{"id":6751,"date":"2024-07-11T12:53:50","date_gmt":"2024-07-11T19:53:50","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=6751"},"modified":"2025-07-15T10:03:49","modified_gmt":"2025-07-15T17:03:49","slug":"logarithms-lesson-4-episode-3-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/logarithms-unit-teachers\/logarithms-lesson-4-teachers\/logarithms-lesson-4-episode-3-teachers\/","title":{"rendered":"Logarithms Lesson 4 Episode 3 (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=\"N7v131xtLNQ\"><\/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=\"QPyE9zY6uts\"><\/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\/U3L4E3_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> <a href=\"https:\/\/www.geogebra.org\/m\/bu5jpabt\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-484\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/geogebra.jpg\" alt=\"Link to Geogebra applet\"><\/a><\/p>\n\n\n\n<p>The students use their number line and a calculator to determine the amount of time it takes for the mold on the pizza to increase by a factor of 1.5.<\/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='69d91f0ddbb5b8051103605' value='69d91f0ddbb5b8051103605'><input type='hidden' id='bg-show-more-text-69d91f0ddbb5b8051103605' value=' '><input type='hidden' id='bg-show-less-text-69d91f0ddbb5b8051103605' value=' '><button id='bg-showmore-action-69d91f0ddbb5b8051103605' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69d91f0ddbb5b8051103605' ><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Some students may struggle to interpret logarithmic expressions and the result of calculating logarithms. If you notice students struggling with this unproductively, encourage them to represent the mathematics using exponential notation and ask them to make connections between that notation and the logarithmic notation they are just now working with.<\/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='69d91f0ddbc220046351036' value='69d91f0ddbc220046351036'><input type='hidden' id='bg-show-more-text-69d91f0ddbc220046351036' value=' '><input type='hidden' id='bg-show-less-text-69d91f0ddbc220046351036' value=' '><button id='bg-showmore-action-69d91f0ddbc220046351036' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69d91f0ddbc220046351036' ><\/p>\n\n\n\n<p>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 0:21]<\/strong>&nbsp;How long does it take for the mold to increase by a factor of 1.5?<\/li>\n\n\n\n<li><strong>[Pause the video at 2:36]<\/strong>&nbsp;Josh and Arobindo used logarithms to find the time for the mold to increase by a factor of 1.5. How does the log<sub>3<\/sub>1.5 relate to the growth factor, and what does the calculated value (0.36) signify?<\/li>\n<\/ol>\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='69d91f0ddbca91065397913' value='69d91f0ddbca91065397913'><input type='hidden' id='bg-show-more-text-69d91f0ddbca91065397913' value=' '><input type='hidden' id='bg-show-less-text-69d91f0ddbca91065397913' value=' '><button id='bg-showmore-action-69d91f0ddbca91065397913' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69d91f0ddbca91065397913' ><\/p>\n\n\n\n<p>Ask your students to share their understanding of how logarithms (in base three) were used by Arobindo and Josh to calculate the amount of time for the mold to increase by a factor of 1.5. How do logarithms help model exponential growth, and what insights does logarithmic notation provide into the context of the moldy pizza?<\/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\/logarithms-unit-teachers\/logarithms-lesson-4-teachers\/logarithms-lesson-4-episode-2-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-4-teachers\/logarithms-lesson-4-episode-4-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-4-teachers\/\" style=\"background-color:#2d4059\">Lesson 4<\/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 their number line and a calculator to determine the amount of time it takes for the mold on the pizza to increase by a factor of 1.5. [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":6416,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6751","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6751","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=6751"}],"version-history":[{"count":5,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6751\/revisions"}],"predecessor-version":[{"id":8215,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6751\/revisions\/8215"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6416"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=6751"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}