{"id":3065,"date":"2025-12-05T11:19:47","date_gmt":"2025-12-05T14:19:47","guid":{"rendered":"https:\/\/hotpixel.me\/geogebra\/?p=3065"},"modified":"2025-12-05T11:19:54","modified_gmt":"2025-12-05T14:19:54","slug":"movimento-real-grafico-ideal-explorando-grandezas-diretamente-proporcionais","status":"publish","type":"post","link":"https:\/\/hotpixel.me\/geogebra\/movimento-real-grafico-ideal-explorando-grandezas-diretamente-proporcionais\/","title":{"rendered":"Movimento real, gr\u00e1fico ideal: explorando grandezas diretamente proporcionais"},"content":{"rendered":"<p class=\"qwen-markdown-paragraph\"><span class=\"qwen-markdown-text\" data-spm-anchor-id=\"a2ty_o01.29997173.0.i99.266551713suZjG\">\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\">Reconhecer situa\u00e7\u00f5es de proporcionalidade direta no cotidiano.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Representar grandezas proporcionais em gr\u00e1ficos cartesianos.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Interpretar o significado do coeficiente angular em contextos reais.<\/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\">Dados simples de situa\u00e7\u00f5es proporcionais (ex: pre\u00e7o por kg, dist\u00e2ncia por tempo em velocidade constante)<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Projetor<\/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\">Entrada com situa\u00e7\u00e3o cotidiana (5 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Exemplo: <em>\u201cSe 1 kg de ma\u00e7\u00e3 custa R$ 4, quanto custam 2 kg? E 5 kg?\u201d<\/em><\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Pergunte: <em>\u201cComo isso ficaria num gr\u00e1fico?\u201d<\/em><\/span><\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Constru\u00e7\u00e3o da rela\u00e7\u00e3o no GeoGebra (25 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Abra o <strong class=\"qwen-markdown-strong\">GeoGebra Cl\u00e1ssico<\/strong>.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Na <strong class=\"qwen-markdown-strong\">planilha integrada<\/strong>, digite:<\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Coluna A: quantidade (1, 2, 3, 4, 5)<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Coluna B: pre\u00e7o (4, 8, 12, 16, 20)<\/span><\/li>\n<\/ul>\n<div class=\"qwen-markdown-space\"><\/div>\n<\/li>\n<li><span class=\"qwen-markdown-text\">Selecione os dados e clique em <strong class=\"qwen-markdown-strong\">\u201cAn\u00e1lise de Regress\u00e3o\u201d<\/strong> \u2192 <strong class=\"qwen-markdown-strong\">\u201cLinear\u201d<\/strong>.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Aparecer\u00e1 a reta <span class=\"qwen-markdown-latex\" translate=\"no\"><span class=\"katex\"><span class=\"katex-mathml\">y=4x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span>.<\/span><\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Explora\u00e7\u00e3o interativa (10 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Adicione um <strong class=\"qwen-markdown-strong\">slider<\/strong> (controle deslizante) chamado <code class=\"qwen-markdown-codespan\">k<\/code>.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Digite na barra de entrada: <code class=\"qwen-markdown-codespan\">y = k*x<\/code><\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Pe\u00e7a que movam o slider e observem:<\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">O que acontece com a reta quando <code class=\"qwen-markdown-codespan\">k<\/code> aumenta?<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">O que representa <code class=\"qwen-markdown-codespan\">k<\/code> no contexto das ma\u00e7\u00e3s? (resposta: pre\u00e7o por kg)<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li><span class=\"qwen-markdown-text\"><strong class=\"qwen-markdown-strong\">Discuss\u00e3o conceitual (10 min)<\/strong><\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\">Perguntas-chave:<\/span>\n<ul class=\"qwen-markdown-list\" dir=\"auto\">\n<li><span class=\"qwen-markdown-text\"><em>\u201cPor que a reta sempre passa pela origem (0,0)?\u201d<\/em><\/span><\/li>\n<li><span class=\"qwen-markdown-text\"><em>\u201cO que aconteceria se o gr\u00e1fico n\u00e3o passasse por (0,0)? Ainda seria proporcional?\u201d<\/em><\/span><\/li>\n<\/ul>\n<div class=\"qwen-markdown-space\"><\/div>\n<\/li>\n<li><span class=\"qwen-markdown-text\">Reforce: <strong class=\"qwen-markdown-strong\">proporcionalidade direta = reta pela origem<\/strong>.<\/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\">contextos variados<\/strong>: velocidade constante, receitas, tarifas fixas.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Compare com situa\u00e7\u00f5es <strong class=\"qwen-markdown-strong\">n\u00e3o proporcionais<\/strong> (ex: conta de luz com taxa m\u00ednima) para contrastar.<\/span><\/li>\n<li><span class=\"qwen-markdown-text\">Incentive os alunos a <strong class=\"qwen-markdown-strong\">criar sua pr\u00f3pria situa\u00e7\u00e3o proporcional<\/strong> e model\u00e1-la no GeoGebra.<\/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 Interdisciplinar:<\/span><\/strong><br \/>\n<span class=\"qwen-markdown-text\">Esta atividade dialoga com <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Ci\u00eancias<\/span><\/strong><span class=\"qwen-markdown-text\"> (movimento uniforme) e <\/span><strong class=\"qwen-markdown-strong\"><span class=\"qwen-markdown-text\">Educa\u00e7\u00e3o Financeira<\/span><\/strong><span class=\"qwen-markdown-text\"> (compras, or\u00e7amento).<\/span><\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udd39 Objetivos de Aprendizagem Reconhecer situa\u00e7\u00f5es de proporcionalidade direta no cotidiano. Representar grandezas proporcionais em gr\u00e1ficos cartesianos. Interpretar o significado do coeficiente angular em contextos reais. \ud83d\udd39 Tempo Estimado 1 aula de 50 minutos \ud83d\udd39 Recursos Necess\u00e1rios Dispositivos com acesso ao GeoGebra Dados simples de situa\u00e7\u00f5es proporcionais (ex: pre\u00e7o por kg, dist\u00e2ncia por tempo em [&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":[33],"tags":[],"class_list":["post-3065","post","type-post","status-publish","format-standard","hentry","category-8o-ano"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3065","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=3065"}],"version-history":[{"count":1,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3065\/revisions"}],"predecessor-version":[{"id":3066,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/posts\/3065\/revisions\/3066"}],"wp:attachment":[{"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/media?parent=3065"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/categories?post=3065"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hotpixel.me\/geogebra\/wp-json\/wp\/v2\/tags?post=3065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}