{"id":978,"date":"2020-06-05T13:22:03","date_gmt":"2020-06-05T20:22:03","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=978"},"modified":"2025-08-04T11:34:31","modified_gmt":"2025-08-04T18:34:31","slug":"parabolas-lesson-2-episode-3-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-2-teachers\/parabolas-lesson-2-episode-3-teachers\/","title":{"rendered":"Parabolas Lesson 2 Episode 3 (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=\"0gAskiH_0kc\"><\/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=\"jSyNeeaQNS4\"><\/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_l2_e3_student-worksheet.pdf\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"46\" class=\"wp-image-486\" style=\"width: 150px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/download_worksheets.jpg\" alt=\"Download Math Task\"><\/a> <a rel=\"noreferrer noopener\" href=\"http:\/\/web2.0calc.com\/\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-485\" style=\"width: 150px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/calculator.jpg\" alt=\"Link to on-line calculator\"><\/a> <a href=\"https:\/\/www.youtube.com\/watch?v=LtkAIQcACqY\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"46\" class=\"wp-image-483\" style=\"width: 150px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/more_info.jpg\" alt=\"Link to more information\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni justify how their three methods for finding points on a parabola satisfy the criteria in the definition of a 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-l2e3-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='6a1b8d80a17799097983959' value='6a1b8d80a17799097983959'><input type='hidden' id='bg-show-more-text-6a1b8d80a17799097983959' value=' '><input type='hidden' id='bg-show-less-text-6a1b8d80a17799097983959' value=' '><button id='bg-showmore-action-6a1b8d80a17799097983959' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b8d80a17799097983959' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Representing an unknown distance on the grid can be challenging. Here the distance from the point on the parabola when y = 5 and the y-axis is unknown <strong>[1:32]<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sasha and Keoni incorrectly label this distance as b<sup>2<\/sup> <strong>[1:37]<\/strong> but correctly treat it as b, which is&nbsp; 4.5 <strong>[2:42]<\/strong>. This inconsistency is addressed later in Lesson 3, Episode 4. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a1b8d80a18445022500730' value='6a1b8d80a18445022500730'><input type='hidden' id='bg-show-more-text-6a1b8d80a18445022500730' value=' '><input type='hidden' id='bg-show-less-text-6a1b8d80a18445022500730' value=' '><button id='bg-showmore-action-6a1b8d80a18445022500730' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b8d80a18445022500730' ><\/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>1:40<\/strong>]. How does Keoni know that the distance from the point on the parabola to the focus is 6?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. [Pause video at <strong>2:50<\/strong>]. Sasha wrote 4.5 above the b<sup>2<\/sup>.&nbsp; What does the 4.5 represent? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a1b8d80a18a15053453678' value='6a1b8d80a18a15053453678'><input type='hidden' id='bg-show-more-text-6a1b8d80a18a15053453678' value=' '><input type='hidden' id='bg-show-less-text-6a1b8d80a18a15053453678' value=' '><button id='bg-showmore-action-6a1b8d80a18a15053453678' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b8d80a18a15053453678' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ask your students to reflect on the usefulness of the Pythagorean theorem by asking:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. Why does the Pythagorean theorem work here?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. How do the lengths of the sides of the triangle help you find the coordinates of the point on the parabola? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Math Extensions <input type='hidden' bg_collapse_expand='6a1b8d80a18e12048116044' value='6a1b8d80a18e12048116044'><input type='hidden' id='bg-show-more-text-6a1b8d80a18e12048116044' value=' '><input type='hidden' id='bg-show-less-text-6a1b8d80a18e12048116044' value=' '><button id='bg-showmore-action-6a1b8d80a18e12048116044' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b8d80a18e12048116044' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1. A circle is the set of points that are equal distance from a fixed point (called the center).&nbsp; The graph below is of a circle with the center at the origin. Can you find the x-value of a point on the circle below when the y-value is 4? Explain your reasoning.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2. Find the x-value of a point on the circle shown below when the y-value is 2. Explain your reasoning.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> <img loading=\"lazy\" decoding=\"async\" width=\"224\" height=\"211\" class=\"wp-image-988\" style=\"width: 224px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/06\/parabolas-l2-e3-teachers.jpg\" alt=\"Parabolas L2 E3 Math extension image\">  <\/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-2-teachers\/parabolas-lesson-2-episode-2-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-2-teachers\/parabolas-lesson-2-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\">Teacher 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-2-teachers\/\" style=\"background-color:#2d4059\">Lesson 2<\/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. Sasha and Keoni justify how their three methods for finding points on a parabola satisfy the criteria in the definition of a parabola. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":947,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-978","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/978","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=978"}],"version-history":[{"count":16,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/978\/revisions"}],"predecessor-version":[{"id":8327,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/978\/revisions\/8327"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/947"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}