{"id":584,"date":"2020-04-27T14:10:13","date_gmt":"2020-04-27T21:10:13","guid":{"rendered":"http:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=584"},"modified":"2025-08-04T11:28:55","modified_gmt":"2025-08-04T18:28:55","slug":"parabolas-lesson-1-episode-1-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-1-teachers\/parabolas-lesson-1-episode-1-teachers\/","title":{"rendered":"Parabolas Lesson 1 Episode 1 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Making Sense<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n\n<div class=\"youtube-player\" data-id=\"XzQLSVtVj6Y\"><\/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=\"xIjQs-VjQPc\"><\/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_l1_e1_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=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/download_worksheets.jpg\" alt=\"Download Math Task\"><\/a><\/p>\n\n\n\n<p>Sasha &amp; Keoni make sense of the definition of a parabola.<\/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-l1e1-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='69efcd2fbb6f30069711424' value='69efcd2fbb6f30069711424'><input type='hidden' id='bg-show-more-text-69efcd2fbb6f30069711424' value=' '><input type='hidden' id='bg-show-less-text-69efcd2fbb6f30069711424' value=' '><button id='bg-showmore-action-69efcd2fbb6f30069711424' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69efcd2fbb6f30069711424' ><\/p>\n\n\n\n<p><strong>1. <\/strong>Keoni thinks the focus should be on the directrix <strong>[2:35]<\/strong>.&nbsp;<\/p>\n\n\n\n<p>Sasha and Keoni investigate how putting the focus on the directrix leads to the construction of a line rather than a parabola.<\/p>\n\n\n\n<p><strong>2.<\/strong> When Sasha and Keoni try to measure the distance between a point and the directrix, they get different distances depending on which line segment they draw to connect the point and the line <strong>[7:52]<\/strong>.&nbsp;<\/p>\n\n\n\n<p>They use string to establish that the distance along the direction perpendicular to a line is the shortest distance between a point and the line.<\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69efcd2fbb8340050236130' value='69efcd2fbb8340050236130'><input type='hidden' id='bg-show-more-text-69efcd2fbb8340050236130' value=' '><input type='hidden' id='bg-show-less-text-69efcd2fbb8340050236130' value=' '><button id='bg-showmore-action-69efcd2fbb8340050236130' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69efcd2fbb8340050236130' ><\/p>\n\n\n\n<p>For use in a classroom, pause the video and ask these questions:&nbsp;<\/p>\n\n\n\n<p><strong>1. <\/strong>[Pause video at <strong>2:01<\/strong>]. Carefully analyze the definition of a parabola: What parts of the definition did Keoni and Sasha use when they drew these 3 points? What parts are not represented in their diagram?&nbsp;<\/p>\n\n\n\n<p><strong>2. <\/strong>[Pause video at <strong>8:22<\/strong>]. What do we mean by the distance between a point and a line? How would you define it? How would you measure it? What do Keoni and Sasha need to understand about the distance between a point and a line?<\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69efcd2fbb8ac7038062931' value='69efcd2fbb8ac7038062931'><input type='hidden' id='bg-show-more-text-69efcd2fbb8ac7038062931' value=' '><input type='hidden' id='bg-show-less-text-69efcd2fbb8ac7038062931' value=' '><button id='bg-showmore-action-69efcd2fbb8ac7038062931' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69efcd2fbb8ac7038062931' ><\/p>\n\n\n\n<p>When students are working on the task in class, you can support dialogue as follows:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ask a student to repeat what another student just said, i.e., \u201cAlex, can you share what you heard Lani say?\u201d<\/li>\n\n\n\n<li>Ask students to relate their actions to the definition, i.e., \u201cDo your points fit the definition of a parabola?\u201d<\/div><\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">Math Extensions <input type='hidden' bg_collapse_expand='69efcd2fbb9456036209704' value='69efcd2fbb9456036209704'><input type='hidden' id='bg-show-more-text-69efcd2fbb9456036209704' value=' '><input type='hidden' id='bg-show-less-text-69efcd2fbb9456036209704' value=' '><button id='bg-showmore-action-69efcd2fbb9456036209704' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69efcd2fbb9456036209704' ><\/p>\n\n\n\n<p>These questions allow students to extend the concepts and terminology from the episode.<\/p>\n\n\n\n<p><strong>1. <\/strong>Draw two points on a piece of paper. Find the points that are the same distance from the two points. Explain your solution. How do you know those points you found are the same distance from the two given points that you drew?<\/p>\n\n\n\n<p><strong>2. <\/strong>With a pencil and a ruler, draw two lines that intersect. What are the points that are the same distance from the two lines that you drew? Explain your solution. How do you know those points you found are the same distance from the two given lines that you drew?<\/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-1-teachers\/parabolas-lesson-1-episode-2-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\/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\/parabolas-lesson-1-teachers\/\" style=\"background-color:#2d4059\">Lesson 1<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Making Sense No captions CaptionsStop the video above first if it is playing. No captions CaptionsStop the video above first if it is playing. Sasha &amp; Keoni make sense of the definition of a parabola. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue Math Extensions Next Episode<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":572,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-584","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/584","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=584"}],"version-history":[{"count":18,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/584\/revisions"}],"predecessor-version":[{"id":8320,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/584\/revisions\/8320"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/572"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}