{"id":5452,"date":"2024-01-19T14:56:54","date_gmt":"2024-01-19T22:56:54","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5452"},"modified":"2024-01-23T09:36:14","modified_gmt":"2024-01-23T17:36:14","slug":"exponentials-lesson-6-episode-6-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/exponential-functions-unit-teachers\/exponentials-lesson-6-teachers\/exponentials-lesson-6-episode-6-teachers\/","title":{"rendered":"Exponentials Lesson 6 Episode 6 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Reflecting<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n<div class=\"youtube-player\" data-id=\"1CbPXVcvRqw\"><\/div>\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<\/div>\n<div id=\"video_hidden_first\" style=\"display:none\">\n<p>\n<div class=\"youtube-player\" data-id=\"1Dos6jcueAk\"><\/div>\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')\"><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\/2023\/01\/Exponents_L6E6_Student_Worksheet.pdf\"><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 rel=\"noreferrer noopener\" href=\"https:\/\/www.wolframalpha.com\/\" target=\"_blank\"><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>Josh and Arobindo reflect the possible values for y in the equation they created that gives the height of the beanstalk on Day <em>x<\/em>, <em>y<\/em>=1(3<sup><em>x<\/em><\/sup>). <\/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='69f3b022290688002583266' value='69f3b022290688002583266'><input type='hidden' id='bg-show-more-text-69f3b022290688002583266' value=' '><input type='hidden' id='bg-show-less-text-69f3b022290688002583266' value=' '><button id='bg-showmore-action-69f3b022290688002583266' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b022290688002583266' ><\/p>\n\n\n\n<p>This episode reveals some of the difficulties students might have in understanding the range of an exponential function. Initially Josh and Arobindo decided that for the function y =&nbsp;1 \u2022 3<sup>x<\/sup>, y must be greater than or equal to zero&nbsp;<strong>[0:16].<\/strong>&nbsp;However, as they investigated the function through the context of the height of the beanstalk in the days prior to Jack receiving it, they realized that the height, represented by y in the equation, will never be 0&nbsp;<strong>[1:30]<\/strong>.<\/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='69f3b022290f91017271664' value='69f3b022290f91017271664'><input type='hidden' id='bg-show-more-text-69f3b022290f91017271664' value=' '><input type='hidden' id='bg-show-less-text-69f3b022290f91017271664' value=' '><button id='bg-showmore-action-69f3b022290f91017271664' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b022290f91017271664' ><\/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><\/strong><strong>[Pause the video at 0:21]<\/strong>&nbsp;Before listening to Josh and Arobindo\u2019s reasoning about values for y, decide for yourself what kind of values make sense for y.<\/li>\n\n\n\n<li><strong><\/strong><strong>[Pause the video at 0:45]<\/strong>&nbsp;What do you think about Arobindo\u2019s claim that y must be greater than or equal to zero. Do you agree or disagree with that claim? Can y be negative?<\/li>\n\n\n\n<li><strong><\/strong><strong>[Pause the video at 1:33]<\/strong>&nbsp;Arobindo has just finished arguing that \u201cwhen you\u2019re going backwards, you\u2019re dividing by three, so that\u2019s the opposite of multiplying by three.\u201d Can you rephrase what Arobindo has said? What do you think he means by \u201cgoing backwards.\u201d<\/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='69f3b022291a39095202912' value='69f3b022291a39095202912'><input type='hidden' id='bg-show-more-text-69f3b022291a39095202912' value=' '><input type='hidden' id='bg-show-less-text-69f3b022291a39095202912' value=' '><button id='bg-showmore-action-69f3b022291a39095202912' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b022291a39095202912' ><\/p>\n\n\n\n<p>After watching the video, ask your students to talk with one or two other students to summarize the key ideas from the last two videos. There is quite a bit to make sense of, so you may consider prompting each idea, one at a time. These ideas include what types of values make sense for both x and y in an exponential function set in the beanstalk context and the meaning of negative exponents. Afterward, ask them to reflect on their own understanding by telling their peers something they\u2019ve figured out in this lesson and something they are still thinking about or working through.<\/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\/exponential-functions-unit-teachers\/exponentials-lesson-6-teachers\/exponentials-lesson-6-episode-5-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\/exponential-functions-unit-teachers\/exponentials-lesson-7-teachers\/exponentials-lesson-7-episode-1-teachers\/\">Lesson 7 Episode 1<\/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\/exponential-functions-unit-teachers\/\" style=\"background-color:#2d4059\">Exponentials<\/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\/exponential-functions-unit-teachers\/exponentials-lesson-6-teachers\/\" style=\"background-color:#2d4059\">Lesson 6<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Reflecting No captions CaptionsStop the video above first if it is playing. No captions CaptionsStop the video above first if it is playing. Josh and Arobindo reflect the possible values for y in the equation they created that gives the height of the beanstalk on Day x, y=1(3x). Episode Supports Students\u2019 Conceptual Challenges Focus Questions [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":4692,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5452","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5452","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=5452"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5452\/revisions"}],"predecessor-version":[{"id":5613,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5452\/revisions\/5613"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4692"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}