{"id":1128,"date":"2020-06-08T14:54:36","date_gmt":"2020-06-08T21:54:36","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1128"},"modified":"2025-08-04T11:51:16","modified_gmt":"2025-08-04T18:51:16","slug":"parabolas-lesson-4-episode-6-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-4-teachers\/parabolas-lesson-4-episode-6-teachers\/","title":{"rendered":"Parabolas Lesson 4 Episode 6 (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=\"7V2oxNwj1kA\"><\/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=\"qwHWk4xHi4k\"><\/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 rel=\"noreferrer noopener\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-student-docs\/parabolas_l4e6_student-worksheet.pdf\" target=\"_blank\"><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 return to the equation y = x<sup>2<\/sup>\/4 and derive it using the definition of a parabola, the Pythagorean theorem, and their method from Episode 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-l4e6-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='6a1b642b759a35041134520' value='6a1b642b759a35041134520'><input type='hidden' id='bg-show-more-text-6a1b642b759a35041134520' value=' '><input type='hidden' id='bg-show-less-text-6a1b642b759a35041134520' value=' '><button id='bg-showmore-action-6a1b642b759a35041134520' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b642b759a35041134520' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni struggle when the teacher asks them to \u201cmark something that would stand for a general point on the parabola\u201d [<strong>2:14<\/strong>].<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Once Sasha marks a point on the parabola, Keoni wants to identify the coordinates of that particular location on the grid, rather than understanding that the point is meant to stand in for all points on the parabola. Sasha is unsure how to represent the point and wants to call is \u201cPoint X.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4It helps them to explore the meaning of a particular point (6,9). They use the fact that the 6 is represented on the x-axis and the 9 on the y-axis to similarly label their general point as (x,y). They continue to work with the idea of a general point in future episodes. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a1b642b84d163022053641' value='6a1b642b84d163022053641'><input type='hidden' id='bg-show-more-text-6a1b642b84d163022053641' value=' '><input type='hidden' id='bg-show-less-text-6a1b642b84d163022053641' value=' '><button id='bg-showmore-action-6a1b642b84d163022053641' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b642b84d163022053641' ><\/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>2:35<\/strong>]. What does it mean to be a general point on the parabola?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>7:06<\/strong>]. Keoni drew a horizontal line. What property does every point on that line share? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a1b642b84dcd1073073761' value='6a1b642b84dcd1073073761'><input type='hidden' id='bg-show-more-text-6a1b642b84dcd1073073761' value=' '><input type='hidden' id='bg-show-less-text-6a1b642b84dcd1073073761' value=' '><button id='bg-showmore-action-6a1b642b84dcd1073073761' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b642b84dcd1073073761' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ask several students to respond to the question below.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Keoni and Sasha are often drawing a horizontal or vertical line. How are they using those lines in their problem solving? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a1b642b84e151022248710' value='6a1b642b84e151022248710'><input type='hidden' id='bg-show-more-text-6a1b642b84e151022248710' value=' '><input type='hidden' id='bg-show-less-text-6a1b642b84e151022248710' value=' '><button id='bg-showmore-action-6a1b642b84e151022248710' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b642b84e151022248710' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Consider the circle below. Can you find an equation of the circle that is solved for y? What about for x?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" width=\"268\" height=\"243\" class=\"wp-image-1036\" style=\"width: 268px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l3-e1-teachers.jpg\" alt=\"Parabolas L3 E1 Math Extension circle\"> <\/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-4-teachers\/parabolas-lesson-4-episode-5-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-1-teachers\/\">Lesson 5 Episode 1<\/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\" 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-4-teachers\/\" style=\"background-color:#2d4059\">Lesson 4<\/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 return to the equation y = x2\/4 and derive it using the definition of a parabola, the Pythagorean theorem, and their method from Episode 2. Episode Supports Students\u2019 Conceptual [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1080,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1128","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1128","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=1128"}],"version-history":[{"count":9,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1128\/revisions"}],"predecessor-version":[{"id":8343,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1128\/revisions\/8343"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1080"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}