{"id":1582,"date":"2020-06-22T15:29:56","date_gmt":"2020-06-22T22:29:56","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1582"},"modified":"2020-09-25T14:28:37","modified_gmt":"2020-09-25T21:28:37","slug":"parabolas-lesson-10-episode-5-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-5-teachers\/","title":{"rendered":"Parabolas Lesson 10 Episode 5 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Exploring<\/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 10 Episode 5\" width=\"580\" height=\"326\" src=\"https:\/\/www.youtube.com\/embed\/plmwhSuu9Ig?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><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-student-docs\/parabolas_l10_e5-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 href=\"https:\/\/www.youtube.com\/watch?v=fmLM8xt-YIg\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"46\" class=\"wp-image-483\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/more_info.jpg\" alt=\"Link to more information\"><\/a><\/p>\n\n\n\n<p>Sasha and Keoni examine yet another equation of a parabola that is not in vertex form, y = x<sup>2<\/sup> \u2013 4x + 5. They start out by seeking a method to re-express the equation in vertex form.<\/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-l10e5-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\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='69d45f7199cbc1063889878' value='69d45f7199cbc1063889878'><input type='hidden' id='bg-show-more-text-69d45f7199cbc1063889878' value=' '><input type='hidden' id='bg-show-less-text-69d45f7199cbc1063889878' value=' '><button id='bg-showmore-action-69d45f7199cbc1063889878' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69d45f7199cbc1063889878' ><\/p>\n\n\n\n<p>Re-expressing this equation in vertex form is challenging. Many students have experiences re-expressing quadratic expressions in factored form. Keoni writes (x \u2013 5)(x + 1).&nbsp; While this is true, it does not support their problem solving goal.<\/p>\n\n\n\n<p>\u27a4 After looking for geometric information, Keoni erases his factored representation. Sasha and Keoni keep working to find a way to re-express the equation in vertex form. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69d45f7199dc43058060062' value='69d45f7199dc43058060062'><input type='hidden' id='bg-show-more-text-69d45f7199dc43058060062' value=' '><input type='hidden' id='bg-show-less-text-69d45f7199dc43058060062' value=' '><button id='bg-showmore-action-69d45f7199dc43058060062' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69d45f7199dc43058060062' ><\/p>\n\n\n\n<p>For use in a classroom, pause the video and ask these questions:<\/p>\n\n\n\n<p>1. [Pause the video at <strong>1:38<\/strong>].&nbsp; Why did Keoni erase (x \u2013 5)(x + 1)? What\u2019s wrong?<\/p>\n\n\n\n<p>2. [Pause the video at<strong> 3:00<\/strong>]. What do think of Sasha\u2019s expression x(x \u2013 4) + 5? Is it correct? Does it help? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69d45f7199e171042943264' value='69d45f7199e171042943264'><input type='hidden' id='bg-show-more-text-69d45f7199e171042943264' value=' '><input type='hidden' id='bg-show-less-text-69d45f7199e171042943264' value=' '><button id='bg-showmore-action-69d45f7199e171042943264' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69d45f7199e171042943264' ><\/p>\n\n\n\n<p>Invite students to reflect on problem solving as a whole class. Elicit multiple answers from the class:<\/p>\n\n\n\n<p>1. At <strong>2:23<\/strong>, Keoni says \u201clet\u2019s not give up.\u201d What do you do when you get stuck?<\/p>\n\n\n\n<p>2. It seems that Sasha and Keoni make progress when the teacher asks how the equation y = x<sup>2<\/sup> \u2013 4x + 5 is different from y = x<sup>2<\/sup> \u2013 4x + 4.&nbsp; How does that question help them? How can they check that y = x<sup>2<\/sup> \u2013 4x + 5 is the same as y = (x \u2013 2)<sup>2<\/sup> + 1? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Math Extensions <input type='hidden' bg_collapse_expand='69d45f7199e594010536565' value='69d45f7199e594010536565'><input type='hidden' id='bg-show-more-text-69d45f7199e594010536565' value=' '><input type='hidden' id='bg-show-less-text-69d45f7199e594010536565' value=' '><button id='bg-showmore-action-69d45f7199e594010536565' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69d45f7199e594010536565' ><\/p>\n\n\n\n<p>1. Rewrite the equation y = x<sup>2<\/sup> \u2013 4x + 7 in vertex form. How do you know the two equations are equivalent?<\/p>\n\n\n\n<p>2. Rewrite the equation y = x<sup>2<\/sup> \u2013 4x + 3 in vertex form. How do you know the two equations are equivalent? <\/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-10-teachers\/parabolas-lesson-10-episode-4-teachers\/\">Previous 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-10-teachers\/\" style=\"background-color:#2d4059\">Lesson 10<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Exploring Sasha and Keoni examine yet another equation of a parabola that is not in vertex form, y = x2 \u2013 4x + 5. They start out by seeking a method to re-express the equation in vertex form. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue Math Extensions<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1538,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1582","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1582","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=1582"}],"version-history":[{"count":10,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1582\/revisions"}],"predecessor-version":[{"id":2631,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1582\/revisions\/2631"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1538"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1582"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}