{"id":129355,"date":"2024-07-31T12:09:25","date_gmt":"2024-07-31T19:09:25","guid":{"rendered":"https:\/\/youcubed2stg.wpengine.com\/?post_type=wim_post&#038;p=129355"},"modified":"2025-07-29T06:55:04","modified_gmt":"2025-07-29T13:55:04","slug":"pontos-na-grade","status":"publish","type":"wim_post","link":"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/","title":{"rendered":"Pontos na Grade"},"content":{"rendered":"<p><span style=\"font-weight: 400\">Esta atividade apresenta aos alunos a Teoria de Ehrhart, uma \u00e1rea da matem\u00e1tica que aparece em cursos avan\u00e7ados de faculdade &#8211; ou al\u00e9m &#8211; mas que, em sua ess\u00eancia, pode ser explorada e compreendida sem a necessidade de conceitos particularmente avan\u00e7ados. A Teoria de Ehrhart trata-se de contar os pontos de valor inteiro dentro de formas convexas. Um conceito simples, mas com profundidade not\u00e1vel e fascinante. Nesta atividade, os alunos pensar\u00e3o sobre isso em duas dimens\u00f5es, usando quadros geom\u00e9tricos e considerando o n\u00famero de pinos dentro das formas.<\/span><\/p>\n<p><span style=\"font-weight: 400\">O plano de aula e os materiais est\u00e3o dispon\u00edveis no Google Slides \u2014 clique abaixo para visualizar os slides ou fazer uma c\u00f3pia para voc\u00ea. Os slides marcados com um &#8220;T&#8221; no canto superior direito, trazem informa\u00e7\u00f5es para o professor sobre a aula. Os slides marcados com um &#8220;S&#8221; no canto superior direito, s\u00e3o para os alunos. Se precisar de material de apoio, use os links dispon\u00edveis nos slides do professor. Todos os slides podem ser adaptados.<\/span><\/p>\n","protected":false},"featured_media":129356,"template":"","meta":{"_acf_changed":false,"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"_links_to":"","_links_to_target":""},"wim_category":[323],"wim_topic":[325],"wim_grade":[338,339,340],"class_list":["post-129355","wim_post","type-wim_post","status-publish","has-post-thumbnail","hentry"],"featured_image":{"id":129356,"alt_text":"","caption":"","description":"","media_type":"image","media_details":{"width":1024,"height":835,"file":"2024\/07\/cover-image-dots-on-the-grid-9-14-1024x835-1.webp","filesize":181360,"sizes":{"thumbnail":{"file":"cover-image-dots-on-the-grid-9-14-1024x835-1-150x150.webp","width":150,"height":150,"mime-type":"image\/webp","source_url":"https:\/\/www.youcubed.org\/wp-content\/uploads\/2024\/07\/cover-image-dots-on-the-grid-9-14-1024x835-1-150x150.webp"},"medium":{"file":"cover-image-dots-on-the-grid-9-14-1024x835-1-300x245.webp","width":300,"height":245,"mime-type":"image\/webp","source_url":"https:\/\/www.youcubed.org\/wp-content\/uploads\/2024\/07\/cover-image-dots-on-the-grid-9-14-1024x835-1-300x245.webp"},"large":{"file":"cover-image-dots-on-the-grid-9-14-1024x835-1-1024x835.webp","width":1024,"height":835,"mime-type":"image\/webp","source_url":"https:\/\/www.youcubed.org\/wp-content\/uploads\/2024\/07\/cover-image-dots-on-the-grid-9-14-1024x835-1-1024x835.webp"},"500x410":{"file":"cover-image-dots-on-the-grid-9-14-1024x835-1-500x410.webp","width":500,"height":410,"mime-type":"image\/webp","source_url":"https:\/\/www.youcubed.org\/wp-content\/uploads\/2024\/07\/cover-image-dots-on-the-grid-9-14-1024x835-1-500x410.webp"}},"image_meta":{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0","keywords":[]}},"post":129355,"source_url":"https:\/\/www.youcubed.org\/wp-content\/uploads\/2024\/07\/cover-image-dots-on-the-grid-9-14-1024x835-1.webp"},"downloads":[{"download":{"ID":129340,"post_author":"18","post_date":"2024-07-31 11:56:59","post_date_gmt":"2024-07-31 18:56:59","post_content":"","post_title":"Pontos na Grade","post_excerpt":"","post_status":"publish","comment_status":"closed","ping_status":"closed","post_password":"","post_name":"pontos-na-grade","to_ping":"","pinged":"","post_modified":"2024-07-31 11:56:59","post_modified_gmt":"2024-07-31 18:56:59","post_content_filtered":"","post_parent":0,"guid":"https:\/\/youcubed2stg.wpengine.com\/?post_type=tracked_post&#038;p=129340","menu_order":0,"post_type":"tracked_post","post_mime_type":"","comment_count":"0","filter":"raw"},"download_text":"Baixar c\u00f3pia da apresenta\u00e7\u00e3o","url":"https:\/\/www.youcubed.org\/pt-br\/downloadable\/pontos-na-grade\/","video_url":"","video_embed":"","button_text":"Baixar c\u00f3pia da apresenta\u00e7\u00e3o"}],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v15.8.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pontos na Grade - YouCubed\" \/>\n<meta property=\"og:description\" content=\"Esta atividade apresenta aos alunos a Teoria de Ehrhart, uma \u00e1rea da matem\u00e1tica que aparece em cursos avan\u00e7ados de faculdade &#8211; ou al\u00e9m &#8211; mas que, em sua ess\u00eancia, pode [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/\" \/>\n<meta property=\"og:site_name\" content=\"YouCubed\" \/>\n<meta property=\"article:modified_time\" content=\"2025-07-29T13:55:04+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.youcubed.org\/wp-content\/uploads\/2018\/08\/youcubed-logo-with-TM-Computer-Courage.png\" \/>\n\t<meta property=\"og:image:width\" content=\"936\" \/>\n\t<meta property=\"og:image:height\" content=\"243\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. tempo de leitura\">\n\t<meta name=\"twitter:data1\" content=\"1 minuto\">\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/#website\",\"url\":\"https:\/\/www.youcubed.org\/pt-br\/\",\"name\":\"YouCubed\",\"description\":\"Inspire ALL Students with Open, Creative Mindset Mathematics\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":\"https:\/\/www.youcubed.org\/pt-br\/?s={search_term_string}\",\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-BR\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/#primaryimage\",\"inLanguage\":\"pt-BR\",\"url\":\"https:\/\/www.youcubed.org\/wp-content\/uploads\/2024\/07\/cover-image-dots-on-the-grid-9-14-1024x835-1.webp\",\"width\":1024,\"height\":835},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/#webpage\",\"url\":\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/\",\"name\":\"Pontos na Grade - YouCubed\",\"isPartOf\":{\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/#primaryimage\"},\"datePublished\":\"2024-07-31T19:09:25+00:00\",\"dateModified\":\"2025-07-29T13:55:04+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/#breadcrumb\"},\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"item\":{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/\",\"url\":\"https:\/\/www.youcubed.org\/pt-br\/\",\"name\":\"Home\"}},{\"@type\":\"ListItem\",\"position\":2,\"item\":{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/\",\"url\":\"https:\/\/www.youcubed.org\/pt-br\/wim\/pontos-na-grade\/\",\"name\":\"Pontos na Grade\"}}]}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","_links":{"self":[{"href":"https:\/\/www.youcubed.org\/pt-br\/wp-json\/wp\/v2\/wim_post\/129355","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.youcubed.org\/pt-br\/wp-json\/wp\/v2\/wim_post"}],"about":[{"href":"https:\/\/www.youcubed.org\/pt-br\/wp-json\/wp\/v2\/types\/wim_post"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.youcubed.org\/pt-br\/wp-json\/wp\/v2\/media\/129356"}],"wp:attachment":[{"href":"https:\/\/www.youcubed.org\/pt-br\/wp-json\/wp\/v2\/media?parent=129355"}],"wp:term":[{"taxonomy":"wim_category","embeddable":true,"href":"https:\/\/www.youcubed.org\/pt-br\/wp-json\/wp\/v2\/wim_category?post=129355"},{"taxonomy":"wim_topic","embeddable":true,"href":"https:\/\/www.youcubed.org\/pt-br\/wp-json\/wp\/v2\/wim_topic?post=129355"},{"taxonomy":"wim_grade","embeddable":true,"href":"https:\/\/www.youcubed.org\/pt-br\/wp-json\/wp\/v2\/wim_grade?post=129355"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}