{"id":7447,"date":"2024-07-18T15:46:19","date_gmt":"2024-07-18T22:46:19","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7447"},"modified":"2024-09-19T11:19:01","modified_gmt":"2024-09-19T18:19:01","slug":"trigonometry-lesson-7-episode-1-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-1-teachers\/","title":{"rendered":"Trigonometry Lesson 7 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=\"4yyB328cl6I\"><\/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=\"ky8RdVXo7tM\"><\/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\/2024\/07\/U4L7E1_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6584\" 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\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The students draw a picture of April\u2019s Ferris wheel and estimate her height at several points on her journey.an object at various stops as it travels along a circular path.<\/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 wp-block-paragraph\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='6a142f458eef57096424911' value='6a142f458eef57096424911'><input type='hidden' id='bg-show-more-text-6a142f458eef57096424911' value=' '><input type='hidden' id='bg-show-less-text-6a142f458eef57096424911' value=' '><button id='bg-showmore-action-6a142f458eef57096424911' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a142f458eef57096424911' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Claire explores whether a point below the midline would be negative or the opposite of a different point they investigated previously. Mary expresses confusion about what exactly they are measuring&nbsp;<strong>[2:45]<\/strong>, wondering if the height should be negative, as Claire seems to suggest, or positive since they are measuring height above ground. This kind of confusion often occurs when students contextualize mathematics. Note how Mary grounds the task back in the context to make sure she knows whether or not they should use negative heights as they had done in the previous lesson when they were discussing height above or below the midline.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a142f458ef9b8063237867' value='6a142f458ef9b8063237867'><input type='hidden' id='bg-show-more-text-6a142f458ef9b8063237867' value=' '><input type='hidden' id='bg-show-less-text-6a142f458ef9b8063237867' value=' '><button id='bg-showmore-action-6a142f458ef9b8063237867' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a142f458ef9b8063237867' ><\/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<ol class=\"wp-block-list\">\n<li><strong>[Pause the video at 0:49]&nbsp;<\/strong>Try this task before watching Mary and Claire. Suppose April is riding a Ferris wheel with a radius of 36 ft, and whose center is 40 ft high. Draw a diagram to represent this context and show April\u2019s height above the ground at various points on the Ferris wheel.<\/li>\n\n\n\n<li><strong>[Pause the video at 3:53]<\/strong>&nbsp;Use the drawing that Claire and Mary made to estimate April\u2019s height at some of the points they have marked in their diagram.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a142f458f0707070976269' value='6a142f458f0707070976269'><input type='hidden' id='bg-show-more-text-6a142f458f0707070976269' value=' '><input type='hidden' id='bg-show-less-text-6a142f458f0707070976269' value=' '><button id='bg-showmore-action-6a142f458f0707070976269' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a142f458f0707070976269' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>[Pause the video at 1:59]<\/strong>&nbsp;Summarize in your own words what Claire and Mary have done and said so far. Talk with a partner to share your ideas. Why did they mark a small section below the circle as 4 ft?<\/li>\n\n\n\n<li><strong>[Pause the video at 2:57]<\/strong>&nbsp;Mary expresses some confusion about whether the height at one point along the circle should be negative or positive. Talk with a partner and decide what you think is correct.<\/li>\n\n\n\n<li><strong>[Pause the video at 6:31]<\/strong>&nbsp;Claire asks Mary if her process for finding the height at the second stop makes sense. Does it make sense to you? Talk with a partner to revoice Claire\u2019s method. Would you change anything? Is there anything that doesn\u2019t make sense?<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"> <\/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-6-teachers\/trigonometry-lesson-6-episode-6-teachers\/\">Lesson 6 EPisode 6<\/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-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-7-teachers\/\" style=\"background-color:#2d4059\">Lesson 7<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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 draw a picture of April\u2019s Ferris wheel and estimate her height at several points on her journey.an object at various stops as it travels along a circular path. Episode [&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-7447","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7447","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=7447"}],"version-history":[{"count":6,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7447\/revisions"}],"predecessor-version":[{"id":8090,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7447\/revisions\/8090"}],"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=7447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}