{"id":7369,"date":"2024-07-18T14:21:52","date_gmt":"2024-07-18T21:21:52","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7369"},"modified":"2024-09-19T11:06:35","modified_gmt":"2024-09-19T18:06:35","slug":"trigonometry-lesson-4-episode-1-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/trigonometric-concepts-unit-teachers\/trigonometry-lesson-4-teachers\/trigonometry-lesson-4-episode-1-teachers\/","title":{"rendered":"Trigonometry Lesson 4 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=\"XpTI6egLUOs\"><\/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=\"AXWTQhTXw-4\"><\/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\/U4L4E1_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6598\" 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 class=\"wp-block-paragraph\">The students investigate the radian as a unit of measure. They start by estimating the measure of two angles in radians.&nbsp;<\/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='6a142f43d6f878073418064' value='6a142f43d6f878073418064'><input type='hidden' id='bg-show-more-text-6a142f43d6f878073418064' value=' '><input type='hidden' id='bg-show-less-text-6a142f43d6f878073418064' value=' '><button id='bg-showmore-action-6a142f43d6f878073418064' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a142f43d6f878073418064' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Claire\u2019s initial method for estimating radians is to create a radian protractor using circular patty paper. This is an effective tool for the task, but Claire decides it won\u2019t work&nbsp;<strong>[3:00]<\/strong>. She thinks that her method won\u2019t work since the circular patty paper is larger than the circle the arc is part of. She claims that they won\u2019t be \u201cequal radians\u201d because they are working with larger and smaller circles. However, radians scale proportionally according to the size of the radius\/circle, and her method would work, as Mary eventually points out.<\/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='6a142f43d70892059676072' value='6a142f43d70892059676072'><input type='hidden' id='bg-show-more-text-6a142f43d70892059676072' value=' '><input type='hidden' id='bg-show-less-text-6a142f43d70892059676072' value=' '><button id='bg-showmore-action-6a142f43d70892059676072' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a142f43d70892059676072' ><\/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 0:40]&nbsp;<\/strong>Before hearing ideas from Mary and Claire, decide for yourself how you would determine about how many radians each angle is for the given arcs. What tools or methods would you use? How would you check your work?<\/li>\n\n\n\n<li><strong>[Pause the video at 7:39]&nbsp;<\/strong>What do you think about the claim made by Mary (and later echoed by Claire) that every radian has the same angle measure? What would you say to someone who claims that since radians are based on the radius of a circle, different circles would produce radians of different sizes?<\/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='6a142f43d712c6017322924' value='6a142f43d712c6017322924'><input type='hidden' id='bg-show-more-text-6a142f43d712c6017322924' value=' '><input type='hidden' id='bg-show-less-text-6a142f43d712c6017322924' value=' '><button id='bg-showmore-action-6a142f43d712c6017322924' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a142f43d712c6017322924' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>[Pause the video at 1:49]&nbsp;<\/strong>Talk with a partner and discuss Mary\u2019s method for finding the radian measure of the given arcs. What purpose did the pipe cleaners serve? Why is she measuring the arc when she is finding an angle measure? How does her method compare with yours or your neighbors?<\/li>\n\n\n\n<li><strong>[Pause the video at 4:09]&nbsp;<\/strong>What do you think: When measuring in radians, does the size of the protractor matter? Talk with a partner to share your ideas.<\/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-3-teachers\/trigonometry-lesson-3-episode-7-teachers\/\">Lesson 3 EPisode 7<\/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-4-teachers\/trigonometry-lesson-4-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-4-teachers\/\" style=\"background-color:#2d4059\">Lesson 4<\/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 investigate the radian as a unit of measure. They start by estimating the measure of two angles in radians.&nbsp; Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":7256,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7369","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7369","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=7369"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7369\/revisions"}],"predecessor-version":[{"id":8075,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7369\/revisions\/8075"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7256"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=7369"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}