{"id":1413,"date":"2020-06-17T13:27:17","date_gmt":"2020-06-17T20:27:17","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1413"},"modified":"2025-08-04T12:12:54","modified_gmt":"2025-08-04T19:12:54","slug":"parabolas-lesson-8-episode-5-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-8-teachers\/parabolas-lesson-8-episode-5-teachers\/","title":{"rendered":"Parabolas Lesson 8 Episode 5 (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=\"jktf-yEjMHg\"><\/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=\"u39e2gOLv7g\"><\/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_l8e5_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\/GNdneRts\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-484\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/geogebra.jpg\" alt=\"Link to Geogebra applet\"><\/a><a rel=\"noreferrer noopener\" href=\"http:\/\/www.virtualnerd.com\/algebra-2\/polynomials\/operations\/multiply\/trinomial-multiplication\" target=\"_blank\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni now consider how the equation of the parabola will change if the parabola moves up on the coordinate grid. They derive an equation for a parabola with a vertex at (0, 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-l8e5-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='6a1b2dc10fb2a9055784654' value='6a1b2dc10fb2a9055784654'><input type='hidden' id='bg-show-more-text-6a1b2dc10fb2a9055784654' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc10fb2a9055784654' value=' '><button id='bg-showmore-action-6a1b2dc10fb2a9055784654' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc10fb2a9055784654' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha seems unsure of the placement of the directrix <strong>[2:13-2:28]<\/strong>. This is the first time the directrix and focus have not been equidistant from the origin.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4 They resolve the issue by using \u201cspecial points\u201d and the definition of a parabola. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a1b2dc10fbe05028411814' value='6a1b2dc10fbe05028411814'><input type='hidden' id='bg-show-more-text-6a1b2dc10fbe05028411814' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc10fbe05028411814' value=' '><button id='bg-showmore-action-6a1b2dc10fbe05028411814' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc10fbe05028411814' ><\/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>0:51<\/strong>]. What is your prediction for an equation of a parabola where the p-value stays at 3, the h-value stays at 0, and the k-value changes to a value such as 2?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>5:57<\/strong>]. What do you notice about the lengths of the right triangle? How are they like the representations of the lengths of the sides of the triangles when you derived the equations of other parabolas? How are they different? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a1b2dc10fc3b5099923615' value='6a1b2dc10fc3b5099923615'><input type='hidden' id='bg-show-more-text-6a1b2dc10fc3b5099923615' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc10fc3b5099923615' value=' '><button id='bg-showmore-action-6a1b2dc10fc3b5099923615' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc10fc3b5099923615' ><\/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 prediction for the equation of parabola with a p-value of 3 and a vertex at (0, 2). Prepare your answers to share with the whole class.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. With your partner answer Focus Question 2. Where are the differences and similarities coming from? Prepare to share your answers 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='6a1b2dc10fc823084590282' value='6a1b2dc10fc823084590282'><input type='hidden' id='bg-show-more-text-6a1b2dc10fc823084590282' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc10fc823084590282' value=' '><button id='bg-showmore-action-6a1b2dc10fc823084590282' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc10fc823084590282' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Derive an equation for a parabola with its vertex at (0, 5) and a p-value of 3. What do you notice? <\/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-8-teachers\/parabolas-lesson-8-episode-4-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-8-teachers\/parabolas-lesson-8-episode-6-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-8-teachers\/\" style=\"background-color:#2d4059\">Lesson 8<\/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. Sasha and Keoni now consider how the equation of the parabola will change if the parabola moves up on the coordinate grid. They derive an equation for a parabola with a vertex [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1362,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1413","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1413","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=1413"}],"version-history":[{"count":12,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1413\/revisions"}],"predecessor-version":[{"id":8369,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1413\/revisions\/8369"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1362"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}