{"id":5450,"date":"2024-01-19T14:54:55","date_gmt":"2024-01-19T22:54:55","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5450"},"modified":"2024-01-22T17:28:53","modified_gmt":"2024-01-23T01:28:53","slug":"exponentials-lesson-6-episode-5-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-5-teachers\/","title":{"rendered":"Exponentials Lesson 6 Episode 5 (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=\"0giCOusFATY\"><\/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=\"cfXMQjmzQ30\"><\/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_L6E5_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>The students reflect on the values they can plug into 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='69f3b04529dba7098888099' value='69f3b04529dba7098888099'><input type='hidden' id='bg-show-more-text-69f3b04529dba7098888099' value=' '><input type='hidden' id='bg-show-less-text-69f3b04529dba7098888099' value=' '><button id='bg-showmore-action-69f3b04529dba7098888099' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b04529dba7098888099' ><\/p>\n\n\n\n<p>In this episode, Josh and Arobindo are asked to consider if it makes sense to let x be a negative number in the equation y =\u00a01 \u2022 3<sup>x<\/sup>.\u00a0Initially, the pair seem to believe that it would not make sense\u00a0<strong>[0:16]<\/strong>. Over the course of the episode, they shift their thinking to making sense of a negative exponent as relating to the number of days\u00a0<em>before<\/em>\u00a0Jack was given the beanstalk. Notice how the contextual representation of a growing beanstalk provides opportunities for Josh and Arobindo to make sense of the mathematics, and ultimately helps them make sense of negative exponents.<\/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='69f3b04529e8a2028334775' value='69f3b04529e8a2028334775'><input type='hidden' id='bg-show-more-text-69f3b04529e8a2028334775' value=' '><input type='hidden' id='bg-show-less-text-69f3b04529e8a2028334775' value=' '><button id='bg-showmore-action-69f3b04529e8a2028334775' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b04529e8a2028334775' ><\/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 0:16]<\/strong>\u00a0<em>The supporting dialogue prompt at the end of Lesson 4 asked students to consider the different kinds of values that x could be in an exponential equation. Consider using the following focus question to bring students\u2019 attention back to this important idea:<\/em><br><br>What numbers can we \u201cplug in\u201d to x in the equation y =\u00a01 \u2022 3<sup>x<\/sup>?<br><\/li>\n\n\n\n<li><strong><\/strong><strong>[Pause the video at 0:45]<\/strong>&nbsp;What does it mean to use a negative number in place of x in the equation y =&nbsp;1 \u2022 3<sup>x<\/sup>? Remember that Josh and Arobindo initially said you couldn\u2019t use negative numbers, but then they changed their minds to say it would be weird and perhaps a fraction. Discuss with a partner what Arobindo and Josh might mean by those claims.<\/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='69f3b0452a0567028259084' value='69f3b0452a0567028259084'><input type='hidden' id='bg-show-more-text-69f3b0452a0567028259084' value=' '><input type='hidden' id='bg-show-less-text-69f3b0452a0567028259084' value=' '><button id='bg-showmore-action-69f3b0452a0567028259084' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b0452a0567028259084' ><\/p>\n\n\n\n<p>The students initially thought there were restrictions on using negative numbers for x. After watching the video, ask your students to restate Josh and Arobindo\u2019s explanation for making sense of negative exponents. Ask them to consider why it makes sense to think of a negative exponent representing some number of days before Jack got the beanstalk. Ask them to discuss why it makes sense for the expression\u00a03<sup>-1<\/sup>\u00a0to equal 1\/3. Encourage them to discuss these ideas through the lens of the context, rather than using or making up any rules about negative exponents.<\/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-4-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-6-teachers\/exponentials-lesson-6-episode-6-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\/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. The students reflect on the values they can plug into 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-5450","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5450","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=5450"}],"version-history":[{"count":2,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5450\/revisions"}],"predecessor-version":[{"id":5595,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5450\/revisions\/5595"}],"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=5450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}