{"id":1489,"date":"2020-06-19T09:44:29","date_gmt":"2020-06-19T16:44:29","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1489"},"modified":"2020-08-03T10:56:18","modified_gmt":"2020-08-03T17:56:18","slug":"parabolas-lesson-9-episode-3-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-9-teachers\/parabolas-lesson-9-episode-3-teachers\/","title":{"rendered":"Parabolas Lesson 9 Episode 3 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Making Sense<\/h3>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Lesson 9 Episode 3\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/RhYXAX9fRcQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-student-docs\/parabolas_l9e3_student-worksheet.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\/myQ4WTtx\" 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><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Keoni and Sasha use the applet to explore the graphs of parabolas with a vertex at (9, 13) and an unknown p-value. Sasha and Keoni determine how to represent the coordinates of the focus and the equation of the directrix when p can take on any value.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-background has-vivid-cyan-blue-background-color has-vivid-cyan-blue-color\"\/>\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-l9e3-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='6a406ef3b1e5b2036543880' value='6a406ef3b1e5b2036543880'><input type='hidden' id='bg-show-more-text-6a406ef3b1e5b2036543880' value=' '><input type='hidden' id='bg-show-less-text-6a406ef3b1e5b2036543880' value=' '><button id='bg-showmore-action-6a406ef3b1e5b2036543880' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a406ef3b1e5b2036543880' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni struggle with the equation for the directrix when the p-value is unknown <strong>[4:00-4:27]<\/strong>. Keoni thinks it\u2019s y=p. Both Sasha and Keoni seem unsure about how to determine the equation. Part of the difficulty is that this is first time they need to use the variable p in the equation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a4 It helps them resolve the difficulty by identifying every distance that they do know.&nbsp; Adding the line y=13 to the graph also supports their reasoning. Testing a conjectured equation for the directrix with a previous result helps them resolve their uncertainty <strong>[6:23]<\/strong>. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a406ef3b1f003082543951' value='6a406ef3b1f003082543951'><input type='hidden' id='bg-show-more-text-6a406ef3b1f003082543951' value=' '><input type='hidden' id='bg-show-less-text-6a406ef3b1f003082543951' value=' '><button id='bg-showmore-action-6a406ef3b1f003082543951' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a406ef3b1f003082543951' ><\/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 the video at <strong>1:30<\/strong>]. Can the p-value be more than 6? What will happen?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause the video at <strong>7:43<\/strong>]. What is your conjecture for the coordinates of the focus? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a406ef3b1f8c3087681674' value='6a406ef3b1f8c3087681674'><input type='hidden' id='bg-show-more-text-6a406ef3b1f8c3087681674' value=' '><input type='hidden' id='bg-show-less-text-6a406ef3b1f8c3087681674' value=' '><button id='bg-showmore-action-6a406ef3b1f8c3087681674' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a406ef3b1f8c3087681674' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Provide opportunities to revoice the mathematical ideas of others:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Sasha and Keoni noticed that they could represent several distances. What are those distances? Come up here to show us.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Revoice what Sasha and Keoni said about why there is a \u20137 in the equation instead of a +7.&nbsp; How about someone else? Revoice what Sasha and Keoni and saying. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a406ef3b1fee8020009797' value='6a406ef3b1fee8020009797'><input type='hidden' id='bg-show-more-text-6a406ef3b1fee8020009797' value=' '><input type='hidden' id='bg-show-less-text-6a406ef3b1fee8020009797' value=' '><button id='bg-showmore-action-6a406ef3b1fee8020009797' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a406ef3b1fee8020009797' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Consider a parabola of any value of p with a vertex at (\u20139, 13). Find the coordinates and the equation of the directrix for this parabola. Explain your thinking.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Consider a parabola of any value of p with a vertex at (9, \u201313). Find the coordinates and the equation of the directrix for this parabola. Explain your thinking. <\/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\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-9-teachers\/parabolas-lesson-9-episode-2-teachers\/\">Previous Lesson<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-9-teachers\/parabolas-lesson-9-episode-4-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-9-teachers\/\" style=\"background-color:#2d4059\">Lesson 9<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Making Sense Keoni and Sasha use the applet to explore the graphs of parabolas with a vertex at (9, 13) and an unknown p-value. Sasha and Keoni determine how to represent the coordinates of the focus and the equation of the directrix when p can take on any value. Episode Supports Students\u2019 Conceptual Challenges Focus [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1444,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1489","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1489","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=1489"}],"version-history":[{"count":10,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1489\/revisions"}],"predecessor-version":[{"id":2453,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1489\/revisions\/2453"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1444"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1489"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}