{"id":924,"date":"2020-06-04T13:19:08","date_gmt":"2020-06-04T20:19:08","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=924"},"modified":"2025-08-04T11:29:41","modified_gmt":"2025-08-04T18:29:41","slug":"parabolas-lesson-1-episode-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-1-teachers\/parabolas-lesson-1-episode-2-teachers\/","title":{"rendered":"Parabolas Lesson 1 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=\"st3JcgnFkes\"><\/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=\"sTELRm2gBXU\"><\/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\/proportions-student-docs\/proportions_l1e2_studentworksheet.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><\/p>\n\n\n\n<p>Keoni and Sasha create three different methods for constructing points on the 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-l1e2-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='69f4c2619d7f92015779232' value='69f4c2619d7f92015779232'><input type='hidden' id='bg-show-more-text-69f4c2619d7f92015779232' value=' '><input type='hidden' id='bg-show-less-text-69f4c2619d7f92015779232' value=' '><button id='bg-showmore-action-69f4c2619d7f92015779232' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2619d7f92015779232' ><\/p>\n\n\n\n<p>1.The phrase \u201cset of points\u201d in the definition of a parabola may be misinterpreted as \u201cpair of points.\u201d After finding their first point on the parabola (the point halfway between the focus and directrix), Keoni places a second point close to the first one to form a \u201cpair\u201d <strong>[2:11]<\/strong>.<\/p>\n\n\n\n<p>Sasha and Keoni test this point using the definition and conclude that it doesn\u2019t work.<\/p>\n\n\n\n<p>2. Students may think that a point on the parabola can also be on the directrix <strong>[8:24]<\/strong>.<\/p>\n\n\n\n<p>Because Keoni is concentrating on points that are 3 inches from the focus, he places a point on the directrix. But he quickly realizes that the point will not satisfy the definition of a parabola because it is not also 3 inches from the directrix.<\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69f4c2619d8f55099158279' value='69f4c2619d8f55099158279'><input type='hidden' id='bg-show-more-text-69f4c2619d8f55099158279' value=' '><input type='hidden' id='bg-show-less-text-69f4c2619d8f55099158279' value=' '><button id='bg-showmore-action-69f4c2619d8f55099158279' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2619d8f55099158279' ><\/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>0:48<\/strong>]. Sasha drew a point that she thinks is on the parabola. Keoni suggests that they test her idea. What would be a way to test the point?<\/p>\n\n\n\n<p>2. [Pause video at <strong>4:16<\/strong>]. Sasha seems to have a question about the point Keoni proposed. Can you restate her question? <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69f4c2619d95c6004774048' value='69f4c2619d95c6004774048'><input type='hidden' id='bg-show-more-text-69f4c2619d95c6004774048' value=' '><input type='hidden' id='bg-show-less-text-69f4c2619d95c6004774048' value=' '><button id='bg-showmore-action-69f4c2619d95c6004774048' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2619d95c6004774048' ><\/p>\n\n\n\n<p>When students are working on the task in class, you can support dialogue as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ask a student to repeat what another student just said, i.e., \u201cAlex, can you share what you heard Lani say?\u201d<br><\/li>\n\n\n\n<li>Ask students to relate their actions to the definition, i.e., \u201cDo your points fit the definition of a parabola?\u201d <\/div><\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">Math Extensions <input type='hidden' bg_collapse_expand='69f4c2619da2f0047091414' value='69f4c2619da2f0047091414'><input type='hidden' id='bg-show-more-text-69f4c2619da2f0047091414' value=' '><input type='hidden' id='bg-show-less-text-69f4c2619da2f0047091414' value=' '><button id='bg-showmore-action-69f4c2619da2f0047091414' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2619da2f0047091414' ><\/p>\n\n\n\n<p>These questions allow students to extend the concepts and terminology from the episode:<\/p>\n\n\n\n<p>1. With a pencil and a ruler, draw two parallel lines. What are the points that are the same distance from the two lines that you drew? Explain your solution. How do you know those points you found are the same distance from the two given lines that you drew?<\/p>\n\n\n\n<p>2. Draw three points on a piece of paper. Find the points that are the same distance from each of the three points. Explain your solution. How do you know those points you found are the same distance from the three given points that you drew? <\/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-1-teachers\/parabolas-lesson-1-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\/parabolas-lesson-1-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\/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\/parabolas-lesson-1-teachers\/\" style=\"background-color:#2d4059\">Lesson 1<\/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 create three different methods for constructing points on the parabola. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue Math Extensions Previous Episode Next Episode<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":572,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-924","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/924","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=924"}],"version-history":[{"count":10,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/924\/revisions"}],"predecessor-version":[{"id":8321,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/924\/revisions\/8321"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/572"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}