{"id":1064,"date":"2020-06-08T11:10:00","date_gmt":"2020-06-08T18:10:00","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1064"},"modified":"2025-08-04T11:43:17","modified_gmt":"2025-08-04T18:43:17","slug":"parabolas-lesson-3-episode-5-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-5-teachers\/","title":{"rendered":"Parabolas Lesson 3 Episode 5 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Reflecting<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n\n<div class=\"youtube-player\" data-id=\"-Cue0Vod8ko\"><\/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=\"x0s4MbpjKwA\"><\/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><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-student-docs\/parabolas_l3e5_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>Sasha and Keoni share ideas about the usefulness of the equation<br>x = \u221a(4y), which they derived in Episode 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-l3e5-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='69e1a249af2b11067639285' value='69e1a249af2b11067639285'><input type='hidden' id='bg-show-more-text-69e1a249af2b11067639285' value=' '><input type='hidden' id='bg-show-less-text-69e1a249af2b11067639285' value=' '><button id='bg-showmore-action-69e1a249af2b11067639285' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e1a249af2b11067639285' ><\/p>\n\n\n\n<p>Students might not notice the connection between the general equation and the earlier procedure they used several times to solve for the x value for a known y value of a point on the parabola.<\/p>\n\n\n\n<p>When asked to find the x value of when y is 50, Keoni writes down the equation that represents the Pythagorean theorem. Sasha jokes with him that he likes the \u201clong way.\u201d Sasha is prompted to clarify what she means by the long way. Together they solve for x using both procedures, the Pythagorean theorem equation and the general equation, x = \u221a(4y). They notice that they get the same answers. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69e1a249af3300037547786' value='69e1a249af3300037547786'><input type='hidden' id='bg-show-more-text-69e1a249af3300037547786' value=' '><input type='hidden' id='bg-show-less-text-69e1a249af3300037547786' value=' '><button id='bg-showmore-action-69e1a249af3300037547786' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e1a249af3300037547786' ><\/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 video at <strong>2:27<\/strong>]. Sasha says \u201cyou just like the long way.\u201d What does she mean by the long way?<\/p>\n\n\n\n<p>2. [Pause video at <strong>4:26<\/strong>].What do you think? Will Sasha\u2019s method get the same answer? Why or why not? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69e1a249af3752045692513' value='69e1a249af3752045692513'><input type='hidden' id='bg-show-more-text-69e1a249af3752045692513' value=' '><input type='hidden' id='bg-show-less-text-69e1a249af3752045692513' value=' '><button id='bg-showmore-action-69e1a249af3752045692513' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e1a249af3752045692513' ><\/p>\n\n\n\n<p>Build on students\u2019 responses to the question: \u201cwhat does Sasha mean by the long way?\u201d by asking:<\/p>\n\n\n\n<p>1. Kara, can you repeat what Dan said about the long way?<\/p>\n\n\n\n<p>2. How about someone else? What do you think about what Keoni has written? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Math Extensions <input type='hidden' bg_collapse_expand='69e1a249af3a42027714861' value='69e1a249af3a42027714861'><input type='hidden' id='bg-show-more-text-69e1a249af3a42027714861' value=' '><input type='hidden' id='bg-show-less-text-69e1a249af3a42027714861' value=' '><button id='bg-showmore-action-69e1a249af3a42027714861' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e1a249af3a42027714861' ><\/p>\n\n\n\n<p>The points on the circle below can be represented by equations. There are two possible representations in the table below.<\/p>\n\n\n\n<p>\u200b<img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"157\" class=\"wp-image-1072\" style=\"width: 300px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l3-e5a-teachers.jpg\" alt=\"Table for When y is 3\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l3-e5a-teachers.jpg 354w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l3-e5a-teachers-300x133.jpg 300w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><\/p>\n\n\n\n<p>1. What is the difference between the two representations? Solve for the x-value when the y-value is 1.5.<\/p>\n\n\n\n<p>2. What is meant by the symbol \u00b1? How does it relate to the shape of the circle?<\/p>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" width=\"268\" height=\"243\" class=\"wp-image-1036\" style=\"width: 268px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l3-e1-teachers.jpg\" alt=\"Parabolas L3 E1 Math Extension circle\"><\/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-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-4-teachers\/parabolas-lesson-4-episode-1-teachers\/\">Lesson 4 Episode 1<\/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>Reflecting 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 share ideas about the usefulness of the equationx = \u221a(4y), which they derived in Episode 2. 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-1064","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1064","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=1064"}],"version-history":[{"count":12,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1064\/revisions"}],"predecessor-version":[{"id":8335,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1064\/revisions\/8335"}],"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=1064"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}