{"id":1040,"date":"2020-06-08T09:46:31","date_gmt":"2020-06-08T16:46:31","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1040"},"modified":"2025-08-04T11:39:32","modified_gmt":"2025-08-04T18:39:32","slug":"parabolas-lesson-3-episode-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-3-teachers\/parabolas-lesson-3-episode-2-teachers\/","title":{"rendered":"Parabolas Lesson 3 Episode 2 (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=\"aE4pCkKOHyE\"><\/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=\"p3uOznnxLoM\"><\/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_l3e2_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:\/\/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\">Keoni and Sasha develop an equation that relates the x-value to the y-value for a general point on a particular parabola.<\/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-l3e2-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='6a3bf96491a6b3093103668' value='6a3bf96491a6b3093103668'><input type='hidden' id='bg-show-more-text-6a3bf96491a6b3093103668' value=' '><input type='hidden' id='bg-show-less-text-6a3bf96491a6b3093103668' value=' '><button id='bg-showmore-action-6a3bf96491a6b3093103668' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3bf96491a6b3093103668' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Students might wonder how to interpret more than one symbol in a general equation. Students are often asked to isolate a variable on one side of the equals sign with a number on the other side, e.g., they \u201csolve for x\u201d by finding a numerical value for x. Having it make sense that the symbols are representing a general point in the parabola is challenging.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Keoni protests \u201cbut there are two variables\u201d when Sasha writes (y\u20131)<sup>2<\/sup> + b<sup>2<\/sup>&nbsp; = (y+1)<sup>2<\/sup> <strong>[1:11-1:34]<\/strong>. By going back to work through a specific example 6<sup>2<\/sup> + b<sup>2<\/sup> =&nbsp; 8<sup>2<\/sup>, Sasha and Keoni identify the method to solve for b in the general case <strong>[1:47-4:50]<\/strong>. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a3bf96491b430028855179' value='6a3bf96491b430028855179'><input type='hidden' id='bg-show-more-text-6a3bf96491b430028855179' value=' '><input type='hidden' id='bg-show-less-text-6a3bf96491b430028855179' value=' '><button id='bg-showmore-action-6a3bf96491b430028855179' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3bf96491b430028855179' ><\/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>1:34<\/strong>]. What problem are Sasha and Keoni trying to solve?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>2:44<\/strong>]. Sasha and Keoni are working to solve for b. Work ahead from here. Then we will compare our work with theirs. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a3bf96491ba20052342176' value='6a3bf96491ba20052342176'><input type='hidden' id='bg-show-more-text-6a3bf96491ba20052342176' value=' '><input type='hidden' id='bg-show-less-text-6a3bf96491ba20052342176' value=' '><button id='bg-showmore-action-6a3bf96491ba20052342176' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3bf96491ba20052342176' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Invite students to engage in revoicing. Place a blank student worksheet under a document camera.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Can someone come up to the graph to draw and label the right triangle that Sasha and Keoni used in this problem?<br><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Ask a student to revoice how a fellow student determined the side lengths. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a3bf96491beb5062194624' value='6a3bf96491beb5062194624'><input type='hidden' id='bg-show-more-text-6a3bf96491beb5062194624' value=' '><input type='hidden' id='bg-show-less-text-6a3bf96491beb5062194624' value=' '><button id='bg-showmore-action-6a3bf96491beb5062194624' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3bf96491beb5062194624' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Use the Pythagorean theorem to represent the lengths of the right triangles described below.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. A right triangle where one leg is half the length of the other leg.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. A right triangle where the two legs are the same length. <\/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-3-teachers\/parabolas-lesson-3-episode-1-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-3-teachers\/parabolas-lesson-3-episode-3-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-3-teachers\/\" style=\"background-color:#2d4059\">Lesson 3<\/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. Keoni and Sasha develop an equation that relates the x-value to the y-value for a general point on a particular parabola. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue Math Extensions<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1015,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1040","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1040","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=1040"}],"version-history":[{"count":12,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1040\/revisions"}],"predecessor-version":[{"id":8332,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1040\/revisions\/8332"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1015"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1040"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}