{"id":1218,"date":"2020-06-10T11:24:32","date_gmt":"2020-06-10T18:24:32","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1218"},"modified":"2025-08-04T11:58:45","modified_gmt":"2025-08-04T18:58:45","slug":"parabolas-lesson-5-episode-7-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-7-teachers\/","title":{"rendered":"Parabolas Lesson 5 Episode 7 (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=\"MkclyhQUTFw\"><\/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=\"MkclyhQUTFw\"><\/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_l5e7_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\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-485\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/calculator.jpg\" alt=\"Link to on-line calculator\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni discuss what the equation y = x<sup>2<\/sup>\/(4p) means. They also use it to find the equation of a parabola with a vertex at the origin and a focus at (0, 0.5).<\/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-l5e7-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='6a8d50576b8d59019620298' value='6a8d50576b8d59019620298'><input type='hidden' id='bg-show-more-text-6a8d50576b8d59019620298' value=' '><input type='hidden' id='bg-show-less-text-6a8d50576b8d59019620298' value=' '><button id='bg-showmore-action-6a8d50576b8d59019620298' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a8d50576b8d59019620298' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Students may have difficulty understanding the role that the parameter, p, plays in the equation y = x<sup>2<\/sup>\/(4p). It may be confusing that the equation represents a family of parabolas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4 By using the equation y = x<sup>2<\/sup>\/(4p)&nbsp; to graph a particular parabola (when p = 0.5), Keoni and Sasha gain insight into how the equation y = x<sup>2<\/sup>\/(4p) can generate different parabolas, all with a vertex at the origin, by changing the p-value. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a8d50576b96a4099383075' value='6a8d50576b96a4099383075'><input type='hidden' id='bg-show-more-text-6a8d50576b96a4099383075' value=' '><input type='hidden' id='bg-show-less-text-6a8d50576b96a4099383075' value=' '><button id='bg-showmore-action-6a8d50576b96a4099383075' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a8d50576b96a4099383075' ><\/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>0:59<\/strong>]. List everything you know about the parabola with a vertex at the origin and a focus 1\/2 unit above the origin.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>6:35<\/strong>]. List everything you know about the equation y=x<sup>2<\/sup>\/(4p). <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a8d50576b9d36001495797' value='6a8d50576b9d36001495797'><input type='hidden' id='bg-show-more-text-6a8d50576b9d36001495797' value=' '><input type='hidden' id='bg-show-less-text-6a8d50576b9d36001495797' value=' '><button id='bg-showmore-action-6a8d50576b9d36001495797' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a8d50576b9d36001495797' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Invite students to engage in a pair-share activity as they respond to each focus question:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. With your partner, make a list of what you know about the parabola with a vertex at the origin and a focus 1\/2 unit above the origin. Prepare your answers to share with the whole class.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. With your partner, make a list of what you know about the equation y = x<sup>2<\/sup>\/(4p). Prepare your answers to share with the whole class. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a8d50576ba3b4022108835' value='6a8d50576ba3b4022108835'><input type='hidden' id='bg-show-more-text-6a8d50576ba3b4022108835' value=' '><input type='hidden' id='bg-show-less-text-6a8d50576ba3b4022108835' value=' '><button id='bg-showmore-action-6a8d50576ba3b4022108835' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a8d50576ba3b4022108835' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Consider the graph below.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Consider the two parabolas graphed below. Use the equations for each graph and geometric reasoning to label the coordinates of 4 points on each graph.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Compare the points and coordinates across the two parabolas. List any patterns that you notice.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em><strong>Graph of parabolas is missing\u2014in the original document<\/strong><\/em>. <\/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-6-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-6-teachers\/parabolas-lesson-6-episode-1-teachers\/\">Lesson 6 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\" 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. Sasha and Keoni discuss what the equation y = x2\/(4p) means. They also use it to find the equation of a parabola with a vertex at the origin and a focus at [&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-1218","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1218","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=1218"}],"version-history":[{"count":13,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1218\/revisions"}],"predecessor-version":[{"id":8350,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1218\/revisions\/8350"}],"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=1218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}