{"id":5357,"date":"2024-01-19T12:56:53","date_gmt":"2024-01-19T20:56:53","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5357"},"modified":"2024-01-22T11:29:21","modified_gmt":"2024-01-22T19:29:21","slug":"exponentials-lesson-1-episode-1-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/exponential-functions-unit-teachers\/exponentials-lesson-1-teachers\/exponentials-lesson-1-episode-1-teachers\/","title":{"rendered":"Exponentials Lesson 1 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=\"RS9TXhMG-2Q\"><\/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=\"ScG4QG8Wv9s\"><\/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 class=\"wp-block-paragraph\"><a rel=\"noreferrer noopener\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2023\/01\/Exponents_L1E1_Student_Worksheet.pdf\" target=\"_blank\"><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.desmos.com\/scientific\" target=\"_blank\" rel=\"noreferrer noopener\"><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 class=\"wp-block-paragraph\">Josh and Arobindo explore the growth of a beanstalk whose height quadruples each day. They create drawings that show the growth of the beanstalk over several days.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">ET and Haleemah make sense of a swimming pool context and create a method for finding the number of tiles in the border of the pool.&nbsp;&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='6a158db54a8380006710032' value='6a158db54a8380006710032'><input type='hidden' id='bg-show-more-text-6a158db54a8380006710032' value=' '><input type='hidden' id='bg-show-less-text-6a158db54a8380006710032' value=' '><button id='bg-showmore-action-6a158db54a8380006710032' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a158db54a8380006710032' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Drawing the beanstalk&#8217;s growth posed a challenge in terms of interpreting and accurately representing the quadrupling pattern visually. Initially, Josh and Arobindo drew lines to represent the beanstalk at different days, but did not attend to the relationship between the heights across successive drawings&nbsp;<strong>[1:24]<\/strong>.&nbsp;<\/li>\n\n\n\n<li>In asking Arobindo and Josh to label each beanstalk with a corresponding day, the students were challenged to quantify\u00a0<em>days<\/em>\u00a0as a measure of time from when the beanstalk was first planted\u00a0<strong>[3:35].<\/strong>\u00a0Understanding the significance of counting days from the moment the beanstalk was planted, required clarity in quantifying time not as a just a label, but as a measure of how much time has passed.<\/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\">Focus Questions <input type='hidden' bg_collapse_expand='6a158db54a8e25057003985' value='6a158db54a8e25057003985'><input type='hidden' id='bg-show-more-text-6a158db54a8e25057003985' value=' '><input type='hidden' id='bg-show-less-text-6a158db54a8e25057003985' value=' '><button id='bg-showmore-action-6a158db54a8e25057003985' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a158db54a8e25057003985' ><\/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 1:58 and\/or 5:24]<\/strong>&nbsp;How do Josh and Arobindo visually represent the quadrupling growth of the beanstalk in their drawings? What elements in their drawings signify the increase in height each day?<\/li>\n\n\n\n<li><strong>[Pause the video at 4:07]&nbsp;<\/strong>Arobindo described two different ways to label the days. Why might you label the first day as Day 1? Why might you label the first day as Day 0? How does the labeling of the days impact your understanding of time in the context of the problem?<\/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='6a158db54a9462009056644' value='6a158db54a9462009056644'><input type='hidden' id='bg-show-more-text-6a158db54a9462009056644' value=' '><input type='hidden' id='bg-show-less-text-6a158db54a9462009056644' value=' '><button id='bg-showmore-action-6a158db54a9462009056644' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a158db54a9462009056644' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> Consider asking students to make their own drawings (either before or after watching Josh and Arobindo make theirs). As they do, encourage them to explain to a partner, and later to the class, how they are linking elements of their visual representation to the contextual representation of the story of the beanstalk.<\/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\"><\/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-1-teachers\/exponentials-lesson-1-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-1-teachers\/\" style=\"background-color:#2d4059\">Lesson 1<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\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. Josh and Arobindo explore the growth of a beanstalk whose height quadruples each day. They create drawings that show the growth of the beanstalk over several days.&nbsp; ET and Haleemah make [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":4665,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5357","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5357","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=5357"}],"version-history":[{"count":6,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5357\/revisions"}],"predecessor-version":[{"id":5520,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5357\/revisions\/5520"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4665"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}