{"id":133239,"date":"2021-10-27T16:47:37","date_gmt":"2021-10-27T19:47:37","guid":{"rendered":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/?post_type=eaja&#038;p=133239"},"modified":"2021-12-22T10:44:00","modified_gmt":"2021-12-22T12:44:00","slug":"matematica-polinomios-perimetro-area-e-volume","status":"publish","type":"eaja","link":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/eaja\/matematica-polinomios-perimetro-area-e-volume\/","title":{"rendered":"Matem\u00e1tica &#8211; Polin\u00f4mios: per\u00edmetro, \u00e1rea e volume"},"content":{"rendered":"\n<p class=\"has-black-color has-vivid-red-background-color has-text-color has-background\" style=\"font-size:25px\">Ol\u00e1! Esta aula de&nbsp;<strong>Matem\u00e1tica&nbsp;<\/strong>\u00e9 destinada a estudantes da<strong>&nbsp;7\u00aa S\u00e9rie<\/strong>&nbsp;da Eaja. <\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"512\" height=\"552\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/10\/image7-e1635362826359.png\" alt=\"\" class=\"wp-image-133240\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/10\/image7-e1635362826359.png 512w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/10\/image7-e1635362826359-278x300.png 278w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><figcaption>Cubos Geometria Caixas &#8211; Gr\u00e1fico vetorial gr\u00e1tis no Pixabay<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"has-black-color has-cyan-bluish-gray-background-color has-text-color has-background\" style=\"font-size:25px\">Nesta atividade voc\u00ea ir\u00e1 associar os polin\u00f4mios aos modelos geom\u00e9tricos de figuras planas e s\u00f3lidos espaciais, no c\u00e1lculo de per\u00edmetros, \u00e1reas e volumes, al\u00e9m de resolver situa\u00e7\u00f5es-problema que envolvam o c\u00e1lculo do valor num\u00e9rico de express\u00f5es alg\u00e9bricas.  <\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-pale-cyan-blue-background-color has-text-color has-background\" style=\"font-size:25px\">Assista \u00e0 videoaula do professor H\u00e9lio sobre essa tem\u00e1tica.<\/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<p class=\"responsive-video-wrap clr\"><iframe title=\"Polin\u00f4mios: per\u00edmetro, \u00e1rea e volume | Matem\u00e1tica - aula10 | Eaja - 7\u00aa s\u00e9rie\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/7-I1xtApFFc?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<\/div><figcaption>Polin\u00f4mios: per\u00edmetro, \u00e1rea e volume | Matem\u00e1tica &#8211; aula10 | Eaja &#8211; 7\u00aa s\u00e9rie<\/figcaption><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">Antes de come\u00e7armos a resolver problemas envolvendo per\u00edmetros, \u00e1rea, volumes envolvendo polin\u00f4mios, vamos fazer um breve resumo do conte\u00fado b\u00e1sico deste assunto.<\/p>\n\n\n\n<p class=\"has-black-color has-light-green-cyan-background-color has-text-color has-background\" style=\"font-size:25px\"><strong>Express\u00f5es Alg\u00e9bricas (Defini\u00e7\u00e3o): <\/strong>s\u00e3o as express\u00f5es matem\u00e1ticas que utilizam as letras, os n\u00fameros e os s\u00edmbolos das opera\u00e7\u00f5es matem\u00e1ticas para realizar determinados c\u00e1lculos. As letras s\u00e3o utilizadas para expressar valores desconhecidos ou valores que podem variar.&nbsp;<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Exemplos<\/strong><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">a) O dobro de um n\u00famero real adicionado a 2: 2.x + 2. <\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">b) A soma entre o quadrado de um n\u00famero real e seu triplo: x<sup>2<\/sup>+3x<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Valor num\u00e9rico de uma Express\u00e3o Alg\u00e9brica<\/strong><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">Em uma express\u00e3o alg\u00e9brica, \u00e9 poss\u00edvel estimar um valor para as suas vari\u00e1veis. Quanto substitu\u00edmos as vari\u00e1veis de uma EA por n\u00fameros e efetuamos os c\u00e1lculos indicados, obtemos o <strong>VALOR NUM\u00c9RICO DA EXPRESS\u00c3O <\/strong>dada para esses n\u00fameros.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Exemplos<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/H-AfF0PsZ21EAQLR4IpnYl4hednl6FK-I2TS6y9CpQN1PwS2uZ8xjZwyY4aI5B5ne_KB6VmN3xmfDu0lf8Usmjg_EDyLR8zacHXW0Okll62KCBuH0FOHDbUsoDYiQCKO9KOSnio\" width=\"840\" height=\"163\"><\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-light-green-cyan-background-color has-text-color has-background\" style=\"font-size:25px\"><strong>Mon\u00f4mios e Polin\u00f4mios<\/strong><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">S\u00e3o casos particulares de express\u00f5es alg\u00e9bricas<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Mon\u00f4mios (Defini\u00e7\u00e3o):<\/strong> denomina-se <strong>mon\u00f4mio <\/strong>ou <strong>termo alg\u00e9brico <\/strong>toda express\u00e3o alg\u00e9brica representada apenas por um n\u00famero, ou apenas por uma vari\u00e1vel, ou por uma multiplica\u00e7\u00e3o de n\u00fameros e vari\u00e1veis, em que a vari\u00e1vel n\u00e3o esteja nem no denominador nem no radical. Ele \u00e9 composto por duas partes: a <strong>parte literal<\/strong>, que s\u00e3o as letras que comp\u00f5e o termo, e o <strong>coeficiente<\/strong>, que \u00e9 o n\u00famero que acompanha o termo.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Mon\u00f4mios semelhantes (Defini\u00e7\u00e3o): <\/strong>s\u00e3o aqueles mon\u00f4mios que possuem a mesma parte literal.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Polin\u00f4mios (Defini\u00e7\u00e3o):<\/strong> s\u00e3o adi\u00e7\u00f5es alg\u00e9bricas (adi\u00e7\u00e3o ou subtra\u00e7\u00e3o) composta exclusivamente por mon\u00f4mios.&nbsp;<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Per\u00edmetro (Defini\u00e7\u00e3o):<\/strong> \u00e9 a linha que forma o contorno de uma figura (pol\u00edgono) tra\u00e7ada no plano e \u00e9 determinado pela soma das medidas dos lados desse pol\u00edgono (figura).<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>\u00c1rea (Defini\u00e7\u00e3o):<\/strong> \u00e9 a medida de uma superf\u00edcie. \u00c9 determinada de acordo com o tipo da superf\u00edcie, por exemplo, se for retangular \u00e9 dada pelo produto entre o comprimento e a largura.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Volume (Defini\u00e7\u00e3o):<\/strong> \u00e9 o espa\u00e7o ocupado por um corpo (s\u00f3lido geom\u00e9trico) ou a capacidade que esse corpo tem de comportar uma quantidade de subst\u00e2ncia. \u00c9 determinado, na maioria das vezes, pelo produto entre a \u00e1rea da base e a altura desse s\u00f3lido.<\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-light-green-cyan-background-color has-text-color has-background\" style=\"font-size:25px\"><strong>C\u00e1lculo de per\u00edmetros, \u00e1reas e volumes<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/g4JEnhpD9oAusocOcCMIHqmVMIoxJbGKTox0cQNU-u1Ypq0K-cLhYsWYhG_EYh3kJ0AH2qQCEd1oqDSyJcWQ7iwyW8gfmqFVhFeHTD171ixNrp8mV5vynmNA13OvGZMxWivZ7v4\" width=\"899\" height=\"417\"><\/p>\n\n\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/Hr8anpwx0K40qNpX8BFO9LbxUEqmdW7Xoh2U4Ddb35LYHjq5IqSazm5pjUsYGmoEUJyFHYQND803HfL3s12MI0DYX7JmAzWBlr-Pww9viNLdGW9qODSVRBa_Q7xq9aM1bmeOakY\" width=\"849\" height=\"369\"><\/p>\n\n\n\n<p class=\"has-text-align-center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/FlmSm2uiY9wDco3xMWk6nMfmLjMxZkcCwXcN394UAnZ-glLX0_Tsf9WXR1bE1T4GWiutrDNAfdYpoXDKicOKYm5w6BFnVk-8qDJ9otvRbRiYN9lKk8mG8bnb39TYu3bQVE07pac\" width=\"899\" height=\"430\"><\/p>\n\n\n\n<p class=\"has-black-color has-pale-cyan-blue-background-color has-text-color has-background\" style=\"font-size:25px\"><strong>Para finalizar, vou propor a voc\u00ea alguns exerc\u00edcios.<\/strong><\/p>\n\n\n\n<ol class=\"has-black-color has-text-color wp-block-list\" style=\"font-size:25px\"><li>Determine uma express\u00e3o alg\u00e9brica para determinar o per\u00edmetro do tri\u00e2ngulo abaixo, em seguida determine o valor do per\u00edmetro para x = 4cm.<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/aE_XqK0vjqx_1JzFc7dNuoV0XA-hdKA8xJR2IF8nuL0JkiAHXxJHomlWShbJvYvslryIuwPB1pqZae0QQd8WPRwnlx91JigdG0f7Zoe7EAQuegxhx3GKYfeIXZuM_5Pbfu3L8GU\" alt=\"\"\/><figcaption>Imagem: arquivo pessoal do Prof. H\u00e9lio Roberto &#8211; NEC\/SME<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">2. Escreva uma express\u00e3o alg\u00e9brica para representar o per\u00edmetro do pol\u00edgono abaixo. Determinar o valor desse per\u00edmetro para x = 3 cm.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/8bGuqyVi9RBxLhIYGvNNtcrc8CZ7GEig5SZYAuMqlVMBdrQ5UWqheBs9EUR9LKQDhH0a8LFIp3kGc-3EOIE78WubyqlnveRNHC0tt448nD86EpESmE1H9Sk7O6kVgg\" alt=\"\"\/><figcaption> Imagem: arquivo pessoal do Prof. H\u00e9lio Roberto &#8211; NEC\/SME <\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">3. A \u00e1rea do pol\u00edgono abaixo \u00e9 a soma das \u00e1reas de um quadrado e de um ret\u00e2ngulo, escreva uma express\u00e3o alg\u00e9brica para representar essa \u00e1rea. Determine o valor da \u00e1rea para x = 6 cm.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/I64zNL_wm3rN1pB6QHNj1dbhR1fRDtPNWamtQav8GqM4ksb9s2ZH7PAvFH7egzhI5LgtMBrRKsmwnJ3G2qBRWXetNd9CzCtVZTK1oCqG9zPLHSrpfkr7qgKGI2Z-pA\" alt=\"\"\/><figcaption>  Imagem: arquivo pessoal do Prof. H\u00e9lio Roberto &#8211; NEC\/SME <\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">4. Determine a express\u00e3o alg\u00e9brica que representa o volume da caixa abaixo. Qual \u00e9 o volume para x = 5cm.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/YaQsDLkRPlHaFZUdoeBG84hNaCbNvurn9pY85IDonW-qIDzatnFA2XCfhNkDef2oP0rxfP_Bq2_iKonW5mpWvEa9Sk_QX_yf6g2iF5H2sGAl10jQgOHjWnLr-sG20w\" alt=\"\"\/><figcaption>  Imagem: arquivo pessoal do Prof. H\u00e9lio Roberto &#8211; NEC\/SME <\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"has-black-color has-pale-cyan-blue-background-color has-text-color has-background\" style=\"font-size:25px\">Assista aos v\u00eddeos no canal do Prof. H\u00e9lio para aprender um pouco mais. Link: <a href=\"https:\/\/youtu.be\/OTc-9pLAmNc\">https:\/\/youtu.be\/OTc-9pLAmNc<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table><tbody><tr><td><br><strong>Objetivos de Aprendizagem e Desenvolvimento:<\/strong><\/td><td>(EAJAMA0709) Associar os polin\u00f4mios aos modelos geom\u00e9tricos de figuras planas (c\u00e1lculo de per\u00edmetros e \u00e1reas), aos modelos de s\u00f3lidos geom\u00e9tricos (c\u00e1lculo de \u00e1reas da base, \u00e1reas laterais em planifica\u00e7\u00f5es e c\u00e1lculo de volumes).&nbsp;<br>(EAJAMA0710) Resolver e elaborar situa\u00e7\u00f5es-problema que envolvam c\u00e1lculo do valor num\u00e9rico de express\u00f5es alg\u00e9bricas, utilizando as propriedades das opera\u00e7\u00f5es fundamentais.&nbsp;<\/td><\/tr><tr><td><strong>Refer\u00eancias<\/strong><\/td><td>GIOVANNI J\u00daNIOR, Jos\u00e9 Ruy &#8211; A conquista da matem\u00e1tica: 8o ano: ensino fundamental: anos finais \/ Jos\u00e9 Ruy Giovanni J\u00fanior, Benedicto Castrucci. \u2014 4. ed. \u2014 S\u00e3o Paulo: FTD, 2018.<br>SOUZA, Joamir Roberto de: Matem\u00e1tica realidade &amp; tecnologia: 8\u00ba ano: ensino fundamental: anos finais \/ Joamir Roberto de Souza. \u2013 1. ed. \u2013 S\u00e3o Paulo: FTD, 2018.<br><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-cyan-bluish-gray-background-color has-background\" style=\"font-size:25px\"> Professor, essa aula segue a Matriz Estruturante para a Eaja 2021. Foi elaborada no ano de 2020, com a suspens\u00e3o das aulas presenciais devido a pandemia da Covid-19 e segue as orienta\u00e7\u00f5es de flexibiliza\u00e7\u00e3o curricular para o bi\u00eanio 2020\/2021 (Of\u00edcio Circular 149\/2020 Dirped). <\/p>\n","protected":false},"author":42,"featured_media":133240,"template":"","meta":{"_acf_changed":false,"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":""},"eaja_categoria":[69],"serie":[76],"eaja_componente":[78],"class_list":["post-133239","eaja","type-eaja","status-publish","has-post-thumbnail","hentry","eaja_categoria-2o-segmento-7a-e-8a-serie","serie-7a-serie","eaja_componente-matematica","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja\/133239","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja"}],"about":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/types\/eaja"}],"author":[{"embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/users\/42"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media\/133240"}],"wp:attachment":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media?parent=133239"}],"wp:term":[{"taxonomy":"eaja_categoria","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_categoria?post=133239"},{"taxonomy":"serie","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/serie?post=133239"},{"taxonomy":"eaja_componente","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_componente?post=133239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}