{"id":1173,"date":"2020-06-10T09:18:34","date_gmt":"2020-06-10T16:18:34","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1173"},"modified":"2025-08-04T11:55:48","modified_gmt":"2025-08-04T18:55:48","slug":"parabolas-lesson-5-episode-3-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-3-teachers\/","title":{"rendered":"Parabolas Lesson 5 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=\"ex8XBwWF24U\"><\/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=\"hWksk-U6K_4\"><\/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_l5e3_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 compare the equations for two parabolas: y = x<sup>2<\/sup>\/8 and y = x<sup>2<\/sup>\/4. They make two different conjectures about the equation for a parabola with a focus at 3 units above the vertex.<\/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-l5e3-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='6a159eca240648010459824' value='6a159eca240648010459824'><input type='hidden' id='bg-show-more-text-6a159eca240648010459824' value=' '><input type='hidden' id='bg-show-less-text-6a159eca240648010459824' value=' '><button id='bg-showmore-action-6a159eca240648010459824' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159eca240648010459824' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">With only two equations, differing patterns can emerge that might not work in the general case.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4 Sasha and Keoni offer two different conjectures for the equation of a third parabola: y = x<sup>2<\/sup>\/12 and y = x<sup>2<\/sup>\/16 [<strong>1:16-1:45<\/strong>].&nbsp; They resolve their differences in Episode 4. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a159eca241540016636658' value='6a159eca241540016636658'><input type='hidden' id='bg-show-more-text-6a159eca241540016636658' value=' '><input type='hidden' id='bg-show-less-text-6a159eca241540016636658' value=' '><button id='bg-showmore-action-6a159eca241540016636658' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159eca241540016636658' ><\/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>0:57<\/strong>]. Take a moment to examine the focus and directrix that Sasha just drew. When the vertex of the parabola is on the origin, how are the positions of the focus and directrix related?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>1:09<\/strong>]. What are <em>your<\/em> conjectures about the equation for the third parabola? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a159eca241e66065194633' value='6a159eca241e66065194633'><input type='hidden' id='bg-show-more-text-6a159eca241e66065194633' value=' '><input type='hidden' id='bg-show-less-text-6a159eca241e66065194633' value=' '><button id='bg-showmore-action-6a159eca241e66065194633' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159eca241e66065194633' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Provide opportunities for productive disagreement by asking:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Keoni and Sasha have two conjectures. Who thinks the next parabola will have an equations of y = x<sup>2<\/sup>\/16? Who thinks the equation will be y = x<sup>2<\/sup>\/12?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Can we have one person to defend the first conjecture? What about someone for the other? Let\u2019s hear each case. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a159eca242f43073816499' value='6a159eca242f43073816499'><input type='hidden' id='bg-show-more-text-6a159eca242f43073816499' value=' '><input type='hidden' id='bg-show-less-text-6a159eca242f43073816499' value=' '><button id='bg-showmore-action-6a159eca242f43073816499' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159eca242f43073816499' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. The graph below represents the equation y = x<sup>2<\/sup>\/4 . Consider the part of the graph colored blue. Label some coordinates of points on the blue part of the graph. What is common about the coordinates of every point on the blue part of the graph?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Notice the point (a, b) on the graph. Represent the coordinates of the red point using the a and the b.&nbsp; Explain your thinking.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3. Notice the line segment shown in green. In mathematics, it is a convention to represent distances with positive numbers. Coordinates can be negative, but distances and lengths must be positive. How can you use the coordinates to represent the length of the green line, which is the distance from the blue parabola to the y-axis?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" width=\"311\" height=\"237\" class=\"wp-image-1180\" style=\"width: 311px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l5-ep3-teachers.jpg\" alt=\"Parabolas L5 E3 Math Extension\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l5-ep3-teachers.jpg 311w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l5-ep3-teachers-300x229.jpg 300w\" sizes=\"auto, (max-width: 311px) 100vw, 311px\" \/> <\/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-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-5-teachers\/parabolas-lesson-5-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-5-teachers\/\" style=\"background-color:#2d4059\">Lesson 5<\/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 compare the equations for two parabolas: y = x2\/8 and y = x2\/4. They make two different conjectures about the equation for a parabola with a focus at 3 [&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-1173","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1173","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=1173"}],"version-history":[{"count":11,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1173\/revisions"}],"predecessor-version":[{"id":8346,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1173\/revisions\/8346"}],"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=1173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}