{"id":1237,"date":"2020-06-10T15:16:09","date_gmt":"2020-06-10T22:16:09","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1237"},"modified":"2025-08-04T11:59:23","modified_gmt":"2025-08-04T18:59:23","slug":"parabolas-lesson-6-episode-1-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-1-teachers\/","title":{"rendered":"Parabolas Lesson 6 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=\"ixdylwhUabk\"><\/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=\"R9oWvVMdZAM\"><\/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 class=\"wp-block-paragraph\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-student-docs\/parabolas_l6e1_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\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni use the equation y = x<sup>2<\/sup>\/(4p) to plot a parabola for p = 1\/4. They make a conjecture for how the shape of the parabola will change as&nbsp; gets larger.<\/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-l6e1-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 wp-block-paragraph\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='6a3c58811a4137006610296' value='6a3c58811a4137006610296'><input type='hidden' id='bg-show-more-text-6a3c58811a4137006610296' value=' '><input type='hidden' id='bg-show-less-text-6a3c58811a4137006610296' value=' '><button id='bg-showmore-action-6a3c58811a4137006610296' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3c58811a4137006610296' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After using the equation to plot points on the parabola y = x<sup>2<\/sup> with a p-value of 1\/4, Keoni struggles to locate coordinates of the focus of the parabola <strong>[5:06-5:24]<\/strong>. He first places the focus at (0,1) <strong>[5:35-5:59]<\/strong>. Keoni states that (0,1) is a \u201cgeneral place\u201d to put the focus.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4Sasha and Keoni notice a conflict when asked to state the p-value for the parabola when the focus is one unit above the origin. They restate that p is the distance between the focus and the vertex. Keoni notices that they are currently working with a p-value of 1\/4. Consequently, Sasha and Keoni adjust the focus location <strong>[6:02-6:19]<\/strong>. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a3c58811a4c33086962352' value='6a3c58811a4c33086962352'><input type='hidden' id='bg-show-more-text-6a3c58811a4c33086962352' value=' '><input type='hidden' id='bg-show-less-text-6a3c58811a4c33086962352' value=' '><button id='bg-showmore-action-6a3c58811a4c33086962352' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3c58811a4c33086962352' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For use in a classroom, pause the video and ask these questions:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. [Pause video at <strong>5:05<\/strong>]. What are some other points that you know are on the parabola because of the geometry of the parabola?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>9:16<\/strong>]. What are the coordinates of the red point that Keoni says is on the parabola? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a3c58811a5206084598049' value='6a3c58811a5206084598049'><input type='hidden' id='bg-show-more-text-6a3c58811a5206084598049' value=' '><input type='hidden' id='bg-show-less-text-6a3c58811a5206084598049' value=' '><button id='bg-showmore-action-6a3c58811a5206084598049' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3c58811a5206084598049' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Invite students attend to the reasoning of others while reflecting on multiple strategies:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Stop the video at [<strong>10:00<\/strong>]. Ask one student to present one method for checking to see if the point (\u00bd, \u00bc) is on the parabola. Ask a second student to use the first student\u2019s method to check a different point, say (1,1).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Repeat the process for a new method of checking. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a3c58811a5699053736026' value='6a3c58811a5699053736026'><input type='hidden' id='bg-show-more-text-6a3c58811a5699053736026' value=' '><input type='hidden' id='bg-show-less-text-6a3c58811a5699053736026' value=' '><button id='bg-showmore-action-6a3c58811a5699053736026' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3c58811a5699053736026' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. What happens when the focus is below the vertex? Graph the parabola with a focus at (0, \u2013\u00bc) and vertex at (0, 0). Label the focus, the directrix, and several points on 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-5-teachers\/parabolas-lesson-5-episode-7-teachers\/\">Lesson 5 Episode 7<\/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-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\/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>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 and Keoni use the equation y = x2\/(4p) to plot a parabola for p = 1\/4. They make a conjecture for how the shape of the parabola will change as&nbsp; [&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-1237","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1237","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=1237"}],"version-history":[{"count":14,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1237\/revisions"}],"predecessor-version":[{"id":8351,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1237\/revisions\/8351"}],"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=1237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}