{"id":3069,"date":"2025-12-05T11:31:05","date_gmt":"2025-12-05T14:31:05","guid":{"rendered":"https:\/\/hotpixel.me\/geogebra\/?p=3069"},"modified":"2025-12-05T11:31:05","modified_gmt":"2025-12-05T14:31:05","slug":"area-maxima-com-perimetro-fixo-um-desafio-de-otimizacao-com-retangulos","status":"publish","type":"post","link":"https:\/\/hotpixel.me\/geogebra\/area-maxima-com-perimetro-fixo-um-desafio-de-otimizacao-com-retangulos\/","title":{"rendered":"\u00c1rea m\u00e1xima com per\u00edmetro fixo: um desafio de otimiza\u00e7\u00e3o com ret\u00e2ngulos"},"content":{"rendered":"<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\" data-spm-anchor-id=\"a2ty_o01.29997173.0.i105.266551713suZjG\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Objetivos de Aprendizagem<\/span><\/strong><\/p>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Resolver problemas de otimiza\u00e7\u00e3o envolvendo \u00e1rea e per\u00edmetro.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Modelar situa\u00e7\u00f5es com fun\u00e7\u00f5es quadr\u00e1ticas.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Compreender o conceito de <strong class=\"qwen-markdown-strong\">m\u00e1ximo de uma fun\u00e7\u00e3o<\/strong> por meio de visualiza\u00e7\u00e3o din\u00e2mica.<\/span><\/li>\n<\/ul>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Tempo Estimado<\/span><\/strong><\/p>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">1 aula de 50 minutos<\/span><\/p>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Recursos Necess\u00e1rios<\/span><\/strong><\/p>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Dispositivos com acesso ao GeoGebra<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Projetor<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Caderno de investiga\u00e7\u00f5es<\/span><\/li>\n<\/ul>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Passo a Passo<\/span><\/strong><\/p>\n<ol class=\"qwen-markdown-list\" dir=\"auto\" start=\"1\">\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Desafio inicial (5 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><em>\u201cVoc\u00ea tem 24 metros de cerca para cercar um canteiro retangular. Qual o maior espa\u00e7o poss\u00edvel para plantar?\u201d<\/em><\/span><\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Explora\u00e7\u00e3o com constru\u00e7\u00e3o (25 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">No GeoGebra:<br \/>\na) Crie um <strong class=\"qwen-markdown-strong\">slider<\/strong> <code class=\"qwen-markdown-codespan\">x<\/code> (de 1 a 11) \u2192 representa a largura.<br \/>\nb) Como o per\u00edmetro \u00e9 24, o comprimento ser\u00e1 <code class=\"qwen-markdown-codespan\">12 - x<\/code>.<br \/>\nc) Crie os pontos:<\/span><\/p>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><code class=\"qwen-markdown-codespan\">A = (0, 0)<\/code><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><code class=\"qwen-markdown-codespan\">B = (x, 0)<\/code><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><code class=\"qwen-markdown-codespan\">C = (x, 12 - x)<\/code><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><code class=\"qwen-markdown-codespan\">D = (0, 12 - x)<\/code><br \/>\nd) Use <strong class=\"qwen-markdown-strong\">\u201cPol\u00edgono\u201d<\/strong> para formar o ret\u00e2ngulo.<br \/>\ne) Calcule a \u00e1rea: digite <code class=\"qwen-markdown-codespan\">\u00c1rea = x*(12 - x)<\/code> na barra de entrada.<br \/>\nf) Ative o <strong class=\"qwen-markdown-strong\">\u201cModo Rastro\u201d<\/strong> no ponto <code class=\"qwen-markdown-codespan\">(x, \u00c1rea)<\/code> e mova o slider.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\">Os alunos ver\u00e3o surgir uma <strong class=\"qwen-markdown-strong\">par\u00e1bola<\/strong> \u2014 o gr\u00e1fico da \u00e1rea em fun\u00e7\u00e3o da largura.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">An\u00e1lise e conclus\u00e3o (20 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Perguntas:<\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><em>\u201cQual valor de x d\u00e1 a maior \u00e1rea?\u201d<\/em><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><em>\u201cO que acontece se x = 6?\u201d<\/em> (resposta: quadrado \u2192 \u00e1rea m\u00e1xima = 36 m\u00b2)<\/span><\/li>\n<\/ul>\n<div class=\"qwen-markdown-space\"><\/div>\n<\/li>\n<li><span class=\"qwen-markdown-text\">Discutam: <em>\u201cSer\u00e1 que sempre o quadrado d\u00e1 a maior \u00e1rea com per\u00edmetro fixo?\u201d<\/em><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\">\ud83d\udd39 <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Dicas para Maximizar a Aprendizagem<\/span><\/strong><\/p>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Use <strong class=\"qwen-markdown-strong\">anima\u00e7\u00e3o autom\u00e1tica<\/strong> do slider para mostrar o gr\u00e1fico se formando.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Conecte com <strong class=\"qwen-markdown-strong\">sustentabilidade e uso eficiente de recursos<\/strong> (ex: menos material, mais espa\u00e7o).<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Incentive os alunos a <strong class=\"qwen-markdown-strong\">generalizar<\/strong>: <em>\u201cSe o per\u00edmetro fosse P, qual seria a \u00e1rea m\u00e1xima?\u201d<\/em><\/span><\/li>\n<\/ul>\n<blockquote class=\"qwen-markdown-blockquote\">\n<p class=\"qwen-markdown-paragraph\"><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Extens\u00e3o para alunos avan\u00e7ados:<\/span><\/strong><br \/>\n<span class=\"qwen-markdown-text\">Desafie-os a modelar o mesmo problema com tri\u00e2ngulos ou c\u00edrculos \u2014 e comparar qual forma d\u00e1 a maior \u00e1rea com o mesmo per\u00edmetro.<\/span><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd39 Objetivos de Aprendizagem Resolver problemas de otimiza\u00e7\u00e3o envolvendo \u00e1rea e per\u00edmetro. Modelar situa\u00e7\u00f5es com fun\u00e7\u00f5es quadr\u00e1ticas. Compreender o conceito de m\u00e1ximo de uma fun\u00e7\u00e3o por meio de visualiza\u00e7\u00e3o din\u00e2mica. \ud83d\udd39 Tempo Estimado 1 aula de 50 minutos \ud83d\udd39 Recursos Necess\u00e1rios Dispositivos com acesso ao GeoGebra Projetor Caderno de investiga\u00e7\u00f5es \ud83d\udd39 Passo a Passo Desafio [&hellip;]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[34],"tags":[],"class_list":["post-3069","post","type-post","status-publish","format-standard","hentry","category-9o-ano"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3069","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/comments?post=3069"}],"version-history":[{"count":1,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3069\/revisions"}],"predecessor-version":[{"id":3070,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3069\/revisions\/3070"}],"wp:attachment":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/media?parent=3069"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/categories?post=3069"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/tags?post=3069"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}