{"id":1478,"date":"2020-06-19T09:32:35","date_gmt":"2020-06-19T16:32:35","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1478"},"modified":"2020-08-03T10:55:44","modified_gmt":"2020-08-03T17:55:44","slug":"parabolas-lesson-9-episode-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-9-teachers\/parabolas-lesson-9-episode-2-teachers\/","title":{"rendered":"Parabolas Lesson 9 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 9 Episode 2\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/rIoemb7qOkU?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_l9e2_student-worksheet.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><\/p>\n\n\n\n<p>Keoni and Sasha use the Pythagorean Theorem and the definition of a parabola to derive an equation of parabola with a p-value of 5 and a vertex at (9, 13).<\/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-l9e2-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='69df2f171fb900085541172' value='69df2f171fb900085541172'><input type='hidden' id='bg-show-more-text-69df2f171fb900085541172' value=' '><input type='hidden' id='bg-show-less-text-69df2f171fb900085541172' value=' '><button id='bg-showmore-action-69df2f171fb900085541172' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69df2f171fb900085541172' ><\/p>\n\n\n\n<p>At <strong>[0:48]<\/strong>, Keoni is unsure whether to draw a segment from the general point to the vertex or to the focus.<\/p>\n\n\n\n<p>\u27a4 Sasha and Keoni resolve the issue by reminding themselves of the definition of a parabola. They recall how they can use the definition to represent the lengths of the sides of a right triangle. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69df2f171fd338026321115' value='69df2f171fd338026321115'><input type='hidden' id='bg-show-more-text-69df2f171fd338026321115' value=' '><input type='hidden' id='bg-show-less-text-69df2f171fd338026321115' value=' '><button id='bg-showmore-action-69df2f171fd338026321115' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69df2f171fd338026321115' ><\/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>1:54<\/strong>].&nbsp; What is the distance y? How would you represent it geometrically on the coordinate grid?<\/p>\n\n\n\n<p>2. [Pause the video at <strong>3:46<\/strong>]. What are the coordinates of the third vertex of the triangle? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69df2f171fe113004214480' value='69df2f171fe113004214480'><input type='hidden' id='bg-show-more-text-69df2f171fe113004214480' value=' '><input type='hidden' id='bg-show-less-text-69df2f171fe113004214480' value=' '><button id='bg-showmore-action-69df2f171fe113004214480' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69df2f171fe113004214480' ><\/p>\n\n\n\n<p>Invite students to engage in productive disagreement:<\/p>\n\n\n\n<p>As Sasha and Keoni are completing their algebraic manipulations, Sasha cancels the 20 <strong>[7:34]<\/strong>. But then it shows up in the final version of the equation. What happened? Did she make a mistake? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Math Extensions <input type='hidden' bg_collapse_expand='69df2f171fe721083859080' value='69df2f171fe721083859080'><input type='hidden' id='bg-show-more-text-69df2f171fe721083859080' value=' '><input type='hidden' id='bg-show-less-text-69df2f171fe721083859080' value=' '><button id='bg-showmore-action-69df2f171fe721083859080' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69df2f171fe721083859080' ><\/p>\n\n\n\n<p>In the graph below, the base parabola with p =5, shown in black, is represented by the equation y = x<sup>2<\/sup>\/20. If the base parabola is translated to the right 9 units, it will be the parabola shown in light blue, which is represented by the equation y = (x\u20139)<sup>2<\/sup>\/20. If this parabola is translated up 13 units, it will be the parabola shown in dark blue, which is represented by the equation y = (x\u20139)<sup>2<\/sup>\/20 + 13.<\/p>\n\n\n\n<p>1. Use the equations to prove that each vertex is on a particular parabola; what do you notice?<\/p>\n\n\n\n<p>2. Use the equations to find a \u201cspecial point\u201d (a point aligned horizontally with the focus) for each parabola; what do you notice?<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"337\" height=\"236\" class=\"wp-image-1486\" style=\"width: 337px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l9-ep2-teachers.jpg\" alt=\"Parabolas L9 E2 Math Extension\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l9-ep2-teachers.jpg 337w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l9-ep2-teachers-300x210.jpg 300w\" sizes=\"auto, (max-width: 337px) 100vw, 337px\" \/><\/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-9-teachers\/parabolas-lesson-9-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-9-teachers\/parabolas-lesson-9-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-9-teachers\/\" style=\"background-color:#2d4059\">Lesson 9<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exploring Keoni and Sasha use the Pythagorean Theorem and the definition of a parabola to derive an equation of parabola with a p-value of 5 and a vertex at (9, 13). Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue Math Extensions<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1444,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1478","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1478","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=1478"}],"version-history":[{"count":11,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1478\/revisions"}],"predecessor-version":[{"id":2452,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1478\/revisions\/2452"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1444"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1478"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}