{"id":5417,"date":"2024-01-19T14:20:39","date_gmt":"2024-01-19T22:20:39","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5417"},"modified":"2024-01-22T14:13:13","modified_gmt":"2024-01-22T22:13:13","slug":"exponentials-lesson-4-episode-5-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/exponential-functions-unit-teachers\/exponentials-lesson-4-teachers\/exponentials-lesson-4-episode-5-teachers\/","title":{"rendered":"Exponentials Lesson 4 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=\"ryJ7kRqD0F0\"><\/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=\"qbn-aT6TR24\"><\/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_L4E5_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 are given an equation that models the growth of a magical beanstalk. They explain how the beanstalk is growing.<\/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='69dff8bee420a8085578260' value='69dff8bee420a8085578260'><input type='hidden' id='bg-show-more-text-69dff8bee420a8085578260' value=' '><input type='hidden' id='bg-show-less-text-69dff8bee420a8085578260' value=' '><button id='bg-showmore-action-69dff8bee420a8085578260' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69dff8bee420a8085578260' ><\/p>\n\n\n\n<p>Josh and Arobindo seem to be on their way to generalizing how growth rates can be partitioned and composed. For example, in this episode, they draw an arc to show a growth rate of 4<sup>2<\/sup>&nbsp;between Day 0 and Day 2. When prompted, they also draw two smaller arcs to indicate a growth rate of 4 between Day 0 and Day 1 and another growth rate of 4 between Day 1 and Day 2&nbsp;<strong>[5:00].<\/strong>&nbsp;This is one of the key ideas that will be explored for the remainder of this unit, and some students may still be putting this important concept together.<\/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='69dff8bee434f9050401116' value='69dff8bee434f9050401116'><input type='hidden' id='bg-show-more-text-69dff8bee434f9050401116' value=' '><input type='hidden' id='bg-show-less-text-69dff8bee434f9050401116' value=' '><button id='bg-showmore-action-69dff8bee434f9050401116' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69dff8bee434f9050401116' ><\/p>\n\n\n\n<p>For use in a classroom, pause the video and ask this question:\u00a0<\/p>\n\n\n\n<p><strong>[Pause the video at 3:59]<\/strong>&nbsp;Predict what Arobindo and Josh will draw on this new timeline. What relationships might Josh and Arobindo illustrate, and how will they show them? After you make your predictions, resume the video and note similarities and differences between what you predicted and what Arobindo and Josh do.<\/p>\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='69dff8bee43a11050674620' value='69dff8bee43a11050674620'><input type='hidden' id='bg-show-more-text-69dff8bee43a11050674620' value=' '><input type='hidden' id='bg-show-less-text-69dff8bee43a11050674620' value=' '><button id='bg-showmore-action-69dff8bee43a11050674620' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69dff8bee43a11050674620' ><\/p>\n\n\n\n<p>Before viewing the video, ask students to pretend they need to help a classmate who missed the previous lessons. Ask them to come up with a short list of key ideas about the beanstalk context and how to represent how the height of the beanstalk on any given day. Then ask them to use those key ideas to explain how to interpret the new equation y = 3(4<sup>x<\/sup>).\u00a0<\/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-4-teachers\/exponentials-lesson-4-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-4-teachers\/exponentials-lesson-4-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-4-teachers\/\" style=\"background-color:#2d4059\">Lesson 4<\/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 are given an equation that models the growth of a magical beanstalk. They explain how the beanstalk is growing. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":4685,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5417","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5417","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=5417"}],"version-history":[{"count":2,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5417\/revisions"}],"predecessor-version":[{"id":5561,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5417\/revisions\/5561"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4685"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5417"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}