{"id":1557,"date":"2020-06-22T14:56:00","date_gmt":"2020-06-22T21:56:00","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1557"},"modified":"2020-08-03T11:02:58","modified_gmt":"2020-08-03T18:02:58","slug":"parabolas-lesson-10-episode-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-2-teachers\/","title":{"rendered":"Parabolas Lesson 10 Episode 2 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Exploring<\/h3>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Lesson 10 Episode 2\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/4Afxl5hyieA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-student-docs\/parabolas_l10_e2_studentworksheet.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"46\" class=\"wp-image-486\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/download_worksheets.jpg\" alt=\"Download Math Task\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/web2.0calc.com\/\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-485\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/calculator.jpg\" alt=\"Link to on-line calculator\"><\/a><\/p>\n\n\n\n<p>Sasha and Keoni graph the equation y = (x\u20132.4)<sup>2<\/sup>\/6. They determine the coordinates of the focus and the equation of the directrix from the geometric information in the equation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-background has-vivid-cyan-blue-background-color has-vivid-cyan-blue-color\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Episode Supports <a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-teacher-docs\/parabolas-l10e2-teacher-support-materials.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"34\" height=\"34\" class=\"wp-image-2214\" style=\"width: 34px; vertical-align: middle;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/07\/pdf.jpg\" alt=\"\"><\/a><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='69f63f99007342034102073' value='69f63f99007342034102073'><input type='hidden' id='bg-show-more-text-69f63f99007342034102073' value=' '><input type='hidden' id='bg-show-less-text-69f63f99007342034102073' value=' '><button id='bg-showmore-action-69f63f99007342034102073' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f63f99007342034102073' ><\/p>\n\n\n\n<p>The placement of the focus, which is no longer on the y-axis, is challenging for students. Keoni initially misplaces it at (0, 1.5). He apparently considers the value of p (which is 1.5) but doesn\u2019t move the focus to (2.4, 1.5).<\/p>\n\n\n\n<p>\u27a4 When Keoni examines his graph, he notices that the placement of the focus \u201cdoesn\u2019t look right.\u201d He adjusts the placement of the focus. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69f63f99007db8015099287' value='69f63f99007db8015099287'><input type='hidden' id='bg-show-more-text-69f63f99007db8015099287' value=' '><input type='hidden' id='bg-show-less-text-69f63f99007db8015099287' value=' '><button id='bg-showmore-action-69f63f99007db8015099287' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f63f99007db8015099287' ><\/p>\n\n\n\n<p>For use in a classroom, pause the video and ask these questions:<\/p>\n\n\n\n<p>1. [Pause the video at <strong>0:52<\/strong>]. The upper left window shows Keoni\u2019s work. Where has he placed the focus and directrix? What would justify the placement there?<\/p>\n\n\n\n<p>2. [Pause the video at <strong>3:25<\/strong>]. Look at the expression that Keoni wrote above the graph, y = (0\u20132.4)<sup>2<\/sup>\/6. What geometric information can he get out of that expression? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69f63f99008255089382500' value='69f63f99008255089382500'><input type='hidden' id='bg-show-more-text-69f63f99008255089382500' value=' '><input type='hidden' id='bg-show-less-text-69f63f99008255089382500' value=' '><button id='bg-showmore-action-69f63f99008255089382500' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f63f99008255089382500' ><\/p>\n\n\n\n<p>Invite students to generate multiple strategies to find points on the parabola by asking:<\/p>\n\n\n\n<p>With your partner, reflect on what strategies Sasha and Keoni use to find points on the parabola. What are other strategies that you can use to locate and determine the coordinates of points on a parabola? Prepare to share your strategies with the whole class. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Math Extensions <input type='hidden' bg_collapse_expand='69f63f99008500001978026' value='69f63f99008500001978026'><input type='hidden' id='bg-show-more-text-69f63f99008500001978026' value=' '><input type='hidden' id='bg-show-less-text-69f63f99008500001978026' value=' '><button id='bg-showmore-action-69f63f99008500001978026' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f63f99008500001978026' ><\/p>\n\n\n\n<p>Special points are points on the parabola that are horizontally level with the focus. What are the coordinates of the special points of the parabola represented by the equation y = (x\u20132.4)<sup>2<\/sup>\/6? Explain how you know. <\/div><\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-1-teachers\/\">Previous Episode<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-3-teachers\/\">Next Episode<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/\" style=\"background-color:#2d4059\">Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/\" style=\"background-color:#2d4059\">Teachers Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/\" style=\"background-color:#2d4059\">Parabolas<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/\" style=\"background-color:#2d4059\">Lesson 10<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exploring Sasha and Keoni graph the equation y = (x\u20132.4)2\/6. They determine the coordinates of the focus and the equation of the directrix from the geometric information in the equation. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue Math Extensions<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1538,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1557","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1557","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/comments?post=1557"}],"version-history":[{"count":10,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1557\/revisions"}],"predecessor-version":[{"id":2469,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1557\/revisions\/2469"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1538"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}