{"id":1113,"date":"2026-07-31T13:01:44","date_gmt":"2026-07-31T16:01:44","guid":{"rendered":"https:\/\/www.ime.unicamp.br\/lem\/?page_id=1113"},"modified":"2026-07-31T21:27:01","modified_gmt":"2026-08-01T00:27:01","slug":"fundamental-8-9","status":"publish","type":"page","link":"https:\/\/www.ime.unicamp.br\/lem\/fundamental-8-9\/","title":{"rendered":"Ensino Fundamental II &#8211; 8\u00ba e 9\u00ba Anos"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1113\" class=\"elementor elementor-1113\">\n\t\t\t\t<div class=\"elementor-element elementor-element-bc185f6 e-flex e-con-boxed wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-parent\" data-id=\"bc185f6\" data-element_type=\"container\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-af64530 elementor-widget elementor-widget-heading\" data-id=\"af64530\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Ensino Fundamental II - 8\u00ba e 9\u00ba Anos<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ea44d1c elementor-widget elementor-widget-text-editor\" data-id=\"ea44d1c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Explore nossas oficinas destinadas a alunos dos \u00faltimos anos do ensino fundamental II.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d7338c3 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"d7338c3\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-055ba5c elementor-widget elementor-widget-heading\" data-id=\"055ba5c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><a href=\"#geometria\">Geometria e Medidas<\/a><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-541344d e-flex e-con-boxed wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-parent\" data-id=\"541344d\" data-element_type=\"container\" id=\"geometria\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2b5b66a elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-image\" data-id=\"2b5b66a\" data-element_type=\"widget\" id=\"geometria\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1200\" height=\"250\" src=\"https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/Geometria-e-Medidas-1.svg\" class=\"attachment-full size-full wp-image-1090\" alt=\"\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-e2c8a89 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"e2c8a89\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7b64090 elementor-widget elementor-widget-heading\" data-id=\"7b64090\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Caleidociclo<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0be40c6 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"0be40c6\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2fe4106 elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"2fe4106\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Nesta oficina, os estudantes realizam a constru\u00e7\u00e3o manual de um caleidociclo hexagonal \u2014 um poliedro flex\u00edvel composto por seis tetraedros articulados que pode ser girado infinitamente sem alterar suas faces. A atividade conecta geometria espacial com arte, explorando os padr\u00f5es geom\u00e9tricos envolvidos nas dobras da planifica\u00e7\u00e3o e abrindo espa\u00e7o para discuss\u00f5es sobre as simetrias de Escher e cria\u00e7\u00f5es art\u00edsticas interdisciplinares.\u00a0<\/p><p><b>\u00a0<\/b><\/p><p><b>Tempo estimado: <\/b>1h30 a 2h\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-654df2a e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"654df2a\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1d1d91c elementor-widget elementor-widget-image\" data-id=\"1d1d91c\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1400\" height=\"1050\" src=\"https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/caleidociclo-1.png\" class=\"attachment-full size-full wp-image-1098\" alt=\"\" srcset=\"https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/caleidociclo-1.png 1400w, https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/caleidociclo-1-300x225.png 300w, https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/caleidociclo-1-1024x768.png 1024w, https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/caleidociclo-1-768x576.png 768w\" sizes=\"(max-width: 1400px) 100vw, 1400px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c374fae elementor-widget elementor-widget-text-editor\" data-id=\"c374fae\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em>Caleidociclo hexagonal de papel \/ Polyhedra.net<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-45b109f e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"45b109f\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1552289 elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"1552289\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Objetivos<\/b><\/p><p>\u2022 Compreender e aplicar a Rela\u00e7\u00e3o de Euler em poliedros.\u00a0<\/p><p>\u2022 Estudar o tetraedro a partir de sua planifica\u00e7\u00e3o, analisando o c\u00e1lculo de sua \u00e1rea e volume.\u00a0<\/p><p>\u2022 Desenvolver habilidades de desenho geom\u00e9trico, precis\u00e3o matem\u00e1tica e conceitos de tri\u00e2ngulos is\u00f3sceles atrav\u00e9s da dobradura.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-052a408 elementor-widget-mobile__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"052a408\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Conte\u00fados abordados<\/b><\/p><p>\u2022 Poliedros e Rela\u00e7\u00e3o de Euler.<\/p><p>\u2022 Geometria Espacial: faces, arestas, v\u00e9rtices e o s\u00f3lido tetraedro.\u00a0<\/p><p>\u2022 \u00c1reas e Volumes de s\u00f3lidos geom\u00e9tricos.\u00a0<\/p><p>\u2022 Geometria Plana: tri\u00e2ngulos is\u00f3sceles, \u00e2ngulos e medidas.\u00a0<\/p><div>\u00a0<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-29d137d e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"29d137d\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-83215ce elementor-widget elementor-widget-heading\" data-id=\"83215ce\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Por que as colmeias s\u00e3o hexagonais?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6c706e0 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"6c706e0\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6f03d73 elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"6f03d73\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>A oficina investiga a raz\u00e3o pela qual as abelhas constroem favos hexagonais, introduzindo o conceito de otimiza\u00e7\u00e3o. De forma interativa, os alunos utilizam palitos de sorvete e prismas de papel para comparar tri\u00e2ngulos, quadrados e hex\u00e1gonos regulares. O experimento visual com bolinhas de papel demonstra que o prisma hexagonal armazena o maior volume de mel utilizando a mesma quantidade de material (cera).\u00a0<b>\u00a0<\/b><\/p><p><b>\u00a0<\/b><\/p><p><b>Tempo estimado: <\/b>N\u00e3o especificado<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d4f38d6 e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"d4f38d6\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-078c66b elementor-widget elementor-widget-image\" data-id=\"078c66b\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1400\" height=\"1050\" src=\"https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/oficinas-3.png\" class=\"attachment-full size-full wp-image-1167\" alt=\"\" srcset=\"https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/oficinas-3.png 1400w, https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/oficinas-3-300x225.png 300w, https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/oficinas-3-1024x768.png 1024w, https:\/\/www.ime.unicamp.br\/lem\/wp-content\/uploads\/2026\/07\/oficinas-3-768x576.png 768w\" sizes=\"(max-width: 1400px) 100vw, 1400px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3c09ecb e-con-full e-flex wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-child\" data-id=\"3c09ecb\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4feea7d elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"4feea7d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Objetivos<\/b><\/p><ul><li>Entender a rela\u00e7\u00e3o entre a forma geom\u00e9trica da colmeia e a efici\u00eancia na produ\u00e7\u00e3o e armazenamento de mel.<\/li><li>Desenvolver a habilidade de calcular, descrever e otimizar problemas pr\u00e1ticos do mundo f\u00edsico.<\/li><li>Comparar visualmente e matematicamente diferentes figuras geom\u00e9tricas quanto ao espa\u00e7o delimitado e material utilizado<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f6eea06 elementor-widget-mobile__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"f6eea06\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><b>Conte\u00fados abordados<\/b><\/p><ul><li>Geometria Plana: tri\u00e2ngulos equil\u00e1teros, quadrados e hex\u00e1gonos regulares, incluindo c\u00e1lculo de \u00e1rea. <\/li><li>Geometria Espacial: prismas e c\u00e1lculo de volume. <\/li><li>Otimiza\u00e7\u00e3o matem\u00e1tica e o conceito de malhas uniformes. <\/li><\/ul><div>\u00a0<\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1e33b12 e-flex e-con-boxed wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-parent\" data-id=\"1e33b12\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Ensino Fundamental II &#8211; 8\u00ba e 9\u00ba Anos Explore nossas oficinas destinadas a alunos dos \u00faltimos anos do ensino fundamental II. Geometria e Medidas Caleidociclo Nesta oficina, os estudantes realizam a constru\u00e7\u00e3o manual de um caleidociclo hexagonal \u2014 um poliedro flex\u00edvel composto por seis tetraedros articulados que pode ser girado infinitamente sem alterar suas faces. A atividade conecta geometria espacial com arte, explorando os padr\u00f5es geom\u00e9tricos envolvidos nas dobras da planifica\u00e7\u00e3o e abrindo espa\u00e7o para discuss\u00f5es sobre as simetrias de Escher e cria\u00e7\u00f5es art\u00edsticas interdisciplinares.\u00a0 \u00a0 Tempo estimado: 1h30 a 2h\u00a0 Caleidociclo hexagonal de papel \/ Polyhedra.net Objetivos \u2022 Compreender e aplicar a Rela\u00e7\u00e3o de Euler em poliedros.\u00a0 \u2022 Estudar o tetraedro a partir de sua planifica\u00e7\u00e3o, analisando o c\u00e1lculo de sua \u00e1rea e volume.\u00a0 \u2022 Desenvolver habilidades de desenho geom\u00e9trico, precis\u00e3o matem\u00e1tica e conceitos de tri\u00e2ngulos is\u00f3sceles atrav\u00e9s da dobradura.\u00a0 Conte\u00fados abordados \u2022 Poliedros e Rela\u00e7\u00e3o de Euler. \u2022 Geometria Espacial: faces, arestas, v\u00e9rtices e o s\u00f3lido tetraedro.\u00a0 \u2022 \u00c1reas e Volumes de s\u00f3lidos geom\u00e9tricos.\u00a0 \u2022 Geometria Plana: tri\u00e2ngulos is\u00f3sceles, \u00e2ngulos e medidas.\u00a0 \u00a0 Por que as colmeias s\u00e3o hexagonais? A oficina investiga a raz\u00e3o pela qual as abelhas constroem favos hexagonais, introduzindo o conceito de otimiza\u00e7\u00e3o. De forma interativa, os alunos utilizam palitos de sorvete e prismas de papel para comparar tri\u00e2ngulos, quadrados e hex\u00e1gonos regulares. O experimento visual com bolinhas de papel demonstra que o prisma hexagonal armazena o maior volume de mel utilizando a mesma quantidade de material (cera).\u00a0\u00a0 \u00a0 Tempo estimado: N\u00e3o especificado Objetivos Entender a rela\u00e7\u00e3o entre a forma geom\u00e9trica da colmeia e a efici\u00eancia na produ\u00e7\u00e3o e armazenamento de mel. Desenvolver a habilidade de calcular, descrever e otimizar problemas pr\u00e1ticos do mundo f\u00edsico. Comparar visualmente e matematicamente diferentes figuras geom\u00e9tricas quanto ao espa\u00e7o delimitado e material utilizado Conte\u00fados abordados Geometria Plana: tri\u00e2ngulos equil\u00e1teros, quadrados e hex\u00e1gonos regulares, incluindo c\u00e1lculo de \u00e1rea. Geometria Espacial: prismas e c\u00e1lculo de volume. Otimiza\u00e7\u00e3o matem\u00e1tica e o conceito de malhas uniformes. \u00a0<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1113","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.ime.unicamp.br\/lem\/wp-json\/wp\/v2\/pages\/1113","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ime.unicamp.br\/lem\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.ime.unicamp.br\/lem\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/lem\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ime.unicamp.br\/lem\/wp-json\/wp\/v2\/comments?post=1113"}],"version-history":[{"count":28,"href":"https:\/\/www.ime.unicamp.br\/lem\/wp-json\/wp\/v2\/pages\/1113\/revisions"}],"predecessor-version":[{"id":1287,"href":"https:\/\/www.ime.unicamp.br\/lem\/wp-json\/wp\/v2\/pages\/1113\/revisions\/1287"}],"wp:attachment":[{"href":"https:\/\/www.ime.unicamp.br\/lem\/wp-json\/wp\/v2\/media?parent=1113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}