{"id":1260,"date":"2020-06-10T16:10:56","date_gmt":"2020-06-10T23:10:56","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1260"},"modified":"2025-08-04T12:00:53","modified_gmt":"2025-08-04T19:00:53","slug":"parabolas-lesson-6-episode-3-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-6-teachers\/parabolas-lesson-6-episode-3-teachers\/","title":{"rendered":"Parabolas Lesson 6 Episode 3 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Reflecting<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n\n<div class=\"youtube-player\" data-id=\"7E2_zpVE1Zk\"><\/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=\"MqS_GkaLeMY\"><\/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_l6e2_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>Keoni and Sasha reflect on the two parabolas that they graphed in Episodes 1 and 2 (y=x<sup>2<\/sup> and y=x<sup>2<\/sup>\/2). They notice several features of the parabolas that change when the p-value increases from 1\/4 to 1\/2.<\/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-l6e3-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<h3 class=\"wp-block-heading\">Episode Supports<\/h3>\n\n\n\n<p class=\"has-medium-font-size\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='69f3c5d5bb8486066321377' value='69f3c5d5bb8486066321377'><input type='hidden' id='bg-show-more-text-69f3c5d5bb8486066321377' value=' '><input type='hidden' id='bg-show-less-text-69f3c5d5bb8486066321377' value=' '><button id='bg-showmore-action-69f3c5d5bb8486066321377' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3c5d5bb8486066321377' ><\/p>\n\n\n\n<p>When Keoni and Sasha are asked what things they notice about the two graphs, they hesitate <strong>[0:31-0:43]<\/strong>. They might be struggling to identify the mathematically significant features on their graphs.<\/p>\n\n\n\n<p>\u27a4 They begin with more prominent features, like the p-value, focus and directrix of each parabola. Then the teacher encourages them to look at a more subtle feature\u2014what Sasha and Keoni call \u201cspecial points.\u201d <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69f3c5d5bb8e04079095725' value='69f3c5d5bb8e04079095725'><input type='hidden' id='bg-show-more-text-69f3c5d5bb8e04079095725' value=' '><input type='hidden' id='bg-show-less-text-69f3c5d5bb8e04079095725' value=' '><button id='bg-showmore-action-69f3c5d5bb8e04079095725' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3c5d5bb8e04079095725' ><\/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>1:22]<\/strong>. What else do you notice about the two graphs?<\/p>\n\n\n\n<p>2. [Pause video at <strong>1:30<\/strong>]. What makes a \u201cspecial point\u201d special? What do you notice about the two special points that Sasha and Keoni graphed? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69f3c5d5bb9250034664825' value='69f3c5d5bb9250034664825'><input type='hidden' id='bg-show-more-text-69f3c5d5bb9250034664825' value=' '><input type='hidden' id='bg-show-less-text-69f3c5d5bb9250034664825' value=' '><button id='bg-showmore-action-69f3c5d5bb9250034664825' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3c5d5bb9250034664825' ><\/p>\n\n\n\n<p>Provide opportunities for productive disagreement by asking:<\/p>\n\n\n\n<p>Keoni and Sasha have graphed two parabolas (shown in blue and red) on the same coordinate grid. A student, Tessa, looks at the graphs and says, \u201cThe blue parabola will never be as high as the red parabola.\u201d Do you agree or disagree with Tessa? Why? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Math Extensions <input type='hidden' bg_collapse_expand='69f3c5d5bb9518094446865' value='69f3c5d5bb9518094446865'><input type='hidden' id='bg-show-more-text-69f3c5d5bb9518094446865' value=' '><input type='hidden' id='bg-show-less-text-69f3c5d5bb9518094446865' value=' '><button id='bg-showmore-action-69f3c5d5bb9518094446865' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3c5d5bb9518094446865' ><\/p>\n\n\n\n<p>1. Graph the parabolas represented by the equations y = x<sup>2<\/sup>\/2 and y = \u2013x<sup>2<\/sup>\/2.<\/p>\n\n\n\n<p>2.&nbsp; Compare the two graphs. What is the same and what is different?<\/p>\n\n\n\n<p>3.&nbsp; What do you notice about the focus and directrix of each graph? <\/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-6-teachers\/parabolas-lesson-6-episode-2-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-6-teachers\/parabolas-lesson-6-episode-4-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-6-teachers\/\" style=\"background-color:#2d4059\">Lesson 6<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Reflecting 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 reflect on the two parabolas that they graphed in Episodes 1 and 2 (y=x2 and y=x2\/2). They notice several features of the parabolas that change when the p-value increases [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1229,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1260","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1260","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=1260"}],"version-history":[{"count":11,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1260\/revisions"}],"predecessor-version":[{"id":8353,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1260\/revisions\/8353"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1229"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}