{"id":6680,"date":"2024-07-11T10:25:33","date_gmt":"2024-07-11T17:25:33","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=6680"},"modified":"2025-07-15T09:55:14","modified_gmt":"2025-07-15T16:55:14","slug":"logarithms-lesson-1-episode-7-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-7-teachers\/","title":{"rendered":"Logarithms Lesson 1 Episode 7 (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=\"wp-block-embed__wrapper\">\nhttps:\/\/www.youtube.com\/watch?v=RS9TXhMG-2Q\n<\/div>-->\n<div class=\"youtube-player\" data-id=\"fGeNjyplk8c\"><\/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=\"0s5vNvvhcXs\"><\/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\/U3L1E7_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 two equivalent exponential expressions that both represent the height of the beanstalk any number of days after an unknown start date. They justify these expressions using a number line.<\/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\">Focus Questions <input type='hidden' bg_collapse_expand='69f3b0215ebd07005564647' value='69f3b0215ebd07005564647'><input type='hidden' id='bg-show-more-text-69f3b0215ebd07005564647' value=' '><input type='hidden' id='bg-show-less-text-69f3b0215ebd07005564647' value=' '><button id='bg-showmore-action-69f3b0215ebd07005564647' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b0215ebd07005564647' ><\/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 0:38]<\/strong>&nbsp;Before watching Arobindo and Josh create their own number line, create one for yourself. Draw and label a number line to represent the height of the beanstalk some number of days after it has grown for some number of days.<\/li>\n\n\n\n<li><strong>[Pause the video at 2:27]<\/strong>&nbsp;Josh and Arobindo have written two expressions: 1 \u00d7 3<sup>p+3<\/sup>&nbsp;and 3<sup>p&nbsp;<\/sup>\u00d7<sup>&nbsp;<\/sup>3<sup>e<\/sup>. How do each of these expressions relate to the number line? Are they equivalent expressions? How do you know?<\/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='69f3b0215ecdc3088455823' value='69f3b0215ecdc3088455823'><input type='hidden' id='bg-show-more-text-69f3b0215ecdc3088455823' value=' '><input type='hidden' id='bg-show-less-text-69f3b0215ecdc3088455823' value=' '><button id='bg-showmore-action-69f3b0215ecdc3088455823' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f3b0215ecdc3088455823' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>[Pause the video at 1:33]<\/strong>&nbsp;Ask your students to examine the diagram that Josh and Arobindo have drawn. Ask them to discuss with a partner the significance and meaning for each expression in the diagram. What does p represent? What about e and p+e? Ask them to explain why the Josh and Arobindo have written 3<sup>p<\/sup>, 3<sup>e<\/sup>, and 3<sup>p+e<\/sup>&nbsp;as heights of the beanstalk at various points on the timeline.<\/li>\n\n\n\n<li>After the video, ask students to consider the equation 3<sup>p+e&nbsp;<\/sup>= 3<sup>p&nbsp;<\/sup>\u00d7<sup>&nbsp;<\/sup>3<sup>e<\/sup>&nbsp;and discuss with a partner why this equation is true. Ask them if they can come up with a general rule for when exponential expressions are being multiplied.<\/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-6-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-1-teachers\/\">Lesson 2 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\/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>Reflecting 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 two equivalent exponential expressions that both represent the height of the beanstalk any number of days after an unknown start date. They justify these expressions using a number line. [&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-6680","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6680","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=6680"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6680\/revisions"}],"predecessor-version":[{"id":8203,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6680\/revisions\/8203"}],"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=6680"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}