{"id":5404,"date":"2024-01-19T14:09:34","date_gmt":"2024-01-19T22:09:34","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5404"},"modified":"2024-01-22T13:51:41","modified_gmt":"2024-01-22T21:51:41","slug":"exponentials-lesson-3-episode-4-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/exponential-functions-unit-teachers\/exponentials-lesson-3-teachers\/exponentials-lesson-3-episode-4-teachers\/","title":{"rendered":"Exponentials Lesson 3 Episode 4 (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=\"geZ5dSOlMc4\"><\/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=\"na0yBZI3U_Q\"><\/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 href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2023\/01\/Exponents_L3E3_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.desmos.com\/scientific\" 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 class=\"wp-block-paragraph\">Josh and Arobindo&nbsp;use their timeline to create an expression that represents the height of the beanstalk on Day 100.<\/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='6a147c360bc994004263207' value='6a147c360bc994004263207'><input type='hidden' id='bg-show-more-text-6a147c360bc994004263207' value=' '><input type='hidden' id='bg-show-less-text-6a147c360bc994004263207' value=' '><button id='bg-showmore-action-6a147c360bc994004263207' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a147c360bc994004263207' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The beanstalk story is a contextual representation of the mathematical idea of exponential growth. Josh and Arobindo were asked to create a symbolic representation for this idea by creating an equation that represents the height of the beanstalk on any given day. They do so, but they use descriptive phrases instead of symbols&nbsp;<strong>[2:22]<\/strong>, which illustrates the difficulty students may have transitioning from a contextual representation to a symbolic one. The use of variables and symbols is an important convention for symbolic representations, so push your students to not only use symbols, but also to define them. The teacher models this instructional move in the video.<\/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\">Focus Questions <input type='hidden' bg_collapse_expand='6a147c360bd2e3064538603' value='6a147c360bd2e3064538603'><input type='hidden' id='bg-show-more-text-6a147c360bd2e3064538603' value=' '><input type='hidden' id='bg-show-less-text-6a147c360bd2e3064538603' value=' '><button id='bg-showmore-action-6a147c360bd2e3064538603' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a147c360bd2e3064538603' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For use in a classroom, pause the video and ask this question:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[Pause the video at 1:02]<\/strong>\u00a0What does each component of Josh and Arobindo\u2019s equation represent in the context of the growing beanstalk. What is the significance of the 3? What about the phrase \u201c<em>Day #<\/em>\u201d, and of the phrase \u201c<em>Height of the beanstalk on <\/em><em>Day #<\/em>\u201d?\u00a0<\/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\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a147c360bd938087724405' value='6a147c360bd938087724405'><input type='hidden' id='bg-show-more-text-6a147c360bd938087724405' value=' '><input type='hidden' id='bg-show-less-text-6a147c360bd938087724405' value=' '><button id='bg-showmore-action-6a147c360bd938087724405' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a147c360bd938087724405' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Josh and Arobindo have written a new equation for the height of the beanstalk: 1 \u2022 3<sup>x<\/sup>\u00a0= y\u00a0<strong>[2:22].<\/strong> Encourage your students to argue for why this equation will provide the height of the beanstalk on any given day. Arobindo provides one such explanation\u00a0<strong>[3:46]<\/strong>, and you could ask students to listen and compare his ideas with their own.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> <\/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-3-teachers\/exponentials-lesson-3-episode-3-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-1-teachers\/\">Lesson 4 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-3-teachers\/\" style=\"background-color:#2d4059\">Lesson 3<\/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&nbsp;use their timeline to create an expression that represents the height of the beanstalk on Day 100. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":4678,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5404","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5404","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=5404"}],"version-history":[{"count":2,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5404\/revisions"}],"predecessor-version":[{"id":5551,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5404\/revisions\/5551"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4678"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}