{"id":134317,"date":"2021-11-17T11:44:55","date_gmt":"2021-11-17T13:44:55","guid":{"rendered":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/?post_type=eaja&#038;p=134317"},"modified":"2021-12-22T10:29:20","modified_gmt":"2021-12-22T12:29:20","slug":"matematica-utilizando-equacoes-de-1o-grau-para-resolver-problemas","status":"publish","type":"eaja","link":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/eaja\/matematica-utilizando-equacoes-de-1o-grau-para-resolver-problemas\/","title":{"rendered":"Matem\u00e1tica &#8211; Utilizando equa\u00e7\u00f5es de 1\u00ba grau para resolver problemas"},"content":{"rendered":"\n<p class=\"has-black-color has-vivid-cyan-blue-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;6\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=\"720\" height=\"720\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/11\/image7-1-e1637155485870.jpg\" alt=\"\" class=\"wp-image-134318\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/11\/image7-1-e1637155485870.jpg 720w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/11\/image7-1-e1637155485870-300x300.jpg 300w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2021\/11\/image7-1-e1637155485870-150x150.jpg 150w\" sizes=\"(max-width: 720px) 100vw, 720px\" \/><figcaption>Libra Pan Pesar Balan\u00e7a De &#8211; Imagens 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 resolver problemas que podem ser representados por equa\u00e7\u00f5es de 1\u00ba grau e verificar que a raiz dessas equa\u00e7\u00f5es podem ser a solu\u00e7\u00e3o do problema. <\/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 aligncenter 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=\"Utilizando equa\u00e7\u00f5es de 1\u00ba grau para resolver problemas | Matem\u00e1tica - Aula12 | 6\u00aa s\u00e9rie\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/iQK5XwoRkYs?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<\/div><figcaption>Utilizando equa\u00e7\u00f5es de 1\u00ba grau para resolver problemas | Matem\u00e1tica &#8211; Aula12 | 6\u00aa s\u00e9rie<\/figcaption><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\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>Equa\u00e7\u00e3o (Defini\u00e7\u00e3o):<\/strong> Toda senten\u00e7a matem\u00e1tica expressa por uma igualdade, na qual haja um ou mais s\u00edmbolos que representem n\u00fameros desconhecidos dessa senten\u00e7a, \u00e9 denominada equa\u00e7\u00e3o. Cada s\u00edmbolo que representa um n\u00famero desconhecido chama-se <strong>inc\u00f3gnita<\/strong>. Resolver uma equa\u00e7\u00e3o consiste em obter suas ra\u00edzes ou solu\u00e7\u00f5es, ou seja, determinar o n\u00famero correspondente a cada inc\u00f3gnita que torna a senten\u00e7a verdadeira.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Exemplo<\/strong>:<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">A senten\u00e7a x + y = 10 \u00e9 uma equa\u00e7\u00e3o com duas inc\u00f3gnitas representada pelas letras x e y. O lado esquerdo da igualdade \u00e9 denominado de <strong>1\u00ba membro<\/strong> e o lado direito, <strong>2\u00ba membro<\/strong>.<\/p>\n\n\n\n<p class=\"has-text-align-center has-black-color has-cyan-bluish-gray-background-color has-text-color has-background\" style=\"font-size:25px\"><strong>Problemas resolvidos<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><img decoding=\"async\" width=\"785\" height=\"290\" src=\"https:\/\/lh5.googleusercontent.com\/CPf4HTQEyJNYigHsWDDnrLs1QKBPbAq2a2K55qY2Wr9nl2EIgycX_xjTO9gE0MAY8mRczbbBwZF_zx0m0wEZODtDnHp5P2KbzF-SDR_p9Rfh4ut-gXsn7AzwyHkGI16ZQHTBEBU362DEHALsrg\"><\/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\"><strong>Problemas Propostos<\/strong><\/p>\n\n\n\n<ol class=\"has-black-color has-text-color wp-block-list\" style=\"font-size:25px\"><li>Em um terreno retangular, o comprimento tem 10 metros a mais que a largura. Se representarmos pela letra x o n\u00famero de metros da largura, o comprimento ser\u00e1 representado por x + 10. Sabendo que o per\u00edmetro desse terreno \u00e9 80 metros, escreva uma equa\u00e7\u00e3o que nos permita calcular o comprimento e a largura do terreno.<\/li><li>. Daqui a 5 anos Karina ter\u00e1 37 anos. Usando a letra x, escreva uma equa\u00e7\u00e3o que permita calcular a idade que Karina tem hoje<\/li><\/ol>\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>Equa\u00e7\u00e3o de 1\u00ba grau com uma inc\u00f3gnita (Defini\u00e7\u00e3o):<\/strong> s\u00e3o todas as equa\u00e7\u00f5es que podem ser escritas na forma ax+b=0, onde a e b s\u00e3o n\u00fameros reais, com a diferente de zero. Observe que a equa\u00e7\u00e3o tem apenas uma inc\u00f3gnita e com expoente 1.<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\"><strong>Exemplo:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">Para realizar uma atividade na aula de Arte, o professor vai distribuir barbantes de um rolo de 100 m entre os grupos de alunos. Desse rolo, ele cortou 8 peda\u00e7os id\u00eanticos e sobraram 20 m de barbante. Quantos metros tem cada peda\u00e7o de barbante cortado?<\/p>\n\n\n\n<p class=\"has-black-color has-text-color\" style=\"font-size:25px\">Representando o comprimento de cada peda\u00e7o do barbante por x, podemos escrever a seguinte equa\u00e7\u00e3o:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/i1WQYO-jNTgf-6vBuVE0jxdFMpBDffnPNIhtsFJrEEU7_MjECL42CUpdYhiMZ9D4eEGDnxwergZZspPKG196-9epCMgioZfon97eW93_ywvaQCXZdTIz0MweQtB7UfkNlFctkcf5t8T5kQy2iA\" style=\"width: 700px;\"><\/p>\n\n\n\n<p class=\"has-text-align-center has-small-font-size\">SOUZA, Joamir Roberto de: Matem\u00e1tica realidade &amp; tecnologia: 7\u00ba ano, p.149.<\/p>\n\n\n\n<p class=\"has-text-align-center has-light-green-cyan-background-color has-background\" style=\"font-size:25px\"><strong>Resolu\u00e7\u00e3o de uma Equa\u00e7\u00e3o de 1\u00ba grau<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/71N0uqluNQGE7OcysjWXQheEDkvI0Uu7OHDJ-IiVHAyzD_yOcrdI5oNY3ecxrMwsDMrV-bm-_6dhF90ZxLRE_1lOKEiBs2kffC1G_xxadVjfw_29FXp9Ap4Zc3Kam7quQh9V037DwPVVPWrSWw\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/eoL7nWf-ZvUQFrVBeyEzvFbvEFlHD0wr5RTyUIvff7PEGyXNAWWYfUjAOOYor8wFhJl2O35F8ZO1_f3JpEJmD54YUMT_64Og1fbv-A7xv8jzzadqt3U4TmfXBgWNS8_sekK03d_GI3tvj1gcXg\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center has-cyan-bluish-gray-background-color has-background\" style=\"font-size:25px\"><strong>Problemas Resolvidos<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/v3h1DQ95UZp-7-rR1luoXN8mII_RSxb0UIokjpKzFD0lHzjyDoZqQy1-4hThMRBErez0dJBcWkzUEsBtOyEuJD9pyTUob2gWE733Pl7IuRngpBRnAXuZ1u2OYG2MSgmAb3mXP6aPF1kpN04_rw\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/4qeDWHr1tDUaKib6mOFQN3hqypdhtFCB_ISKbueL-zSJnsrXxNq8fDhJ2aVeiCl8Ah6BNUYTV7lnvetvW3TujqP97pzcbB9KxcGPru_bmLfBdPK5lv8oXTaI3yr7XcWvQOzBGUI1MYqsrY-WoQ\" alt=\"\"\/><\/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\">Como resolver uma do 1\u00ba grau, canal do prof. H\u00e9lio Link: <a href=\"https:\/\/youtu.be\/eCNyCk73CR4\">https:\/\/youtu.be\/eCNyCk73CR4<\/a>&nbsp;| Link: <a href=\"https:\/\/youtu.be\/krL7PPMz3Ns\">https:\/\/youtu.be\/krL7PPMz3Ns<\/a>&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center has-pale-cyan-blue-background-color has-background\" style=\"font-size:25px\"><strong>Problemas Propostos<\/strong><\/p>\n\n\n\n<ol class=\"has-black-color has-text-color wp-block-list\" style=\"font-size:25px\"><li>(CEFET\/RJ &#8211; 2\u00aa fase &#8211; 2016) Carlos e Manoela s\u00e3o irm\u00e3os g\u00eameos. A metade da idade de Carlos mais um ter\u00e7o da idade de Manoela \u00e9 igual a 10 anos. Qual \u00e9 a soma das idades dos dois irm\u00e3os?<\/li><li>(FAETEC &#8211; 2015) Um pacote do biscoito Saboroso custa R$ 1,25. Se Jo\u00e3o comprou N pacotes desse biscoito gastando R$ 13,75, qual o valor de N?<\/li><li>Um terreno retangular possui o comprimento cinco vezes maior que a largura. Sabendo que o per\u00edmetro desse terreno \u00e9 igual a 180 metros, escreva uma equa\u00e7\u00e3o para determinar o comprimento e a largura desse terreno. Qual \u00e9 o valor dessas medidas?<\/li><\/ol>\n\n\n\n<p class=\"has-black-color has-cyan-bluish-gray-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:\/\/www.youtube.com\/channel\/UCKmf3-WVHXY61WgWrz-OO4Q\">Professor Helio Roberto da Rocha &#8211; YouTube<\/a>&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><br><strong>Objetivos de Aprendizagem e Desenvolvimento:<\/strong><\/td><td>(EAJAMA0617) Resolver e elaborar problemas que possam ser representados por equa\u00e7\u00f5es polinomiais de 1\u00ba grau, redut\u00edveis \u00e0 forma ax + b = c, fazendo uso das propriedades da igualdade, em situa\u00e7\u00f5es diversas.&nbsp;(EAJAMA0618) Determinar a raiz de uma equa\u00e7\u00e3o do 1\u00ba grau por meio de equa\u00e7\u00f5es equivalentes, identificando-a como elemento do conjunto universo.<\/td><\/tr><tr><td><strong>Refer\u00eancias:<\/strong><\/td><td>GIOVANNI J\u00daNIOR, Jos\u00e9 Ruy &#8211; A conquista da matem\u00e1tica: 7o ano: ensino fundamental: anos finais \/ Jos\u00e9 Ruy Giovanni J\u00fanior, Benedicto Castrucci. \u2014 4. ed. \u2014 S\u00e3o Paulo: FTD, 2018.&nbsp;<br>SOUZA, Joamir Roberto de: Matem\u00e1tica realidade &amp; tecnologia: 7\u00ba ano: ensino fundamental: anos finais \/ Joamir Roberto de Souza. \u2013 1. ed. \u2013 S\u00e3o Paulo: FTD, 2018.<\/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":134318,"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":[104],"serie":[75],"eaja_componente":[78],"class_list":["post-134317","eaja","type-eaja","status-publish","has-post-thumbnail","hentry","eaja_categoria-2o-segmento-5a-e-6a-serie","serie-6a-serie","eaja_componente-matematica","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja\/134317","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\/134318"}],"wp:attachment":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media?parent=134317"}],"wp:term":[{"taxonomy":"eaja_categoria","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_categoria?post=134317"},{"taxonomy":"serie","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/serie?post=134317"},{"taxonomy":"eaja_componente","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_componente?post=134317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}