{"id":1344,"date":"2020-06-15T10:53:26","date_gmt":"2020-06-15T17:53:26","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1344"},"modified":"2025-08-04T12:08:47","modified_gmt":"2025-08-04T19:08:47","slug":"parabolas-lesson-7-episode-5-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-5-teachers\/","title":{"rendered":"Parabolas Lesson 7 Episode 5 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Making Sense<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n\n<div class=\"youtube-player\" data-id=\"htJxJXT4fcE\"><\/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=\"mgmf8C1X8v4\"><\/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_l7e5_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\"><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 use \u201cthe special points\u201d on the three parabolas to generate another explanation for 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-l7e5-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='6a1bae42eb7e29024140610' value='6a1bae42eb7e29024140610'><input type='hidden' id='bg-show-more-text-6a1bae42eb7e29024140610' value=' '><input type='hidden' id='bg-show-less-text-6a1bae42eb7e29024140610' value=' '><button id='bg-showmore-action-6a1bae42eb7e29024140610' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1bae42eb7e29024140610' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha notices a feature of the special points: the x-value is double the y-value. When asked to explain why that is true, both Keoni and Sasha pause <strong>[1:57]<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4 Keoni returns the definition of the parabola to attend to the distances of the special point from the focus and directrix. Both Sasha and Keoni attend to the features of the coordinate grid as well as to how one assigns coordinates to a point on the parabola. They mark up the coordinate grid to show how the x-value is equivalent to twice the y-value <strong>[3:14-3:26]<\/strong>. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a1bae42eb86f8010782119' value='6a1bae42eb86f8010782119'><input type='hidden' id='bg-show-more-text-6a1bae42eb86f8010782119' value=' '><input type='hidden' id='bg-show-less-text-6a1bae42eb86f8010782119' value=' '><button id='bg-showmore-action-6a1bae42eb86f8010782119' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1bae42eb86f8010782119' ><\/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>2:16<\/strong>]. What is the scale of the coordinate grid? How do you know?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>5:59<\/strong>]. 1. What happens to the special point when the x-value doubles from p = 1 to p= 2? {\/bg_collapse]<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a1bae42eb9037067402550' value='6a1bae42eb9037067402550'><input type='hidden' id='bg-show-more-text-6a1bae42eb9037067402550' value=' '><input type='hidden' id='bg-show-less-text-6a1bae42eb9037067402550' value=' '><button id='bg-showmore-action-6a1bae42eb9037067402550' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1bae42eb9037067402550' ><\/div><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Invite students to engage in a pair-share activity as they respond to each question:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. With your partner, predict the coordinates for the \u201cspecial point\u201d of a parabola for different p-values: p = 2, 4, or 5. How do you know those are the coordinates? Prepare your answers to share with the whole class.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. With your partner, write down your conjecture of what happens to the width of the parabola on the coordinate grid as the p-value increases. Prepare to share your conjecture 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='6a1bae42eb9323069362074' value='6a1bae42eb9323069362074'><input type='hidden' id='bg-show-more-text-6a1bae42eb9323069362074' value=' '><input type='hidden' id='bg-show-less-text-6a1bae42eb9323069362074' value=' '><button id='bg-showmore-action-6a1bae42eb9323069362074' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1bae42eb9323069362074' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Show that the point is on the parabola using both geometric and algebraic reasoning. <\/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-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-7-teachers\/parabolas-lesson-7-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-7-teachers\/\" style=\"background-color:#2d4059\">Lesson 7<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Making Sense 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 \u201cthe special points\u201d on the three parabolas to generate another explanation for why increasing the p-value results in the parabola getting wider on the coordinate grid. Episode [&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-1344","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1344","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=1344"}],"version-history":[{"count":11,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1344\/revisions"}],"predecessor-version":[{"id":8363,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1344\/revisions\/8363"}],"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=1344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}