{"id":5455,"date":"2024-01-19T15:02:36","date_gmt":"2024-01-19T23:02:36","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5455"},"modified":"2024-01-23T10:20:30","modified_gmt":"2024-01-23T18:20:30","slug":"exponentials-lesson-7-episode-1-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/exponential-functions-unit-teachers\/exponentials-lesson-7-teachers\/exponentials-lesson-7-episode-1-teachers\/","title":{"rendered":"Exponentials 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<div class=\"youtube-player\" data-id=\"PphzYUo2hLQ\"><\/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=\"fS01zQADgDc\"><\/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_L7E1_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 critique other students\u2019 reasoning about what the height of the beanstalk should be at Day 2.5. They then use a timeline to create their own argument for what the height should be at that time.<\/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='69f596b9860415019458743' value='69f596b9860415019458743'><input type='hidden' id='bg-show-more-text-69f596b9860415019458743' value=' '><input type='hidden' id='bg-show-less-text-69f596b9860415019458743' value=' '><button id='bg-showmore-action-69f596b9860415019458743' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b9860415019458743' ><\/p>\n\n\n\n<p>A fictional student named Denzel exhibits a common challenge students may face in fully understanding exponential functions, which is conflating a growth factor (in this case,\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"54\" class=\"wp-image-5333\" style=\"width: 32px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/sqrt-3.png\" alt=\"\">\u00a0for each half day) with the functional output (in this case, the height of the beanstalk). Instead of using the growth factor and a known height to compute the height on Day 2.5, Denzel says the height on Day 2.5 is equal to the associated growth factor,\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"54\" class=\"wp-image-5333\" style=\"width: 32px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/sqrt-3.png\" alt=\"\">\u00a0<strong>[0:56].<\/strong>\u00a0It would be more productive if he recognized that the height of the beanstalk on Day 2.5 is\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"54\" class=\"wp-image-5333\" style=\"width: 32px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/sqrt-3.png\" alt=\"\">\u00a0<em>times<\/em>\u00a0greater than it is on Day 2.<\/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='69f596b9862286062773454' value='69f596b9862286062773454'><input type='hidden' id='bg-show-more-text-69f596b9862286062773454' value=' '><input type='hidden' id='bg-show-less-text-69f596b9862286062773454' value=' '><button id='bg-showmore-action-69f596b9862286062773454' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b9862286062773454' ><\/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 2:35]<\/strong>\u00a0Consider both Denzel and Isabella\u2019s ideas. Do you agree that height on Day 2.5 will be\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"54\" class=\"wp-image-5333\" style=\"width: 32px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/sqrt-3.png\" alt=\"\">? How does Isabella\u2019s argument contradict that idea? Can you connect your argument to the beanstalk context or to the timeline from the video?<\/li>\n\n\n\n<li><strong>[Pause the video at 3:28]<\/strong>\u00a0Denzel thinks that the height on Day 2.5 is\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"54\" class=\"wp-image-5333\" style=\"width: 32px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/sqrt-3.png\" alt=\"\">. Is there anything productive about Denzel\u2019s thinking? Tell your partner how you could use Denzel\u2019s idea to correctly compute the height of the beanstalk on Day 2.5.<\/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='69f596b9862e32043197621' value='69f596b9862e32043197621'><input type='hidden' id='bg-show-more-text-69f596b9862e32043197621' value=' '><input type='hidden' id='bg-show-less-text-69f596b9862e32043197621' value=' '><button id='bg-showmore-action-69f596b9862e32043197621' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b9862e32043197621' ><\/p>\n\n\n\n<p>Consider pausing the video at\u00a0<strong>[4:42].<\/strong>\u00a0This is a place where students can check in with their own understanding of the conceptual challenge voiced by the fictional student Denzel. Ask your students to discuss the method of multiplying the height on Day 2, which is 9 cm, by\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"54\" class=\"wp-image-5333\" style=\"width: 32px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/sqrt-3.png\" alt=\"\">. Ask them to explain in two different ways why this method results in the correct height of the beanstalk on Day 2.5. Encourage your students to use a timeline (one that they\u2019ve drawn or the one from the video) to support their argument.<\/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-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\/exponential-functions-unit-teachers\/exponentials-lesson-7-teachers\/exponentials-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\/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-7-teachers\/\" style=\"background-color:#2d4059\">Lesson 7<\/a><\/div>\n<\/div>\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. Josh and Arobindo critique other students\u2019 reasoning about what the height of the beanstalk should be at Day 2.5. They then use a timeline to create their own argument for what [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":4697,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5455","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5455","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=5455"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5455\/revisions"}],"predecessor-version":[{"id":5629,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5455\/revisions\/5629"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4697"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5455"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}