{"id":75,"date":"2020-04-17T07:17:33","date_gmt":"2020-04-17T07:17:33","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=75"},"modified":"2021-10-17T08:07:48","modified_gmt":"2021-10-17T08:07:48","slug":"direkte-proportionalitaet-direkt-proportionale-zuordnung","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=75","title":{"rendered":"direkte Proportionalit\u00e4t &#8211; direkt proportionale Zuordnung"},"content":{"rendered":"\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Oft stellen wir fest, dass bei Zuordnungen das folgende Ph\u00e4nomen auftritt:<\/p>\n\n\n\n<p class=\"has-white-color has-text-color has-background has-medium-font-size\" style=\"background-color:#ff6a8a\">Verdoppelt, Verdreifacht oder  Vervierfacht man die Ausgangsgr\u00f6\u00dfe ( Beispiel: St\u00fcckzahl), so verdoppelt sich auch die Zuordnungsgr\u00f6\u00dfe ( Preis ). Man spricht dann von <strong>direkter Proportionalit\u00e4t<\/strong>.<\/p>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Beispiel 1:<\/p>\n\n\n\n<p><strong>&#8222;4 Stifte kosten 6\u20ac&#8220;<\/strong> &#8230;dann kosten 8 Stifte wohl 12\u20ac und 12 Stifte werden 18\u20ac kosten.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><span class=\"has-inline-color has-black-color\">St\u00fcckzahl der Stifte<\/span><\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><td class=\"has-text-align-center\" data-align=\"center\">12<\/td><td class=\"has-text-align-center\" data-align=\"center\"><strong>1<\/strong><\/td><\/tr><tr><td>Preis f\u00fcr die Stifte<\/td><td class=\"has-text-align-center\" data-align=\"center\">6\u20ac<\/td><td class=\"has-text-align-center\" data-align=\"center\">12\u20ac<\/td><td class=\"has-text-align-center\" data-align=\"center\">18\u20ac<\/td><td class=\"has-text-align-center\" data-align=\"center\"><span style=\"color:#ff0004\" class=\"has-inline-color\"><strong>???<\/strong><\/span><\/td><\/tr><\/tbody><\/table><figcaption>Versuche immer das &#8222;Einser-Paar&#8220; zu ermitteln. (Hier sind es 1 | 1,50\u20ac)<\/figcaption><\/figure>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Beispiel 2:<\/p>\n\n\n\n<p><strong>&#8222;F\u00fcr ein Br\u00f6tchen bezahlt man 0,13\u20ac.&#8220;<\/strong> Dann ist jedem klar, 2 Br\u00f6tchen werden 0,26\u20ac also doppelt so viel kosten.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><span class=\"has-inline-color has-black-color\">St\u00fcckzahl der Br\u00f6tchen<\/span><\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><\/tr><tr><td>Preis f\u00fcr die Br\u00f6tchen<\/td><td class=\"has-text-align-center\" data-align=\"center\">0,13\u20ac<\/td><td class=\"has-text-align-center\" data-align=\"center\">0,26\u20ac<\/td><td class=\"has-text-align-center\" data-align=\"center\">0,39\u20ac<\/td><td class=\"has-text-align-center\" data-align=\"center\"><span style=\"color:#ff0004\" class=\"has-inline-color\"><strong>???<\/strong><\/span><\/td><\/tr><\/tbody><\/table><figcaption>Versuche immer das &#8222;Einser-Paar&#8220; zu ermitteln. (Hier sind es 1 | 1,50\u20ac)<\/figcaption><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Oft nutzt man f\u00fcr solche Sachverhalte Tabellen oder auch Diagramme zur Veranschaulichung:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Proportionale Zuordnung | Was ist proportional? | Mathematik | Lehrerschmidt\" width=\"860\" height=\"484\" src=\"https:\/\/www.youtube.com\/embed\/y-PT_Dr3qIA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\">Hier findest Du \u00dcbungen mit L\u00f6sungen  zum Thema:<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#efdeff\"><a rel=\"noreferrer noopener\" href=\"https:\/\/mathe-lernen.net\/?page_id=174\" target=\"_blank\">\u00dcbungen auf mathe-lernen.net<\/a><br><br><a href=\"https:\/\/mathe-lernen.net\/?p=1986\">\u00dcbung 2 (Textaufgaben)<\/a><\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#c5fff4\"><a rel=\"noreferrer noopener\" href=\"https:\/\/www.uebungskoenig.de\/mathe\/8-klasse\/proportionalitaet\/\" target=\"_blank\">\u00dcbungen auf \u00dcbungsk\u00f6nig.de<\/a><\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#ecffc1\"><a rel=\"noreferrer noopener\" href=\"https:\/\/www.mein-lernen.at\/mathematik\/mathematik-schlussrechnungen\/direkte-proportionalitaet\" target=\"_blank\">\u00dcbungen auf meinLernen.at<\/a><\/p>\n\n\n\n<p><\/p>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_75\" class=\"pvc_stats all  \" data-element-id=\"75\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div> ","protected":false},"excerpt":{"rendered":"<p>Oft stellen wir fest, dass bei Zuordnungen das folgende Ph\u00e4nomen auftritt: Verdoppelt, Verdreifacht oder Vervierfacht man die Ausgangsgr\u00f6\u00dfe ( Beispiel: St\u00fcckzahl), so verdoppelt sich auch die Zuordnungsgr\u00f6\u00dfe ( Preis ). Man spricht dann von direkter Proportionalit\u00e4t. Beispiel 1: &#8222;4 Stifte kosten 6\u20ac&#8220; &#8230;dann kosten 8 Stifte wohl 12\u20ac und 12 Stifte werden 18\u20ac kosten. St\u00fcckzahl der Stifte 4 8 12<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_75\" class=\"pvc_stats all  \" data-element-id=\"75\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[32],"tags":[601,607,609,244,447],"class_list":["post-75","post","type-post","status-publish","format-standard","hentry","category-zuordnungen","tag-dreisatz","tag-proportionalitaet","tag-direkt","tag-textaufgaben","tag-ueben"],"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/75","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=75"}],"version-history":[{"count":0,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/75\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=75"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=75"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=75"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}