{"id":6764,"date":"2024-07-11T13:19:51","date_gmt":"2024-07-11T20:19:51","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=6764"},"modified":"2025-07-15T10:04:51","modified_gmt":"2025-07-15T17:04:51","slug":"logarithms-lesson-5-episode-1-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/logarithms-unit-teachers\/logarithms-lesson-5-teachers\/logarithms-lesson-5-episode-1-teachers\/","title":{"rendered":"Logarithms Lesson 5 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=\"wp-block-embed__wrapper\">\nhttps:\/\/www.youtube.com\/watch?v=RS9TXhMG-2Q\n<\/div>-->\n<div class=\"youtube-player\" data-id=\"qIYFHnp80T8\"><\/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=\"PNaYS-4e9Hs\"><\/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\/U3L5E1_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 the definition of a logarithm to say what log<sub>3<\/sub>&nbsp;(10) means generally. They find its value and discuss why that value makes sense, given the definition.<\/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='69e20c87888931037669037' value='69e20c87888931037669037'><input type='hidden' id='bg-show-more-text-69e20c87888931037669037' value=' '><input type='hidden' id='bg-show-less-text-69e20c87888931037669037' value=' '><button id='bg-showmore-action-69e20c87888931037669037' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e20c87888931037669037' ><\/p>\n\n\n\n<p>Although Josh and Arobindo seem to still be connecting logarithms to exponents, they initially seem unsure that 3<sup>log<\/sup><sub>3<\/sub><sup>10&nbsp;<\/sup>equals 10. Eventually, they talk through the meaning of logarithms and exponents and make this connection, but it isn\u2019t automatic. Expect this to take some time for your students as well. The Focus Questions and Supporting Dialogue prompts can facilitate conversations that help your students make sense of this idea.<\/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='69e20c8788a6f2068557885' value='69e20c8788a6f2068557885'><input type='hidden' id='bg-show-more-text-69e20c8788a6f2068557885' value=' '><input type='hidden' id='bg-show-less-text-69e20c8788a6f2068557885' value=' '><button id='bg-showmore-action-69e20c8788a6f2068557885' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e20c8788a6f2068557885' ><\/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 0:35]<\/strong>&nbsp;What sense do you make of what Arobindo and Josh have written at the beginning of this episode: 3&nbsp;<sup>log<\/sup><sub>3<\/sub><sup>10&nbsp;<\/sup>= ? and 3<sup>x<\/sup>. What does raising a base to a logarithm of that same base do?<\/li>\n\n\n\n<li><strong>[Pause the video at 2:07]<\/strong>&nbsp;Can you rephrase the conversation you just heard? What does it mean that log<sub>3<\/sub>10 \u201cis the exponent that makes 3<sup>x<\/sup>&nbsp;equal 10?\u201d<\/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='69e20c8788bab8076207590' value='69e20c8788bab8076207590'><input type='hidden' id='bg-show-more-text-69e20c8788bab8076207590' value=' '><input type='hidden' id='bg-show-less-text-69e20c8788bab8076207590' value=' '><button id='bg-showmore-action-69e20c8788bab8076207590' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e20c8788bab8076207590' ><\/p>\n\n\n\n<p>After watching the video, ask your students to check in with each other. What does the expression 3<sup>log<\/sup><sub>3<\/sub><sup>10<\/sup>&nbsp;mean? Ask your students to tell a partner one thing they have learned about logarithms and one thing they are still working through or are confused by.<\/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-4-teachers\/\">Lesson 4 EPisode 4<\/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-5-teachers\/logarithms-lesson-5-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\/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-5-teachers\/\" style=\"background-color:#2d4059\">Lesson 5<\/a><\/div>\n<\/div>\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. The students use the definition of a logarithm to say what log3&nbsp;(10) means generally. They find its value and discuss why that value makes sense, given the definition. Episode Supports Students\u2019 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":6419,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6764","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6764","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=6764"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6764\/revisions"}],"predecessor-version":[{"id":8217,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6764\/revisions\/8217"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6419"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=6764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}