{"id":6705,"date":"2024-07-11T10:44:13","date_gmt":"2024-07-11T17:44:13","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=6705"},"modified":"2025-07-15T09:58:38","modified_gmt":"2025-07-15T16:58:38","slug":"logarithms-lesson-2-episode-4-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/logarithms-unit-teachers\/logarithms-lesson-2-teachers\/logarithms-lesson-2-episode-4-teachers\/","title":{"rendered":"Logarithms Lesson 2 Episode 4 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Repeating Your Reasoning<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n<!--<div class=\"wp-block-embed__wrapper\">\nhttps:\/\/www.youtube.com\/watch?v=RS9TXhMG-2Q\n<\/div>-->\n<div class=\"youtube-player\" data-id=\"Z2yEOVbxyso\"><\/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=\"wp-block-embed__wrapper\">\nhttps:\/\/www.youtube.com\/watch?v=ScG4QG8Wv9s\n<\/div>-->\n<div class=\"youtube-player\" data-id=\"gJLaNIR3O_M\"><\/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\/08\/U3L2E4_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>  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The students use a number line to explore the growth of the beanstalk over an unknown number of 1.5-day periods of time. They develop two equivalent exponential expressions to represent this growth.<\/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='6a42aee1cf0808081203645' value='6a42aee1cf0808081203645'><input type='hidden' id='bg-show-more-text-6a42aee1cf0808081203645' value=' '><input type='hidden' id='bg-show-less-text-6a42aee1cf0808081203645' value=' '><button id='bg-showmore-action-6a42aee1cf0808081203645' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a42aee1cf0808081203645' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Some students may have trouble using the context to distinguish between 3<sup>1.5n<\/sup>&nbsp;and (3<sup>1.5<\/sup>)<sup>n<\/sup>. In the video, Arobindo initially claims that (3<sup>1.5<\/sup>)<sup>n<\/sup>&nbsp;can be seen as the growth over 1.5n days&nbsp;<strong>[3:05]<\/strong>, but later clarifies that for this expression, the 1.5 is a 1.5-day period, and the n signifies there are n many of those 1.5-day periods. He then argues that n many 1.5-day periods results in 1.5n many days. This is a subtle idea, but in terms of interpreting the expressions in this video, it is important to note this difference. This can help students see why the two expressions are equivalent.<\/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='6a42aee1cf1c18034389279' value='6a42aee1cf1c18034389279'><input type='hidden' id='bg-show-more-text-6a42aee1cf1c18034389279' value=' '><input type='hidden' id='bg-show-less-text-6a42aee1cf1c18034389279' value=' '><button id='bg-showmore-action-6a42aee1cf1c18034389279' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a42aee1cf1c18034389279' ><\/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 1:52]<\/strong>&nbsp;What significance does 1.5n have in this context?<\/li>\n\n\n\n<li><strong>[Pause the video at 2:25]<\/strong>&nbsp;Can you state in your own words what the expression 3<sup>1.5n<\/sup>&nbsp;means in the beanstalk context?<\/li>\n\n\n\n<li><strong>[Pause the video at 4:09]<\/strong>&nbsp;Can you state in your own words what the expression (3<sup>1.5<\/sup>)<sup>n<\/sup>&nbsp;means in the beanstalk context? How is it different than 3<sup>1.5n<\/sup>? How is it the same?<\/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='6a42aee1cf2948083852022' value='6a42aee1cf2948083852022'><input type='hidden' id='bg-show-more-text-6a42aee1cf2948083852022' value=' '><input type='hidden' id='bg-show-less-text-6a42aee1cf2948083852022' value=' '><button id='bg-showmore-action-6a42aee1cf2948083852022' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a42aee1cf2948083852022' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After watching the video, ask students to restate in their own words why the two expressions&nbsp;(3<sup>1.5<\/sup>)<sup>n<\/sup>and&nbsp;3<sup>1.5n<\/sup>&nbsp;are equivalent. Ask them to describe how they see 1.5n in the diagram Josh and Arobindo drew and to use that in their argument for why the expressions are equivalent.<\/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\/logarithms-unit-teachers\/logarithms-lesson-2-teachers\/logarithms-lesson-2-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\/logarithms-unit-teachers\/logarithms-lesson-2-teachers\/logarithms-lesson-2-episode-5-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\/logarithms-unit-teachers\/\" style=\"background-color:#2d4059\">Logarithms<\/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\/logarithms-unit-teachers\/logarithms-lesson-2-teachers\/\" style=\"background-color:#2d4059\">Lesson 2<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Repeating Your Reasoning No captions CaptionsStop the video above first if it is playing. No captions CaptionsStop the video above first if it is playing. The students use a number line to explore the growth of the beanstalk over an unknown number of 1.5-day periods of time. They develop two equivalent exponential expressions to represent [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":6409,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6705","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6705","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=6705"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6705\/revisions"}],"predecessor-version":[{"id":8207,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6705\/revisions\/8207"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6409"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=6705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}