{"id":6668,"date":"2024-07-11T10:12:24","date_gmt":"2024-07-11T17:12:24","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=6668"},"modified":"2025-07-15T09:52:50","modified_gmt":"2025-07-15T16:52:50","slug":"logarithms-lesson-1-episode-4-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/logarithms-unit-teachers\/logarithms-lesson-1-teachers\/logarithms-lesson-1-episode-4-teachers\/","title":{"rendered":"Logarithms Lesson 1 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=\"daxEqMehMlI\"><\/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=\"7xEd5D0m2fE\"><\/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\/08\/U3L1E4_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>The students create an expression that represents the height of the beanstalk 5 days after an unknown start date, and create a number line to represent this expression.<\/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='69f4c2d2d60236089013896' value='69f4c2d2d60236089013896'><input type='hidden' id='bg-show-more-text-69f4c2d2d60236089013896' value=' '><input type='hidden' id='bg-show-less-text-69f4c2d2d60236089013896' value=' '><button id='bg-showmore-action-69f4c2d2d60236089013896' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2d2d60236089013896' ><\/p>\n\n\n\n<p>Arobindo says, \u201cWe are varying the starting day\u201d and then calls it Day y&nbsp;<strong>[0:23]<\/strong>. Some students might not decide this so quickly and may wonder where the starting day should go and what it should be called. You can prompt them to consider how they have handled similar mathematical situations in the past: What do they do when they have an unknown quantity that they need to represent?<\/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='69f4c2d2d60b57080031052' value='69f4c2d2d60b57080031052'><input type='hidden' id='bg-show-more-text-69f4c2d2d60b57080031052' value=' '><input type='hidden' id='bg-show-less-text-69f4c2d2d60b57080031052' value=' '><button id='bg-showmore-action-69f4c2d2d60b57080031052' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2d2d60b57080031052' ><\/p>\n\n\n\n<p>For use in a classroom, pause the video and ask this question:<\/p>\n\n\n\n<p><strong>[Pause the video at 2:52]<\/strong>&nbsp;Why does the beanstalk grow 3<sup>y<\/sup>&nbsp;for the first part of the number line and 3<sup>5<\/sup>&nbsp;for the second?<\/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='69f4c2d2d60fe3026558919' value='69f4c2d2d60fe3026558919'><input type='hidden' id='bg-show-more-text-69f4c2d2d60fe3026558919' value=' '><input type='hidden' id='bg-show-less-text-69f4c2d2d60fe3026558919' value=' '><button id='bg-showmore-action-69f4c2d2d60fe3026558919' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f4c2d2d60fe3026558919' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>In previous episodes, Arobindo had a method for writing the height of the beanstalk for some number of days after Day 2. In this video, his method seems to be missing. Prompt your students to make a prediction for what expression Arobindo might write for the height of the beanstalk 5 days after some number of days.<\/li>\n\n\n\n<li>Arobindo\u2019s method in previous episodes was to write the height of the beanstalk on Day 2 multiplied by the growth factor over some number of days. For this episode, we might expect him to write&nbsp;3<sup>y&nbsp;<\/sup>\u00d7<sup>&nbsp;<\/sup>3<sup>5<\/sup>. Ask your students if this expression represents the height of the beanstalk 5 days after some number of days. Ask them to make connections between the expression and the beanstalk context or the number line to support their argument.<\/li>\n<\/ol>\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\/logarithms-unit-teachers\/logarithms-lesson-1-teachers\/logarithms-lesson-1-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-1-teachers\/logarithms-lesson-1-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-1-teachers\/\" style=\"background-color:#2d4059\">Lesson 1<\/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 create an expression that represents the height of the beanstalk 5 days after an unknown start date, and create a number line to represent this expression. Episode Supports [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":6403,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6668","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6668","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=6668"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6668\/revisions"}],"predecessor-version":[{"id":8200,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6668\/revisions\/8200"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6403"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=6668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}