producerats som en del av LUMATIKKA-projektet men uppdaterats i det fortsatta projektet LUMATIKKA+. Det n\u00e4mns i beskrivningen. Observera ocks\u00e5 att LUMATIKKA+ material har en logotyp som inkluderar ett plustecken.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:350px\">\n<p>M\u00e5lgrupperna anges med f\u00f6ljande f\u00f6rkortningar:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>SBP = sm\u00e5barnspedagogik<\/li>\n\n\n\n<li>FS = f\u00f6rskola<\/li>\n\n\n\n<li>\u00c5K1\u20136 = grundl\u00e4ggande utbildning,&nbsp;\u00e5rskurserna 1\u20136<\/li>\n\n\n\n<li>\u00c5K7\u20139 = grundl\u00e4ggande utbildning,&nbsp;\u00e5rskurserna 7\u20139<\/li>\n\n\n\n<li>GY = gymnasium<\/li>\n\n\n\n<li>YR = yrkesutbildning<\/li>\n<\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>Samlingarna \u00e4r rubricerade enligt sitt ursprung p\u00e5 f\u00f6ljande s\u00e4tt: <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(L)<\/strong> = LUMATIKKA<\/li>\n\n\n\n<li><strong>(+)<\/strong> = LUMATIKKA+<\/li>\n\n\n\n<li><strong>(u)<\/strong> = Materialet i samlingen har producerats f\u00f6r LUMATIKKA-kurserna, men <strong>sm\u00e5 uppdateringar<\/strong> fr\u00e5n LUMATIKKA+-material har lagts till<\/li>\n\n\n\n<li><strong>(U)<\/strong> = Materialet har producerats f\u00f6r LUMATIKKA-kurserna, men <strong>betydande uppdateringar<\/strong> fr\u00e5n LUMATIKKA+-material har lagts till<\/li>\n<\/ul>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Vad p\u00e5verkar en elevs f\u00f6rm\u00e5ga att l\u00e4ra sig matematik och hur kan den unders\u00f6kas?<\/h3>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17060\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">L\u00e4rande i matematik och \u00e5tg\u00e4rder f\u00f6r gruppspecifikt\u00a0st\u00f6d (+)<\/h4><div id=\"ac-17060\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> matematiksv\u00e5righeter, gruppspecifikt\u00a0st\u00f6d, differentiering, matematiskt kunnande<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/4760\">https:\/\/aoe.fi\/#\/materiaali\/4760<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"890\" height=\"801\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-1.png\" alt=\"\" class=\"wp-image-2473\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-1.png 890w, https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-1-300x270.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-1-768x691.png 768w\" sizes=\"auto, (max-width: 890px) 100vw, 890px\" \/><figcaption class=\"wp-element-caption\">Gruppspecifikt\u00a0st\u00f6d p\u00e5 matematiklektioner -sj\u00e4lvv\u00e4rdering f\u00f6r l\u00e4rare<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17061\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Forskningsresultat kring l\u00e4rande och olika motivationsfaktorer inom det matematiska omr\u00e5det (u)<\/h4><div id=\"ac-17061\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong>M\u00e5lgrupp:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> professionellt l\u00e4rande, hj\u00e4rnforskning, motivationsfaktorer<br><br><strong>Materialtyp:<\/strong> video, presentation<br><br><strong>L\u00e4nk till materialet:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2423\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2423<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/Screenshot-336.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/Screenshot-336.png\" alt=\"P\u00e5 bilden: Markku Hannula, prof. HU.\" class=\"wp-image-7748\"\/><\/a><figcaption class=\"wp-element-caption\">Markku Hannula talar om forskningsresultat kring temat.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17062\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Utmaningar och st\u00f6d f\u00f6r att l\u00e4ra sig matematik (U)<\/h4><div id=\"ac-17062\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> inl\u00e4rningssv\u00e5righeter,<br>spr\u00e5kmedvetenhet, s\u00e4rskilt st\u00f6d<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video (ocks\u00e5 text p\u00e5 finska)<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2424\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2424\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2424<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"574\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-8-1024x574.png\" alt=\"P\u00e5 bilden finns en glad barn med tv\u00e5 klossar framf\u00f6r \u00f6gonen. P\u00e5 bordet finns mera klossar. P\u00e5 bildet finns ocks\u00e5 LUMATIKKA, Skolresurs, LUMA-center Finland och Centret f\u00f6r livsl\u00e5ngt l\u00e4rande -logor och text Matematik och barnets spr\u00e5kliga utveckling.\" class=\"wp-image-1718\" style=\"width:371px;height:207px\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-8-1024x574.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-8-300x168.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-8-768x430.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-8.png 1083w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Ann-Catherine Henriksson ber\u00e4ttar om matematik och barnets spr\u00e5kliga utveckling.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17063\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Kartl\u00e4ggning f\u00f6r att identifiera st\u00f6dbehov (+, endast p\u00e5 finska)<\/h4><div id=\"ac-17063\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> kartl\u00e4ggning i matematik, tester<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, \u00f6vning, guide<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/4760\">https:\/\/aoe.fi\/#\/materiaali\/4760<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-3.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-3.png\" alt=\"\" class=\"wp-image-11078\"\/><\/a><figcaption class=\"wp-element-caption\">I materialen finns t. ex. ett test f\u00f6r att kartl\u00e4gga f\u00f6rst\u00e5elsen av decimaltal.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17064\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Vad best\u00e5r matematiskt kunnande av? (U, endast p\u00e5 finska)<\/h4><div id=\"ac-17064\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> matematikuppfattning, syn p\u00e5 matematik, matematiskt kunnande<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text, audio<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2457\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2457\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2457<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/image-1-edited-1.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/image-1-edited-1.png\" alt=\"Professor Samuli Siltanen.\" class=\"wp-image-7805\" style=\"width:320px\"\/><\/a><figcaption class=\"wp-element-caption\">Professor Samuli Siltanen talar om vilken typ av f\u00e4rdigheter i matematisk t\u00e4nkande och r\u00e4knef\u00e4rdigheter \u00e4r till nytta i maskinernas tidevarv.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17065\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Bed\u00f6mning inom matematikundervisningen (U)<\/h4><div id=\"ac-17065\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> bed\u00f6mning, formativ bed\u00f6mning, sj\u00e4lvv\u00e4rdering<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> audio, text, video<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2426\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2426\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2426<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/arviointimaa.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/arviointimaa.png\" alt=\"P\u00e5 bilden \u00e4r Arviointimaa visuellt illustrerad. Det finns ett tr\u00e4d i mitten av utv\u00e4rderingsmarken. Till v\u00e4nster om tr\u00e4det finns solen och en ljus milj\u00f6. Milj\u00f6n visar t.ex. en luftballong, en vulkan och en labyrint. Till h\u00f6ger om tr\u00e4det kan du se m\u00e5nen som har en nattm\u00f6ssa, och en m\u00f6rkare milj\u00f6. Milj\u00f6n har t.ex. ett slott p\u00e5 toppen av ett moln och ett vattenfall.\" class=\"wp-image-7775\" style=\"width:302px;height:212px\"\/><\/a><figcaption class=\"wp-element-caption\">Hur kan verktyget Arviontimaa\u00a9 (Eero Karvonen) anv\u00e4ndas n\u00e4r eleverna g\u00f6r sj\u00e4lvv\u00e4rderingar av sina matematiska f\u00e4rdigheter?<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17066\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">L\u00e4randeanalytik som en del av bed\u00f6mningen (+, endast p\u00e5 finska)<\/h4><div id=\"ac-17066\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> bed\u00f6mning, l\u00e4randeanalytik, ViLLE, MOODLE, digiportfolio<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/4985\">https:\/\/aoe.fi\/#\/materiaali\/4985<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/Nayttokuva-1447.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/Nayttokuva-1447-1024x576.png\" alt=\"\" class=\"wp-image-11109\"\/><\/a><figcaption class=\"wp-element-caption\">TRILA (Turku Research Institute for Learning Analytics) vid \u00c5bo universitet har utvecklat ViLLE-l\u00e4rmilj\u00f6n som anv\u00e4nds i skolor \u00f6ver hela Finland. I videon f\u00f6rklarar Aleksi Hermonen hur l\u00e4randeanalytiken p\u00e5 plattformen kan anv\u00e4ndas i matematikundervisningen.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Arbetss\u00e4tt som \u00f6kar intresset f\u00f6r och f\u00f6rst\u00e5elsen av matematik<br><\/h3>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17067\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Verbalisering av matematiskt t\u00e4nkande (L)<\/h4><div id=\"ac-17067\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> verbalisering, skriftliga uttrycksformer, modell f\u00f6r matematikens fyra spr\u00e5k<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> audio, \u00f6vning, text, video<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/1866\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/1866\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/1866<\/a> <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/image.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/image-1024x576.png\" alt=\"P\u00e5 bilden \u00e4r modellen f\u00f6r matematikens fyra spr\u00e5k: i mitten av bilden st\u00e5r Matematisk t\u00e4nkande, och runt det matematikens symbolspr\u00e5k, naturliga spr\u00e5k, figurspr\u00e5k och taktilt spr\u00e5k (p\u00e5 finska). \" class=\"wp-image-7791\" style=\"width:398px;height:223px\"\/><\/a><figcaption class=\"wp-element-caption\">Jorma Joutsenlahti, universitetslektor i matematikens didaktik, talar om hur matematiskt t\u00e4nkande uttrycks med hj\u00e4lp av modellen f\u00f6r matematikens fyra spr\u00e5k: matematikens symbolspr\u00e5k, naturliga spr\u00e5k, figurspr\u00e5k och taktilt spr\u00e5k.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17068\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Matematikens m\u00e5nga representationer (u)<\/h4><div id=\"ac-17068\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> representationer, matematikens tre v\u00e4rldar, David Tall<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2429\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2429\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2429<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/Screenshot-349-e1666269313878.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/Screenshot-349-e1666269313878-1024x553.png\" alt=\"Bilden visar olika representationer av funktionen, t. ex. y=3x med f\u00e4rgstavar och ett koordinatsystem. Dessutom en text som listar saker som p\u00e5verkar inl\u00e4rningen och f\u00f6rst\u00e5elsen: tonfall, talrytmer, kroppsspr\u00e5k, r\u00f6relser, ansiktsuttryck, blickar, gester (presentera, beskriva, peka och rytmiskt).\" class=\"wp-image-7807\" style=\"width:354px;height:191px\"\/><\/a><figcaption class=\"wp-element-caption\">P\u00e4ivi Portaankorva-Koivisto, universitetslektor i matematikens didaktik, ger tips f\u00f6r hur l\u00e4raren kan berika sina s\u00e4tt att \u00e5sk\u00e5dligg\u00f6ra matematik.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-17069\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Digitala verktyg och dynamiska representationer i matematik (U, endast p\u00e5 finska)<\/h4><div id=\"ac-17069\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> digitala verktyg, dynamiska representationer, GeoGebra, TinkerCAD, kalkylark<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, presentation<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2430\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2430\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2430<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/image-2-e1666269698167.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/image-2-e1666269698167-1024x543.png\" alt=\"P\u00e5 bilden \u00e4r Lauri Hellsten som talar om f\u00f6rdelarna med dynamiska representationer.\" class=\"wp-image-7810\" style=\"width:450px;height:238px\"\/><\/a><figcaption class=\"wp-element-caption\">\u00c5rets l\u00e4rare i matematiska \u00e4mnen \u00e5r 2023, Lauri Hellsten, talar om f\u00f6rdelarna med dynamiska representationer i matematikundervisningen.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170610\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Mer aktivitet p\u00e5 matematiklektioner (L)<\/h4><div id=\"ac-170610\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K1\u20136, \u00c5K7\u20139<br><br><strong>Nyckelord:<\/strong> funktionella metoder, funktionellt l\u00e4rande, erfarenhetsbaserad undervisning<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2425\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2425\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2425<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"600\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-9-1024x600.png\" alt=\"P\u00e5 bilden finns n\u00e5gra m\u00e4nniskor. En av dem \u00e4r vid tavlan, en annan har en minir\u00e4knare, den tredje t\u00e4nker p\u00e5 siffran 428 med hj\u00e4lp av en p\u00e4rltavla, och den fj\u00e4rde t\u00e4nker p\u00e5 n\u00e5gon ber\u00e4kningsalgoritm. Texten: Aktivera eleverna! Aktiverande uppgifter.\" class=\"wp-image-1721\" style=\"width:348px;height:204px\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-9-1024x600.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-9-300x176.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-9-768x450.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-9.png 1258w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Varf\u00f6r och hur ska funktionella metoder och erfarenheter anv\u00e4ndas i matematikundervisningen?<br>I Aktiverande uppgifter-materialet presenteras olika alternativ f\u00f6r hur man kan g\u00e5 tillv\u00e4ga.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170611\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Arbetsmetoder som st\u00f6der kollaborativt l\u00e4rande inom matematikundervisningen (L)<\/h4><div id=\"ac-170611\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> kollaborativt l\u00e4rande, matematiksamtal<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text <br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <br><a href=\"https:\/\/aoe.fi\/#\/materiaali\/2468\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2468<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"718\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-12-1024x718.png\" alt=\"Texten: KOLLABORATIVT L\u00c4RANDE I MATEMATIK: UPPGIFTSTYPER. P\u00e5 bilden: tre elever, varav tv\u00e5 l\u00e4ser b\u00f6cker och en skriver siffror.\" class=\"wp-image-1732\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-12-1024x718.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-12-300x210.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-12-768x538.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-12.png 1198w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Dessa uppgiftsexempel uppmuntrar eleverna att vara aktivt delaktiga, intressera sig f\u00f6r matematik och v\u00e5ga ta sig an lite mer utmanande uppgifter.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170612\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Misstag och p\u00e5st\u00e5enden som drivkraft f\u00f6r l\u00e4rande \u2013 mot en positiv felkultur (+, endast p\u00e5 finska)<\/h4><div id=\"ac-170612\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> en positiv felkultur, missuppfattning, k\u00e4nslor<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, bild, text <br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <br><a href=\"https:\/\/aoe.fi\/#\/materiaali\/4974\">https:\/\/aoe.fi\/#\/materiaali\/4974<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-6.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-6-1024x576.png\" alt=\"\" class=\"wp-image-11093\"\/><\/a><figcaption class=\"wp-element-caption\">LUMA-koordinatorn Sanna Launiainen ber\u00e4ttar om olika s\u00e4tt att fr\u00e4mja en positiv felkultur i matematikundervisningen. Videon \u00e4r gjord i samarbete med FT Laszlo Major, chef f\u00f6r Sydv\u00e4stra Finlands&nbsp;LUMA-center vid \u00c5bo universitet.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170613\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Slutledning och bevisf\u00f6ring i gymnasiematematik (L, endast p\u00e5 finska)<\/h4><div id=\"ac-170613\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> GY<br><br><strong>Nyckelord:<\/strong> bevisf\u00f6ring, argumentation<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> text, video<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2428\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2428\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2428<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/gg.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/gg.png\" alt=\"Bilden visar en skissad representation av en triangel (gjord med GeoGebra), som verifierar att summan av vinklarna \u00e4r 180 grader.\" class=\"wp-image-7806\" style=\"width:242px;height:185px\"\/><\/a><figcaption class=\"wp-element-caption\">Geometriska bevisf\u00f6ringsuppgifter \u00e4r klassiker inom gymnasiematematiken.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170614\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Verktyg f\u00f6r tr\u00e4ning av probleml\u00f6sningsf\u00f6rm\u00e5ga (U)<\/h4><div id=\"ac-170614\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord: <\/strong>probleml\u00f6sning,<br>problemuppgifter, \u00f6ppna problem<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text, \u00f6vning<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong><a href=\"https:\/\/aoe.fi\/#\/materiaali\/1865\" target=\"_blank\" rel=\"noreferrer noopener\"> https:\/\/aoe.fi\/#\/materiaali\/1865<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"426\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-11-1024x426.png\" alt=\"Fyra olika bilder\n1. Ett j\u00e4mnt antal objekt (p\u00e5 bilden: en box som inneh\u00e5ller 10 bollar).\n2. Tv\u00e5grupper med olika m\u00e5nga objekt i varje (p\u00e5 bilden: tv\u00e5 likadana l\u00e5dor med 5 bollar sida vid sida).\n3. Exakt parbildning (p\u00e5 bilden: tv\u00e5 likadana l\u00e5dor med 5 bollar sida vid sida och pilar mellan intilliggande bollar.\n4. Objekten ordnade i par (p\u00e5 bilden: 5 l\u00e5dor med 2 bollar, staplade p\u00e5 varandra).\n \" class=\"wp-image-1731\" style=\"width:343px;height:142px\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-11-1024x426.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-11-300x125.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-11-768x319.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-11.png 1075w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Materialet inneh\u00e5ller bland annat problemuppgifter som l\u00e4mpar sig f\u00f6r olika utbildningsstadier.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170615\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Guide f\u00f6r unders\u00f6kande l\u00e4rande baserat 5E-modellen (u)<\/h4><div id=\"ac-170615\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord: <\/strong>probleml\u00f6sning,<br>unders\u00f6kande arbetss\u00e4tt, 5E-modellen, \u00f6ppna problem<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, guide, aktivitet<br><br><strong><strong>L\u00e4nk till materialet: <\/strong><\/strong><a href=\"https:\/\/aoe.fi\/#\/materiaali\/4831\">https:\/\/aoe.fi\/#\/materiaali\/4831<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"722\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-2-1024x722.png\" alt=\"\" class=\"wp-image-2485\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-2-1024x722.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-2-300x211.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-2-768x541.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2025\/06\/image-2.png 1118w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Maarit Rossi uppmuntrar l\u00e4rarna att bryta invanda m\u00f6nster: Har man aldrig misslyckats har man heller aldrig pr\u00f6vat p\u00e5 n\u00e5got nytt!<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170616\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Matematiken i vardagen och i samh\u00e4llet (U)<\/h4><div id=\"ac-170616\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord<\/strong>: matematik i samh\u00e4llet, matematik i kulturen, vardagsmatematik<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, \u00f6vning, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong><br><a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2458\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2458<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"646\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-13-1024x646.png\" alt=\"9. Matematik anv\u00e4nds i samh\u00e4llets\noch f\u00f6retagens beslutstagande.\nNya lantbruksf\u00f6retagaren ska best\u00e4lla fr\u00f6 f\u00f6r v\u00e5rs\u00e5dd.\nHan visste att den l\u00e4mpliga t\u00e4theten f\u00f6r v\u00e4xter \u00e4r\nungef\u00e4r 500 per kvadratmeter. Han visste ocks\u00e5 att\n1000 fr\u00f6n v\u00e4gde 40 gram. Hur m\u00e5nga kilogram fr\u00f6\nhan best\u00e4lla d\u00e5 han ska s\u00e5 en hektar odlingsmark?\nHan s\u00e5dde alla de fr\u00f6n han best\u00e4llde p\u00e5 v\u00e5ren, men\ntrots de goda f\u00f6rh\u00e5llandena blev det i genomsnitt\nendast 450 v\u00e4xter per kvadratmeter i f\u00e4ltet? Hur\nkunde det komma sig? Hur mycket fr\u00f6 ska han\nbest\u00e4lla f\u00f6r n\u00e4sta \u00e5r?\" class=\"wp-image-1735\" style=\"width:365px;height:230px\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-13-1024x646.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-13-300x189.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-13-768x485.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-13.png 1307w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Matematik i samh\u00e4llet-uppgiftsexempel.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170617\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Matematik och kreativitet (u)<\/h4><div id=\"ac-170617\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> funktionellt l\u00e4rande, kreativitet, matematisk konst, digital konst<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, \u00f6vning<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong><br><a href=\"https:\/\/aoe.fi\/#\/materiaali\/1882\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/1882<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/03\/LUMATIKKA_vaakatahti.jpg\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/03\/LUMATIKKA_vaakatahti-1024x681.jpg\" alt=\"Stj\u00e4rna med ett snitt. Bild: Veikko Somerpuro.\" class=\"wp-image-6939\" style=\"width:408px;height:271px\"\/><\/a><figcaption class=\"wp-element-caption\">Stj\u00e4rna med ett snitt. Bild: Veikko Somerpuro.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170618\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Matematik i r\u00f6relse (u)<\/h4><div id=\"ac-170618\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> r\u00f6relsebaserad lektion, kroppsbaserad begreppsutveckling, hj\u00e4rnforskning<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text, \u00f6vning<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2437\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2437\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2437<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/Kehollinen-matikka.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/Kehollinen-matikka.png\" alt=\"Bilden visar ett utrymme som \u00e4r delat i tv\u00e5 delar. En ok\u00e4nd rymdf\u00e4rja har landat p\u00e5 andra sidan. Det finns 9 elever p\u00e5 samma sidan som det ok\u00e4nda objektet och 12 elever p\u00e5 den andra sidan.\n\" class=\"wp-image-7836\" style=\"width:474px;height:260px\"\/><\/a><figcaption class=\"wp-element-caption\">Exempel p\u00e5 hur ekvationer och begreppet ok\u00e4nd variabel kan \u00e5sk\u00e5dligg\u00f6ras kroppsligt.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170619\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Textilsl\u00f6jd, musik eller matematik? (u)<\/h4><div id=\"ac-170619\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K7\u20139, GY<br><br><strong>Nyckelord:<\/strong> knutar, handarbete, matematisk konst<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2452\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2452\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2452<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_kassaa-scaled.jpg\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_kassaa-1024x682.jpg\" alt=\"Ett r\u00f6tt virkat f\u00f6rem\u00e5l som liknar en spiral.\" class=\"wp-image-7841\" style=\"width:367px;height:244px\"\/><\/a><figcaption class=\"wp-element-caption\">Det \u00e4r m\u00f6jligt virka olika b\u00f6jda ytor.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170620\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Att st\u00f6dja utvecklingen av matematiska f\u00e4rdigheter inom sm\u00e5barnspedagogik och f\u00f6rskoleundervisning (u)<\/h4><div id=\"ac-170620\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS<br><br><strong>Nyckelord:<\/strong> utveckling av t\u00e4nkande,<br>stadiespecifik pedagogik,<br>vardagsmatematik<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text, guide<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <br><a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2463\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2463<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_vaka_tuki-scaled.jpg\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_vaka_tuki-1024x473.jpg\" alt=\"En tecknad bild av f\u00f6rskolan. L\u00e4raren sitter vid bordet med tv\u00e5 barn. Barn studerar med nummerkort och block. Siffrorna 1\u20139 visas i bakgrunden.\" class=\"wp-image-7843\" style=\"width:471px;height:217px\"\/><\/a><figcaption class=\"wp-element-caption\">Materialet ger l\u00e4rare tips f\u00f6r hur olika barncentrerade arbetss\u00e4tt kan anv\u00e4ndas i sm\u00e5barnspedagogik och f\u00f6rskoleundervisning.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170621\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Skolmatematikens historia (L)<\/h4><div id=\"ac-170621\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K7\u20139, GY<br><br><strong>Nyckelord:<\/strong> matematikens historia, skolmatematik, klassiska problem<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text, \u00f6vning<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2427\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2427\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2427<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"472\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-14-1024x472.png\" alt=\"I materialet betraktas skolmatematiken ur ett historiskt perspektiv. Texten: Stj\u00e4rnhimmel och trigonometri. Trigonometrin utvecklades l\u00e5ngt tillsammans med astronomi i Prolemaios arbete. I ptolemaios jordbaserade v\u00e4rldsbild var himlen b\u00f6jd \u00f6ver jorden. \" class=\"wp-image-1740\" style=\"width:416px;height:191px\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-14-1024x472.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-14-300x138.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-14-768x354.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-14.png 1473w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">I materialet betraktas skolmatematiken ur ett historiskt perspektiv.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170622\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Matematisk modellering (+)<\/h4><div id=\"ac-170622\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K7\u20139, GY<br><br><strong>Nyckelord:<\/strong> matematisk modellering, modelleringscykel, matematisering, till\u00e4mpningsuppgift<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/4989\">https:\/\/aoe.fi\/#\/materiaali\/4989<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-4.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-4-1024x576.png\" alt=\"\" class=\"wp-image-11086\"\/><\/a><figcaption class=\"wp-element-caption\">Docent Mats Brask\u00e9n fr\u00e5n \u00c5bo Akademi introducerar en metod att organisera och f\u00f6rst\u00e5 modelleringsprocessen.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Temaomr\u00e5den i matematik<\/h3>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170623\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Matematik inom sm\u00e5barnspedagogik och f\u00f6rskoleundervisning (L)<\/h4><div id=\"ac-170623\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS<br><br><strong>Nyckelord:<\/strong> utveckling av matematiska f\u00e4rdigheter, f\u00f6rmatematiska f\u00e4rdigheter, matematiska omr\u00e5den<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, guide, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <br><a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2459\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2459<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"501\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-16-1024x501.png\" alt=\"P\u00e5 bilden: Ann-Catherine Henriksson med geometriska former som syns p\u00e5 f\u00f6rel\u00e4sningspresentationen om L\u00e4rande om geometri enligt styrdokumenten.  \" class=\"wp-image-1747\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-16-1024x501.png 1024w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-16-300x147.png 300w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-16-768x376.png 768w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-16.png 1083w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">Ann-Catherine Henriksson fr\u00e5n \u00c5bo Akademi talar om arbetss\u00e4tt f\u00f6r och m\u00f6jligheter med geometriundervisning i sm\u00e5barnspedagogik och f\u00f6rskoleundervisning.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170624\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">M\u00e5ngsidig taluppfattning och goda f\u00e4rdigheter kring decimalsystemet (U)<\/h4><div id=\"ac-170624\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> FS, \u00c5K1\u20136<br><br><strong>Nyckelord:<\/strong> taluppfattning, decimalsystemet, talserier<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, (text och bild p\u00e5 finska)<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2433\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2433\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2433<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_lukukasite_10jarj.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_lukukasite_10jarj.png\" alt=\"Bilden visar antalet 1345,12 representerat med nummerkort och med hj\u00e4lp av olika kuber (redskap f\u00f6r decimalsystemet).\n\" class=\"wp-image-7844\" style=\"width:312px;height:208px\"\/><\/a><figcaption class=\"wp-element-caption\">Kollaborativa redskap st\u00e5r i fokus i utvecklingen av taluppfattningen och tiosystemet.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170625\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Funktionella aktiviteter som st\u00f6d f\u00f6r olika r\u00e4kneoperationer (u)<\/h4><div id=\"ac-170625\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> FS, \u00c5K1\u20136<br><br><strong>Nyckelord:<\/strong> r\u00e4kneoperationer, r\u00e4knestrategier, verktyg f\u00f6r \u00e5sk\u00e5dligg\u00f6rande, algoritm f\u00f6r r\u00e4kning med uppst\u00e4llning<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, verktyg<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2434\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2434\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/aoe.fi\/#\/materiaali\/2434<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"472\" height=\"629\" src=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-15-edited.png\" alt=\"P\u00e5 bilden: Fyra barn som alla har 3 multilink-kuber och ber\u00e4kningen 14:4=3.\" class=\"wp-image-1744\" style=\"width:194px;height:257px\" srcset=\"https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-15-edited.png 472w, https:\/\/lumatikka.luma.fi\/sv\/files\/2022\/12\/image-15-edited-225x300.png 225w\" sizes=\"auto, (max-width: 472px) 100vw, 472px\" \/><figcaption class=\"wp-element-caption\">Konkreta verktyg \u00f6kar elevers f\u00f6rst\u00e5else av de grundl\u00e4ggande r\u00e4kneoperationerna.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170626\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">De rationella talens mystiska v\u00e4rld (U)<\/h4><div id=\"ac-170626\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K1\u20136, \u00c5K7\u20139, YR<br><br><strong>Nyckelord:<\/strong> r\u00e4kneoperationer med tal i br\u00e5kform, rationella tal, verktyg f\u00f6r \u00e5sk\u00e5dligg\u00f6rande, presentationsformer<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, (text p\u00e5 finska)<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/2435\">https:\/\/aoe.fi\/#\/materiaali\/2435<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_murtoluvut.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_murtoluvut.png\" alt=\"P\u00e5 bilden: tre olika representationer f\u00f6r br\u00e5ktalet.\n1. \u2156 visas med en m\u00e4ngdmodell (tv\u00e5 orange och tre gula mor\u00f6tter inuti cirkeln). \n2. \u2154 visas med en tallinjemodell (tallinjen fr\u00e5n noll till ett uppdelad i tre lika delar, varav tv\u00e5 \u00e4r markerade med parenteser). \n3. \u2157 visas med en areamodell  (rektangel uppdelad i fem lika stora kolumner, varav tre \u00e4r f\u00e4rgade).\" class=\"wp-image-7846\" style=\"width:381px;height:246px\"\/><\/a><figcaption class=\"wp-element-caption\">Br\u00e5ktalens m\u00e5nga betydelser kan \u00e5sk\u00e5dligg\u00f6ras med  hj\u00e4lp av olika modeller: m\u00e4ngdmodell, tallinjemodell och areamodell.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170627\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Geometri och m\u00e4tning inom grundl\u00e4ggande utbildning och yrkesutbildning (u)<\/h4><div id=\"ac-170627\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> FS, \u00c5K1\u20136, \u00c5K7\u20139, YR<br><br><strong>Nyckelord:<\/strong> geometri, m\u00e4tning, enhetsomvandlingar<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2454\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2454\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2454<\/a> <\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/image-4.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/image-4.png\" alt=\"Tuula Pesonen \u00e5sk\u00e5dligg\u00f6r plangeometriska begrepp vertikal vinkel\nvisuellt med hj\u00e4lp av garn.\" class=\"wp-image-7813\" style=\"width:394px;height:243px\"\/><\/a><figcaption class=\"wp-element-caption\">Tuula Pesonen \u00e5sk\u00e5dligg\u00f6r plangeometriska begrepp visuellt med hj\u00e4lp av garn.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170628\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Projektiv geometri (L, endast p\u00e5 finska)<\/h4><div id=\"ac-170628\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong>  FS, \u00c5K1\u20136, \u00c5K7\u20139, GY<br><br><strong>Nyckelord:<\/strong> projektiv geometri, Platons kroppar, matematisk konst<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2439\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2439\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2439<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_projektiivinen.jpg\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_projektiivinen-1024x270.jpg\" alt=\"Foto av fyra strukturer med f\u00e4rgglada tr\u00e4pinnar insatta genom ett cirkul\u00e4rt plan. N\u00e5gra av dem \u00e4r sammanbundna.\" class=\"wp-image-7848\" style=\"width:468px;height:123px\"\/><\/a><figcaption class=\"wp-element-caption\">Taneli Luotoniemi ger en inblick i projektiv geometri med hj\u00e4lp av Reye-konfigurationen.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170629\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Rymdkroppar i fj\u00e4rde dimensionen (L, endast p\u00e5 finska)<\/h4><div id=\"ac-170629\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> GY<br><br><strong>Nyckelord:<\/strong> Hintons kuber, h\u00f6gre rymddimensioner, matematisk konst<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, verktyg, text<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2440\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2440\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2440<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_4D.jpg\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_4D-1024x768.jpg\" alt=\"P\u00e5 bilden: f\u00e4rgglada kuber p\u00e5 bordet. I bakgrunden finns en l\u00e4rare med likadana kuber som syns p\u00e5 f\u00f6rel\u00e4sningsbilderna.\" class=\"wp-image-7849\" style=\"width:297px;height:222px\"\/><\/a><figcaption class=\"wp-element-caption\">Taneli Luotoniemi har skapat ett nytt s\u00e4tt att \u00e5sk\u00e5dligg\u00f6ra en tesserakt, dvs. en fyrdimensionell motsvarighet till en kub.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170630\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Aha, algebra! (L)<\/h4><div id=\"ac-170630\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord:<\/strong> r\u00e4kning med ok\u00e4nda variabler, ekvationer, \u00e5sk\u00e5dligg\u00f6rande<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2436\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2436\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2436<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_algebra.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_algebra.png\" alt=\"Jenny Kolstr\u00f6m visar hur matematikens symbolspr\u00e5k 3x + 2 + x ser ut som figurspr\u00e5k. Det ligger tre papperslappar p\u00e5 bordet, tv\u00e5 multilink-kuber och ytterligare ett papper.\" class=\"wp-image-7847\" style=\"width:397px;height:236px\"\/><\/a><figcaption class=\"wp-element-caption\">Jenny Kolstr\u00f6m visar varf\u00f6r det i bokstavsr\u00e4kning ocks\u00e5 \u00e4r en bra id\u00e9 att fr\u00e5n det konkreta till det mer abstrakta.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170631\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Finansmatematik i l\u00e5neber\u00e4kningar (L, endast p\u00e5 finska)<\/h4><div id=\"ac-170631\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> GY, YR<br><br><strong>Nyckelord:<\/strong> finansmatematik, l\u00e5neber\u00e4kning, digital programvara<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> video, \u00f6vning, verktyg<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2431\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/materiaali\/2431\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2431<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_lainat.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_lainat.png\" alt=\"En applet gjord med GeoGebra som visar ackumuleringen av r\u00e4nta p\u00e5 ett l\u00e5n som ett stapeldiagram. Presentationen speglar ett annuitetsl\u00e5n \/ en l\u00e5n med j\u00e4mna rater.\" class=\"wp-image-7851\" style=\"width:320px;height:212px\"\/><\/a><figcaption class=\"wp-element-caption\">Laura Yl\u00f6nen visar hur Geogebra och TI-nspire kan anv\u00e4ndas i l\u00e5neber\u00e4kningar i gymnasiet.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170632\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Digital kompetens och programmeringskunskaper (+, endast p\u00e5 finska)<\/h4><div id=\"ac-170632\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord: <\/strong>digital kompetens, programmeringskunskaper, Scratch, Micro:bit<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> presentation, text, video<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/4988\">https:\/\/aoe.fi\/#\/materiaali\/4988<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-8.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-8.png\" alt=\"\" class=\"wp-image-11098\"\/><\/a><figcaption class=\"wp-element-caption\">Materialet introducerar utvecklingen av digital kompetens och programmeringskunskaper fr\u00e5n barndomen till ungdomen. Det inneh\u00e5ller ocks\u00e5 uppgifter som l\u00e4mpar sig f\u00f6r olika utbildningsniv\u00e5er.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170633\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Programmering i matematikundervisning&nbsp;(L)<\/h4><div id=\"ac-170633\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K5\u20136, \u00c5K7\u20139, GY<br><br><strong>Nyckelord: <\/strong>matematik, programmering, Python<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> text, video<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2473\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2473<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/tietokoneet-toissa-edited.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/tietokoneet-toissa-edited.png\" alt=\"En tecknad dator med tio h\u00e4nder. H\u00e4nderna \u00e4r p\u00e5 minir\u00e4knare.\n\" class=\"wp-image-7795\" style=\"width:215px;height:160px\"\/><\/a><figcaption class=\"wp-element-caption\">Antti Laaksonens bok ger id\u00e9er f\u00f6r programmering med Python i matematikstudier. Bild: Emilia Erfving.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170634\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Bin\u00e4r matematik (+, endast p\u00e5 finska)<\/h4><div id=\"ac-170634\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> \u00c5K1\u20136, \u00c5K7\u20139, GY, YR<br><br><strong>Nyckelord: <\/strong>bin\u00e4ra talsystemet, bin\u00e4ra tal<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> presentation, \u00f6vning<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/4975\">https:\/\/aoe.fi\/#\/materiaali\/4975<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-7.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-7.png\" alt=\"\" class=\"wp-image-11096\"\/><\/a><figcaption class=\"wp-element-caption\">Materialet ger en introduktion till det bin\u00e4ra talsystemet och inneh\u00e5ller \u00f6vningar f\u00f6r att tr\u00e4na p\u00e5 bin\u00e4ra tal.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170635\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Artificiell intelligens (+, endast p\u00e5 finska)<\/h4><div id=\"ac-170635\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> SBP, FS, \u00c5K1\u20136, \u00c5K7\u20139, GY<br><br><strong>Nyckelord: <\/strong>Artificiell intelligens, recommender system<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> text, video<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a href=\"https:\/\/aoe.fi\/#\/materiaali\/4976\">https:\/\/aoe.fi\/#\/materiaali\/4976<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-9.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2025\/06\/image-9-1024x576.png\" alt=\"\" class=\"wp-image-11102\"\/><\/a><figcaption class=\"wp-element-caption\">Doktor Sini Davies vid Helsingfors universitet ger en introduktion till artificiell intelligens. Vad \u00e4r AI och hur syns det i v\u00e5r vardag? Hur kan man behandla det i undervisningen?<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-pb-accordion-item c-accordion__item js-accordion-item no-js\" data-initially-open=\"false\" data-click-to-close=\"true\" data-auto-close=\"true\" data-scroll=\"false\" data-scroll-offset=\"0\"><h4 id=\"at-170636\" class=\"c-accordion__title js-accordion-controller\" role=\"button\">Bank f\u00f6r lektionsplaner f\u00f6r programmeringsundervisning p\u00e5 olika stadier (L, endast p\u00e5 finska)<\/h4><div id=\"ac-170636\" class=\"c-accordion__content\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p class=\"has-background\" style=\"background-color:#e1f1eb\"><strong><strong>M\u00e5lgrupp<\/strong>:<\/strong> FS, \u00c5K1\u20136, \u00c5K7\u20139, GY<br><br><strong>Nyckelord:<\/strong> matematik, programmering, lektionsplan<br><br><strong><strong>Materialtyp<\/strong>:<\/strong> text, \u00f6vning<br><br><strong><strong>L\u00e4nk till materialet<\/strong>:<\/strong> <a rel=\"noreferrer noopener\" href=\"https:\/\/aoe.fi\/#\/materiaali\/2474\" target=\"_blank\">https:\/\/aoe.fi\/#\/materiaali\/2474<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-full is-style-default\"><a href=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_ohjelmointi_tuntisuunnitelmat.png\"><img decoding=\"async\" src=\"https:\/\/lumatikka.luma.fi\/wp-content\/uploads\/2022\/10\/aoe_ohjelmointi_tuntisuunnitelmat.png\" alt=\"Diagram som visar funktionerna och menyerna i MaceCode-milj\u00f6n.\n\" class=\"wp-image-7854\"\/><\/a><figcaption class=\"wp-element-caption\">Microbitar kan programmeras p\u00e5 Makecode-plattformen.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"padding-top:var(--wp--preset--spacing--10);padding-bottom:0\">Hitta flera tips f\u00f6r din undervisning<\/h2>\n\n\n\n<p>I Biblioteket f\u00f6r \u00f6ppna l\u00e4rresurser \u2013&nbsp;AOE \u2013 kan du hitta en stor m\u00e4ngd material f\u00f6r undervisningssektorn, producerat av olika instanser. Biblioteket administreras av Undervisnings- och kulturministeriet, Utbildningsstyrelse och CSC \u2013 IT-centret f\u00f6r vetenskap \u2013 Tieteen tietotekniikan keskus. Du kan l\u00e4sa n\u00e4rmare om AOE p\u00e5 webbplatsen f\u00f6r tj\u00e4nsten <a href=\"https:\/\/aoe.fi\/#\/lisatietoa\" data-type=\"URL\" data-id=\"https:\/\/aoe.fi\/#\/lisatietoa\" target=\"_blank\" rel=\"noreferrer noopener\">via den h\u00e4r l\u00e4nken<\/a>.<\/p>\n\n\n\n<div style=\"height:0px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Materialsamlingar Av allt utbildningsmaterial p\u00e5 LUMATIKKA och LUMATIKKA+ -kurserna har det sammanst\u00e4llts olika tematiska samlingar i Biblioteket f\u00f6r \u00f6ppna l\u00e4rresurser (AOE). Det har ocks\u00e5 gjorts en \u00f6versikt \u00f6ver samlingarna, som du hittar lite l\u00e4ngre ner p\u00e5 den h\u00e4r sidan. Man kan ocks\u00e5 leta fram samlingarna direkt p\u00e5 AOE-tj\u00e4nsten utifr\u00e5n ett tema eller en m\u00e5lgrupp eller [&hellip;]<\/p>\n","protected":false},"author":12,"featured_media":0,"parent":1702,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1706","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/1706","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/comments?post=1706"}],"version-history":[{"count":61,"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/1706\/revisions"}],"predecessor-version":[{"id":2511,"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/1706\/revisions\/2511"}],"up":[{"embeddable":true,"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/pages\/1702"}],"wp:attachment":[{"href":"https:\/\/lumatikka.luma.fi\/sv\/wp-json\/wp\/v2\/media?parent=1706"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}