{"id":7394,"date":"2024-07-18T14:57:09","date_gmt":"2024-07-18T21:57:09","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7394"},"modified":"2024-09-19T11:10:16","modified_gmt":"2024-09-19T18:10:16","slug":"trigonometry-lesson-5-episode-1-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-5-teachers\/trigonometry-lesson-5-episode-1-teachers\/","title":{"rendered":"Trigonometry Lesson 5 Episode 1 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Making Sense<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n\n<div class=\"youtube-player\" data-id=\"DFzKHQW9bSo\"><\/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=\"kDZH94sYr-Y\"><\/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\/2024\/07\/U4L5E1_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6594\" 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.geogebra.org\/m\/hubzqctb\"><\/a><\/p>\n\n\n\n<p>The students get a feel for how the height above a circular midline changes as they trace their fingers along a circular path. They think about when their height changes quickly and when it changes slowly.<\/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 <\/h3>\n\n\n\n<p class=\"has-medium-font-size\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='69e21b07b95c94068644485' value='69e21b07b95c94068644485'><input type='hidden' id='bg-show-more-text-69e21b07b95c94068644485' value=' '><input type='hidden' id='bg-show-less-text-69e21b07b95c94068644485' value=' '><button id='bg-showmore-action-69e21b07b95c94068644485' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e21b07b95c94068644485' ><\/p>\n\n\n\n<p>Claire and Mary are asked to describe when the height changes more quickly or more slowly. Initially, they seem to be confused about this question, with Claire interpreting the question as finding steepness and Mary asking for some clarification&nbsp;<strong>[1:44]<\/strong>.<strong>&nbsp;<\/strong>Check in with your students to elicit their ideas about this question, which lays some groundwork for recognizing trigonometric functions as being nonlinear and periodic.<\/p>\n\n\n\n<p><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69e21b07b96c94002818596' value='69e21b07b96c94002818596'><input type='hidden' id='bg-show-more-text-69e21b07b96c94002818596' value=' '><input type='hidden' id='bg-show-less-text-69e21b07b96c94002818596' value=' '><button id='bg-showmore-action-69e21b07b96c94002818596' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e21b07b96c94002818596' ><\/p>\n\n\n\n<p>For use in a classroom, pause the video and ask this question:<\/p>\n\n\n\n<p><strong>[Pause the video at 1:18]&nbsp;<\/strong>Mary and Claire use a hiking analogy to describe the height as they move around the circle. How do you see the height of an object moving along a circular path changing as the angle of rotation changes?<\/p>\n\n\n\n<p><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69e21b07b97123049409241' value='69e21b07b97123049409241'><input type='hidden' id='bg-show-more-text-69e21b07b97123049409241' value=' '><input type='hidden' id='bg-show-less-text-69e21b07b97123049409241' value=' '><button id='bg-showmore-action-69e21b07b97123049409241' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e21b07b97123049409241' ><\/p>\n\n\n\n<p><strong>[Pause the video at 1:44]&nbsp;<\/strong>Tell a partner your ideas about when the height is changing more quickly and more slowly. Be sure to explain your reasoning and connect your ideas to the circle diagram on the screen or on your paper.<\/p>\n\n\n\n<p> <\/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\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-4-teachers\/trigonometry-lesson-4-episode-4-teachers\/\">Lesson 4 EPisode 4<\/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\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-5-teachers\/trigonometry-lesson-5-episode-2-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 wp-element-button\" 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 wp-element-button\" 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 wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/\" style=\"background-color:#2d4059\">Trigonometry<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-5-teachers\/\" style=\"background-color:#2d4059\">Lesson 5<\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Making Sense No captions CaptionsStop the video above first if it is playing. No captions CaptionsStop the video above first if it is playing. The students get a feel for how the height above a circular midline changes as they trace their fingers along a circular path. They think about when their height changes quickly [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":7259,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7394","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7394","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=7394"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7394\/revisions"}],"predecessor-version":[{"id":8079,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7394\/revisions\/8079"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7259"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=7394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}