
{"id":344,"date":"2019-10-29T12:51:59","date_gmt":"2019-10-29T11:51:59","guid":{"rendered":"https:\/\/lartorget.goteborg.se\/gastbloggen\/?p=344"},"modified":"2019-10-29T12:51:59","modified_gmt":"2019-10-29T11:51:59","slug":"att-forhalla-sig-till-matte-en-mattelektion","status":"publish","type":"post","link":"https:\/\/lartorget.goteborg.se\/gastbloggen\/2019\/10\/29\/att-forhalla-sig-till-matte-en-mattelektion\/","title":{"rendered":"Att f\u00f6rh\u00e5lla sig till matte &#8211; en mattelektion"},"content":{"rendered":"<p>Vi startar lektionen med fr\u00e5gan:<\/p>\n<p>\u00c4r \u2153 ett tal?<\/p>\n<p><em>Lena: &#8221;Ja. Det \u00e4r ju ett tal mellan 0 och 1.&#8221;<\/em><\/p>\n<p><em>Klassen nickar men Daniella s\u00e4ger:<\/em><\/p>\n<p><em>&#8221;Det kan ocks\u00e5 vara tv\u00e5 tal d\u00e4r 1 delas med 3?&#8221; \u00b9<\/em><\/p>\n<p>Fr\u00e5gan \u00e4r om det \u00e4r viktigt, intressant eller bara roligt. Jag tycker nog att det \u00e4r allt det d\u00e4r: viktigt, intressant och roligt. Om \u2153 \u00e4r svaret p\u00e5 fr\u00e5gan: Hur stor del av \u00e4pplet fick du? D\u00e5 \u00e4r det ett tal.<\/p>\n<p>Om \u2153 \u00e4r svaret p\u00e5 fr\u00e5gan: Hur r\u00e4knar jag ut hur stor del av \u00e4pplet jag fick? D\u00e5 \u00e4r det tv\u00e5 tal d\u00e4r 1 divideras med 3.<\/p>\n<h2>Vad \u00e4r 6\/3?<\/h2>\n<p>\u00c4r det s\u00e5 enkelt? Kanske. Vi pr\u00f6var med ett annat tal: 6\/3<\/p>\n<p>Jag fr\u00e5gar: &#8221;Hur \u00e4r det d\u00e5 med 6\/3?&#8221; &#8221;Fundera tyst i en minut och prata sedan med din b\u00e4nkkompis.&#8221;<\/p>\n<p><em>Alvin: &#8221;Det blir ju 2 &#8211; om man r\u00e4knar ut det.&#8221;<\/em><\/p>\n<p>Jag fr\u00e5gar: &#8221;Vad \u00e4r det om man inte r\u00e4knar ut det?&#8221;<\/p>\n<p><em>Alvin: &#8221;6 stycken tredjedelar.&#8221;<\/em><\/p>\n<p><em>Robin: &#8221;Men det \u00e4r ju ocks\u00e5 2.&#8221;<\/em><\/p>\n<p>Jag fr\u00e5gar igen: &#8221;\u00c4r det ett tal?&#8221;<\/p>\n<p><em>Bea: &#8221; Nej det \u00e4r inte ett tal &#8211; det \u00e4r tv\u00e5 tal.&#8221;<\/em><\/p>\n<p>Jag fr\u00e5gar : &#8221;Kan man s\u00e4tta ut 6\/3 p\u00e5 tallinjen?&#8221;<\/p>\n<p><em>Bea: &#8221;Menar du 6 och 3? Det \u00e4r tv\u00e5 olika st\u00e4llen? \u2026 Eller menar du 2? D\u00e5 \u00e4r det ett tal.&#8221;<\/em><\/p>\n<p>Om 6\/3 \u00e4r svaret p\u00e5 fr\u00e5gan: Hur stor del av \u00e4pplet fick du?<\/p>\n<p>D\u00e5 \u00e4r det ett tal\u2026. eller \u2026.?<\/p>\n<p>6\/3 &#8211; S\u00e5 brukar man ju inte skriva&#8230;men betyder det att man inte kan skriva s\u00e5?<\/p>\n<ul>\n<li>Egentligen fick jag ju inte en del av ett \u00e4pple, jag fick ju 2 \u00e4pplen.<\/li>\n<li>Men \u2026 6\/3 = 2 \u2026 &#8221;lika mycket som&#8221; m\u00e5ste v\u00e4l betyda just att det \u00e4r lika mycket?<\/li>\n<li>S\u00e5 jag fick 6\/3 = 2 \u00e4pplen och 2 \u00e4r ett tal d\u00e5 m\u00e5ste v\u00e4l ocks\u00e5 6\/3 vara ett tal.<\/li>\n<\/ul>\n<h2>Substantiv eller verb<\/h2>\n<p>En annan fr\u00e5ga jag f\u00e5r av eleverna under resonemanget \u00e4r:<\/p>\n<p>\u00c4r verkligen 2 \u00e4pplen en del av ett \u00e4pple?<\/p>\n<p>Vi s\u00e4ger ju att procent betyder hundradelar. 1\/100 = 1 % = 0,01. 100% = 1.<\/p>\n<p>Hur m\u00e5nga procent \u00e4r 2 \u00e4pplen av ett \u00e4pple? OK det m\u00e5ste ju bli 200%<\/p>\n<p>Hur stor del \u00e4r 2 \u00e4pplen d\u00e5 av ett \u00e4pple? 200% = 2.<\/p>\n<p>Svaret blir allts\u00e5 2. ( 2 hela kanske k\u00e4nns tydligare)<\/p>\n<p>Men vad har detta att g\u00f6ra med att f\u00f6rh\u00e5lla sig till matte?<\/p>\n<p>Vi betraktar talen:\u00a0 \u2153, 1 och 3.<\/p>\n<p>\u2153 kan antingen vara ett tal, en statisk sak, ett substantiv. Eller s\u00e5 \u00e4r \u2153 en division, en f\u00f6r\u00e4ndring av ett tal (1) , ett g\u00f6rande, ett verb. Samma sak med 6\/3!!<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright size-medium wp-image-350\" src=\"https:\/\/lartorget.goteborg.se\/gastbloggen\/wp-content\/uploads\/sites\/18\/2019\/10\/bild-matteblogg-300x255.jpg\" alt=\"\" width=\"300\" height=\"255\" srcset=\"https:\/\/lartorget.goteborg.se\/gastbloggen\/wp-content\/uploads\/sites\/18\/2019\/10\/bild-matteblogg-300x255.jpg 300w, https:\/\/lartorget.goteborg.se\/gastbloggen\/wp-content\/uploads\/sites\/18\/2019\/10\/bild-matteblogg-360x307.jpg 360w, https:\/\/lartorget.goteborg.se\/gastbloggen\/wp-content\/uploads\/sites\/18\/2019\/10\/bild-matteblogg-350x298.jpg 350w, https:\/\/lartorget.goteborg.se\/gastbloggen\/wp-content\/uploads\/sites\/18\/2019\/10\/bild-matteblogg-260x221.jpg 260w, https:\/\/lartorget.goteborg.se\/gastbloggen\/wp-content\/uploads\/sites\/18\/2019\/10\/bild-matteblogg.jpg 512w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Vi betraktar talen ur olika synvinklar men vi f\u00f6rh\u00e5ller oss p\u00e5 samma s\u00e4tt till dem oavsett synvinkel. Vi g\u00f6r samma, t\u00e4nker samma, vi \u00e4ndrar synvinkel men f\u00f6rs\u00f6ker t\u00e4nka som vi gjorde tidigare. Vi har samma f\u00f6rh\u00e5llningss\u00e4tt.<\/p>\n<p>M\u00e5nga g\u00e5nger v\u00e4njer vi oss vid att \u2153 \u00e4r ett tal och 6\/3 \u00e4r en division eftersom vi oftast ser dem i dessa sammanhang. Men faktum \u00e4r att b\u00e5da \u00e4r tal OCH division.<\/p>\n<p>Den h\u00e4r fr\u00e5gan, om \u2153 \u00e4r ett tal, fyllde en hel lektion. Vi forts\u00e4tter diskutera och s\u00e4tter \u2153 under luppen. En etta, ett divisionstecken och en trea i denna kombination: \u2153.<\/p>\n<p>\u2153 \u00b7 1\u00a0 vad h\u00e4nder nu? Blir det tv\u00e5 g\u00f6rande eller en sak?<\/p>\n<p>\u2153 \u00b7 2 eller \u00a0 2 \u00b7 \u2153\u00a0 Betyder det samma sak?<\/p>\n<p>Produkten blir ju detsamma, \u2154.<\/p>\n<h2>L\u00e4r sig genom att diskutera<\/h2>\n<p>Matematiken m\u00e5ste alltid fungera oavsett ur vilken synvinkel jag betraktar den. Matematiken \u00e4r m\u00e5nga g\u00e5nger stel och or\u00f6rlig, inget man kan \u00e4ndra p\u00e5 genom en diskussion.<\/p>\n<p>Varf\u00f6r skall man d\u00e5 f\u00f6rh\u00e5lla sig till matematiken? Diskutera den? Den \u00e4r ju som den \u00e4r. JO&#8230;det \u00e4r ju just f\u00f6r att den \u00e4r s\u00e5 stel som jag kan l\u00e4gga den under luppen och titta p\u00e5 den ur olika synvinklar. Om matematiken hade f\u00f6r\u00e4ndrat sig, bytt skepnad hade jag inte kunnat f\u00f6rst\u00e5 hur den fungerar. Jag hade inte f\u00f6rst\u00e5tt matte.<\/p>\n<p>S\u00e5 genom att f\u00f6rh\u00e5lla mig till matten kan jag l\u00e4ra mig att f\u00f6rst\u00e5 den.<\/p>\n<p>Genom att diskutera l\u00e4r eleverna matematik.<\/p>\n<p>\/Margareta Laumann<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Margareta Laumann, matematikutvecklare och f\u00f6rstel\u00e4rare i matematik p\u00e5 Fr\u00f6lundaskolan, bloggar om hur elevernas f\u00f6rst\u00e5else f\u00f6r matematik kan utvecklas genom att de f\u00e5r inta olika f\u00f6rh\u00e5llningss\u00e4tt eller perspektiv p\u00e5 ett tal eller en matematisk uppgift. Exemplet \u00e4r h\u00e4mtat fr\u00e5n en matematiklektion som hon h\u00e5llit med sina elever i sjunde klass. Eleverna \u00e4r vana vid att hantera br\u00e5kr\u00e4kning.<\/p>\n","protected":false},"author":264,"featured_media":349,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[74,276,14,3],"coauthors":[320],"class_list":["post-344","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-askim-frolunda-hogsbo","category-grundskola","category-grundskola-7-9","category-matematik"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Att f\u00f6rh\u00e5lla sig till matte - en mattelektion - G\u00e4stbloggen<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lartorget.goteborg.se\/gastbloggen\/2019\/10\/29\/att-forhalla-sig-till-matte-en-mattelektion\/\" \/>\n<meta property=\"og:locale\" content=\"sv_SE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Att f\u00f6rh\u00e5lla sig till matte - en mattelektion - G\u00e4stbloggen\" \/>\n<meta property=\"og:description\" content=\"Margareta Laumann, matematikutvecklare och f\u00f6rstel\u00e4rare i matematik p\u00e5 Fr\u00f6lundaskolan, bloggar om hur elevernas f\u00f6rst\u00e5else f\u00f6r matematik kan utvecklas genom att de f\u00e5r inta olika f\u00f6rh\u00e5llningss\u00e4tt eller perspektiv p\u00e5 ett tal eller en matematisk uppgift. 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