{"id":1381,"date":"2020-06-15T13:49:32","date_gmt":"2020-06-15T20:49:32","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1381"},"modified":"2025-08-04T12:10:46","modified_gmt":"2025-08-04T19:10:46","slug":"parabolas-lesson-8-episode-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-8-teachers\/parabolas-lesson-8-episode-2-teachers\/","title":{"rendered":"Parabolas Lesson 8 Episode 2 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Exploring<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n\n<div class=\"youtube-player\" data-id=\"8ANfpU9tl-8\"><\/div>\n\n<\/p>\n<p style=\"text-align:center;\"><span style=\"font-size:90%\">No captions <a onclick=\"toggle_text('video_shown_first', 'video_hidden_first')\"><img loading=\"lazy\" decoding=\"async\" width=\"60\" height=\"36\" class=\"wp-image-3255\" style=\"width: 60px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-left.png\" alt=\"toggle left\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-left.png 380w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-left-300x178.png 300w\" sizes=\"auto, (max-width: 60px) 100vw, 60px\" \/><\/a> Captions<\/span><br><span style=\"font-size:80%\"><strong>Stop<\/strong> the video above first if it is playing.<\/span>\n<\/p>\n\n<\/div>\n\n<div id=\"video_hidden_first\" style=\"display:none\">\n<p>\n\n<div class=\"youtube-player\" data-id=\"mPnvisGae6U\"><\/div>\n\n<\/p>\n\n<p style=\"text-align:center;\"><span style=\"font-size:90%\">No captions <a onclick=\"toggle_text('video_shown_first', 'video_hidden_first')\"><a onclick=\"toggle_text('video_shown_first', 'video_hidden_first')\"><img loading=\"lazy\" decoding=\"async\" width=\"60\" height=\"36\" class=\"wp-image-3256\" style=\"width: 60px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-right.png\" alt=\"toggle right\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-right.png 380w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-right-300x178.png 300w\" sizes=\"auto, (max-width: 60px) 100vw, 60px\" \/><\/a> Captions<\/span><br><span style=\"font-size:80%\"><strong>Stop<\/strong> the video above first if it is playing.<\/span>\n<\/p>\n<\/div>\n\n\n\n<p><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-student-docs\/parabolas_l8e2_studentworkwheet.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 3 and a vertex at (7, 0).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-vivid-cyan-blue-color has-css-opacity has-vivid-cyan-blue-background-color has-background\"\/>\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-l8e2-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='69f4c2d9c36650034148623' value='69f4c2d9c36650034148623'><input type='hidden' id='bg-show-more-text-69f4c2d9c36650034148623' value=' '><input type='hidden' id='bg-show-less-text-69f4c2d9c36650034148623' value=' '><button id='bg-showmore-action-69f4c2d9c36650034148623' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2d9c36650034148623' ><\/p>\n\n\n\n<p>At <strong>[1:31]<\/strong>, Sasha whispers, \u201cIt looks weird; I don\u2019t get it.\u201d In this new situation where the vertex has shifted over by 7 units, it is challenging to construct a right triangle like they used when the vertex was on the origin..<\/p>\n\n\n\n<p>\u27a4 While examining what they have drawn so far, Keoni adds an important side of the triangle. He chooses the focus as one of the corners of the triangle. His choice of where to place the side of the triangle results in a useful right triangle. As the episode continues, they figure out how to represent the length of each side of the triangle. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69f4c2d9c37114011144092' value='69f4c2d9c37114011144092'><input type='hidden' id='bg-show-more-text-69f4c2d9c37114011144092' value=' '><input type='hidden' id='bg-show-less-text-69f4c2d9c37114011144092' value=' '><button id='bg-showmore-action-69f4c2d9c37114011144092' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2d9c37114011144092' ><\/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 video at <strong>0:47<\/strong>]. How does Keoni know where to place the focus and the directrix for this parabola?<\/p>\n\n\n\n<p>2. [Pause video at <strong>6:15<\/strong>]. Looking at the two right triangles, what is the same and what is different?<\/p>\n\n\n\n<p>3. [Pause the video at <strong>9:29<\/strong>]. What is the difference between the representation of (x \u2013 7)<sup>2<\/sup> and x<sup>2<\/sup> \u2013 14x + 49? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69f4c2d9c37630039138285' value='69f4c2d9c37630039138285'><input type='hidden' id='bg-show-more-text-69f4c2d9c37630039138285' value=' '><input type='hidden' id='bg-show-less-text-69f4c2d9c37630039138285' value=' '><button id='bg-showmore-action-69f4c2d9c37630039138285' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2d9c37630039138285' ><\/p>\n\n\n\n<p>Invite students to engage in stating and justifying mathematical claims with another student:<\/p>\n\n\n\n<p>1. Work with a partner to justify the representation of x \u2013 7 for the length of the horizontal side of the triangle that Sasha and Keoni used to derive the equation of a parabola.<\/p>\n\n\n\n<p>2. Work with a partner to justify the representation of y \u2013 3 for the length of the vertical side of the triangle that Sasha and Keoni used to derive the equation of a parabola. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Math Extensions <input type='hidden' bg_collapse_expand='69f4c2d9c37961085937546' value='69f4c2d9c37961085937546'><input type='hidden' id='bg-show-more-text-69f4c2d9c37961085937546' value=' '><input type='hidden' id='bg-show-less-text-69f4c2d9c37961085937546' value=' '><button id='bg-showmore-action-69f4c2d9c37961085937546' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2d9c37961085937546' ><\/p>\n\n\n\n<p>During the video <strong>[1:09]<\/strong>, Sasha and Keoni have a brief discussion about choosing what point on the parabola to use to derive the equation for the parabola. They mention the \u201cspecial point\u201d and the need not to choose it. They state that they need a general point.<\/p>\n\n\n\n<p>1. What do they mean by a special point? What are the coordinates for a \u201cspecial point\u201d on the parabola in this episode?<\/p>\n\n\n\n<p>2. What do they mean by a general point?<\/p>\n\n\n\n<p>3. What would happen if they used a special point to derive the equation for the parabola? <\/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 wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-8-teachers\/parabolas-lesson-8-episode-1-teachers\/\">Previous Episode<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-8-teachers\/parabolas-lesson-8-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-8-teachers\/\" style=\"background-color:#2d4059\">Lesson 8<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exploring No captions CaptionsStop the video above first if it is playing. No captions CaptionsStop the video above first if it is playing. Keoni and Sasha use the Pythagorean Theorem and the definition of a parabola to derive an equation of parabola with a p-value of 3 and a vertex at (7, 0). Episode Supports [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1362,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1381","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1381","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=1381"}],"version-history":[{"count":14,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1381\/revisions"}],"predecessor-version":[{"id":8366,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1381\/revisions\/8366"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1362"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}