{"id":7452,"date":"2024-07-18T15:49:42","date_gmt":"2024-07-18T22:49:42","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7452"},"modified":"2024-09-19T11:19:56","modified_gmt":"2024-09-19T18:19:56","slug":"trigonometry-lesson-7-episode-2-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-7-teachers\/trigonometry-lesson-7-episode-2-teachers\/","title":{"rendered":"Trigonometry Lesson 7 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=\"o0rc6nHn0dY\"><\/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=\"MGjYyKeDArk\"><\/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\/U4L7E2_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6583\" 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.desmos.com\/scientific\" target=\"_blank\" rel=\"noreferrer noopener\"><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><\/p>\n\n\n\n<p>Claire and Mary use a calculator to find April\u2019s height above the ground when her angle of rotation is 1 radian, 2.5 radians, and when she is at the top of the Ferris wheel.<\/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='69f3b022433d89053516351' value='69f3b022433d89053516351'><input type='hidden' id='bg-show-more-text-69f3b022433d89053516351' value=' '><input type='hidden' id='bg-show-less-text-69f3b022433d89053516351' value=' '><button id='bg-showmore-action-69f3b022433d89053516351' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b022433d89053516351' ><\/p>\n\n\n\n<p>Claire and Mary quickly work through a critical step along the path of understanding trigonometric functions when they write 36&nbsp;\u2022&nbsp;sin(1) to find the height of a stop above the midline&nbsp;<strong>[1:47]<\/strong>.<strong>&nbsp;<\/strong>They seem to understand that the sine function returns values that can be interpreted as portions of a single radius, so multiplying by the radius will yield the correct height. You should not expect your students to quickly or easily grasp this. Thus, consider having a conversation about this with your students to give them opportunities to voice their ideas.<\/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='69f3b022434628029895791' value='69f3b022434628029895791'><input type='hidden' id='bg-show-more-text-69f3b022434628029895791' value=' '><input type='hidden' id='bg-show-less-text-69f3b022434628029895791' value=' '><button id='bg-showmore-action-69f3b022434628029895791' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b022434628029895791' ><\/p>\n\n\n\n<p>For use in a classroom, pause the video and ask these questions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>[Pause the video at 1:38]<\/strong>&nbsp;How would you find the height above the midline for an angle of rotation of 1 radian? How could you use that to find the height above the ground for the same spot along the circle?<\/li>\n\n\n\n<li><strong>[Pause the video at 4:47]<\/strong>&nbsp;Do you agree with Claire that you could subtract sin(1) from 40 to find the height of the first stop, which is below the midline? Why or why not?&nbsp;<\/li>\n<\/ol>\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='69f3b022434ee0010679668' value='69f3b022434ee0010679668'><input type='hidden' id='bg-show-more-text-69f3b022434ee0010679668' value=' '><input type='hidden' id='bg-show-less-text-69f3b022434ee0010679668' value=' '><button id='bg-showmore-action-69f3b022434ee0010679668' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b022434ee0010679668' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>[Pause the video at 0:53]<\/strong>&nbsp;Work with a partner to justify Claire\u2019s claims that the top of the Ferris wheel is 76 ft high, the center is 40 ft high, and the bottom is 4 ft high. Are there any other heights along the Ferris wheel that you know?<\/li>\n\n\n\n<li><strong>[Pause the video at 1:51]<\/strong>&nbsp;Tell your partner why you think Mary and Claire are multiplying sin(1) by 36. What does that result in, in the context of the Ferris wheel?<\/li>\n<\/ol>\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-7-teachers\/trigonometry-lesson-7-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\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-7-teachers\/trigonometry-lesson-7-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 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-7-teachers\/\" style=\"background-color:#2d4059\">Lesson 7<\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>\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. Claire and Mary use a calculator to find April\u2019s height above the ground when her angle of rotation is 1 radian, 2.5 radians, and when she is at the top of the [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":7265,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7452","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7452","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=7452"}],"version-history":[{"count":6,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7452\/revisions"}],"predecessor-version":[{"id":8091,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7452\/revisions\/8091"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7265"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=7452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}