{"id":1332,"date":"2020-06-12T16:16:53","date_gmt":"2020-06-12T23:16:53","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1332"},"modified":"2025-08-04T12:08:11","modified_gmt":"2025-08-04T19:08:11","slug":"parabolas-lesson-7-episode-4-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-7-teachers\/parabolas-lesson-7-episode-4-teachers\/","title":{"rendered":"Parabolas Lesson 7 Episode 4 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Repeating Your Reasoning<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n\n<div class=\"youtube-player\" data-id=\"N--yZAksojg\"><\/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=\"5zPwr6gBjw8\"><\/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_l7e4_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:\/\/www.geogebra.org\/m\/rvJy16Y1\" target=\"_blank\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni use points on three parabolas that share a y-value to explain why increasing the p-value results in the parabola getting wider on the coordinate grid.<\/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-l7e4-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='6a13f25bed17f7025778451' value='6a13f25bed17f7025778451'><input type='hidden' id='bg-show-more-text-6a13f25bed17f7025778451' value=' '><input type='hidden' id='bg-show-less-text-6a13f25bed17f7025778451' value=' '><button id='bg-showmore-action-6a13f25bed17f7025778451' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a13f25bed17f7025778451' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni are examining the equation&nbsp; 16 = x<sup>2<\/sup>\/p when they are asked that happens to x when p increases. They pause as they search for an explanation <strong>[4:21]<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4 By using algebra to rewrite the equation so that the variables are expressed in a direct relation with each other, x = 4\u221ap, Sasha and Keoni find a way to respond to the question.&nbsp; The direct representation supports their reasoning on how a change in the p-value impacts the x-value. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a13f25bed28f5021045968' value='6a13f25bed28f5021045968'><input type='hidden' id='bg-show-more-text-6a13f25bed28f5021045968' value=' '><input type='hidden' id='bg-show-less-text-6a13f25bed28f5021045968' value=' '><button id='bg-showmore-action-6a13f25bed28f5021045968' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a13f25bed28f5021045968' ><\/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>1:53<\/strong>]. Keoni considers a parabola that goes through the origin and contains the point (4.5. 4). Can someone come up here and draw the rest of the parabola and estimate where the focus would be?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>6:44<\/strong>]. How did Keoni and Sasha get the equation x = 4\u221ap? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a13f25bed3205088694899' value='6a13f25bed3205088694899'><input type='hidden' id='bg-show-more-text-6a13f25bed3205088694899' value=' '><input type='hidden' id='bg-show-less-text-6a13f25bed3205088694899' value=' '><button id='bg-showmore-action-6a13f25bed3205088694899' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a13f25bed3205088694899' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Support the opportunity for students to engage in precise language as they articulate mathematical claims:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. As the x-value changes, how does the focus change?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Restate the claim and reasoning Sasha and Keoni use to argue why the parabola gets wider as the p-value increases. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a13f25bed37e5054758070' value='6a13f25bed37e5054758070'><input type='hidden' id='bg-show-more-text-6a13f25bed37e5054758070' value=' '><input type='hidden' id='bg-show-less-text-6a13f25bed37e5054758070' value=' '><button id='bg-showmore-action-6a13f25bed37e5054758070' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a13f25bed37e5054758070' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Find the coordinates of points on each of the three parabolas when the y-value is 1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Considering the ordered pairs that you found, what do you notice about the x-values when the p-value increases? How does that impact the width of the parabola as the p-value changes? <\/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-7-teachers\/parabolas-lesson-7-episode-3-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-7-teachers\/parabolas-lesson-7-episode-5-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-7-teachers\/\" style=\"background-color:#2d4059\">Lesson 7<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Repeating Your Reasoning 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 points on three parabolas that share a y-value to explain why increasing the p-value results in the parabola getting wider on the coordinate grid. Episode Supports [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1294,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1332","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1332","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=1332"}],"version-history":[{"count":11,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1332\/revisions"}],"predecessor-version":[{"id":8362,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1332\/revisions\/8362"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1294"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}