{"id":1159,"date":"2020-06-09T15:57:02","date_gmt":"2020-06-09T22:57:02","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1159"},"modified":"2025-08-04T11:54:24","modified_gmt":"2025-08-04T18:54:24","slug":"parabolas-lesson-5-episode-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-5-teachers\/parabolas-lesson-5-episode-2-teachers\/","title":{"rendered":"Parabolas Lesson 5 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=\"znbqgZ_E-dY\"><\/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=\"x-qWLYM4Szk\"><\/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_l5e2_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\">Keoni and Sasha develop an equation for a parabola with a focus at (0,2) and a directrix of y = \u20132. They use the Pythagorean theorem and 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-l5e2-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='6a13f25bb79b07086430497' value='6a13f25bb79b07086430497'><input type='hidden' id='bg-show-more-text-6a13f25bb79b07086430497' value=' '><input type='hidden' id='bg-show-less-text-6a13f25bb79b07086430497' value=' '><button id='bg-showmore-action-6a13f25bb79b07086430497' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a13f25bb79b07086430497' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Keoni initially thinks that the distance from a general point (x, y) on the parabola to the directrix will be y + 1 [<strong>1:04<\/strong>].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4 Keoni quickly catches himself and realizes that when the distance between the vertex and the focus is 2 units (instead of 1 unit, as it was with the parabola that they worked with in Lessons 2-4), then the distance from the x-axis to the directrix will also be 2 units. Thus, the distance from (x, y) to the directrix will be y + 2.&nbsp;<\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a13f25bb7a5c1038318924' value='6a13f25bb7a5c1038318924'><input type='hidden' id='bg-show-more-text-6a13f25bb7a5c1038318924' value=' '><input type='hidden' id='bg-show-less-text-6a13f25bb7a5c1038318924' value=' '><button id='bg-showmore-action-6a13f25bb7a5c1038318924' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a13f25bb7a5c1038318924' ><\/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>0:52<\/strong>]. Keoni has drawn two lines. What do you know about those two lines?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>3:50<\/strong>]. Solve for x.&nbsp; [Then start the video again and stop at <strong>5:00<\/strong>]. How did your solution method compare with Sasha and Keoni\u2019s? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a13f25bb7aec4029013062' value='6a13f25bb7aec4029013062'><input type='hidden' id='bg-show-more-text-6a13f25bb7aec4029013062' value=' '><input type='hidden' id='bg-show-less-text-6a13f25bb7aec4029013062' value=' '><button id='bg-showmore-action-6a13f25bb7aec4029013062' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a13f25bb7aec4029013062' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Invite students to engage in revoicing (to say what they hear from someone else in their own words).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. In responding to the Focus Question 1, ask one student to revoice what another student said about the two lines.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. After the narrator has highlighted the meaning of the lengths that Sasha and Keoni found for the sides of their right triangle [<strong>2:09 \u2013 3:28<\/strong>], call on different students to revoice the meaning of y+2, y\u20132 and x. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a13f25bb7b432007829808' value='6a13f25bb7b432007829808'><input type='hidden' id='bg-show-more-text-6a13f25bb7b432007829808' value=' '><input type='hidden' id='bg-show-less-text-6a13f25bb7b432007829808' value=' '><button id='bg-showmore-action-6a13f25bb7b432007829808' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a13f25bb7b432007829808' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. The equation y = x<sup>2<\/sup>\/4 represents the parabola shown in red in the figure below.&nbsp; The coordinates for some points on the parabola are given. What do you notice about the red and grey points?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u200b<img loading=\"lazy\" decoding=\"async\" width=\"315\" height=\"224\" class=\"wp-image-1167\" style=\"width: 315px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l5-ep2-teachers.jpg\" alt=\"Parabolas L5 E2 Math Extension\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l5-ep2-teachers.jpg 315w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l5-ep2-teachers-300x213.jpg 300w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Find the coordinates for the red points in the graph above. Explain your reasoning. <\/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-1-teachers\/\">Previous Episdoe<\/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-5-teachers\/parabolas-lesson-5-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-5-teachers\/\" style=\"background-color:#2d4059\">Lesson 5<\/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 develop an equation for a parabola with a focus at (0,2) and a directrix of y = \u20132. They use the Pythagorean theorem and the definition of a parabola. [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1142,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1159","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1159","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=1159"}],"version-history":[{"count":12,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1159\/revisions"}],"predecessor-version":[{"id":8345,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1159\/revisions\/8345"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1142"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}