{"id":5421,"date":"2024-01-19T14:28:01","date_gmt":"2024-01-19T22:28:01","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5421"},"modified":"2024-01-22T14:21:32","modified_gmt":"2024-01-22T22:21:32","slug":"exponentials-lesson-5-episode-1-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/exponential-functions-unit-teachers\/exponentials-lesson-5-teachers\/exponentials-lesson-5-episode-1-teachers\/","title":{"rendered":"Exponentials 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=\"youtube-player\" data-id=\"Nf4Kow-CgpY\"><\/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=\"youtube-player\" data-id=\"ThtL7248WSQ\"><\/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\/01\/Exponents_L5E1_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.wolframalpha.com\/\" 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><\/p>\n\n\n\n<p>Josh and Arobindo review the mathematical relationships on a timeline that represents the growth of a beanstalk that represents the growth of a beanstalk that triples in height each day and has a height of 1 cm on Day 0.<\/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='69f63f77beca33023382326' value='69f63f77beca33023382326'><input type='hidden' id='bg-show-more-text-69f63f77beca33023382326' value=' '><input type='hidden' id='bg-show-less-text-69f63f77beca33023382326' value=' '><button id='bg-showmore-action-69f63f77beca33023382326' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f63f77beca33023382326' ><\/p>\n\n\n\n<p>Early in the video\u00a0<strong>[1:14]<\/strong>, there is more evidence that Josh and Arobindo can compose new multiplicative and additive relationships. For example, Arobindo discusses 243 as being\u00a0<em>times 3<\/em>, five times, while Josh says that over a two-day period, the growth factor is 9. Josh also says that the growth rate being 9 means \u201cit increases by 9,\u201d\u00a0<strong>[2:35].<\/strong>\u00a0Taken literally, this would indicate an additive relationship between the heights of the beanstalk on two successive days (e.g., growing from 2 cm to 2 + 9 = 11 cm) instead of a multiplicative relationship (e.g., growing from 2 cm to 2 \u00d7 9 = 18 cm). This could indicate confusion between multiplicative and additive relationships, though he does immediately clarify afterwards. Other students who have not yet cleared this conceptual hurdle might not be so quick to clarify their meaning.<\/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='69f63f77bed289075663424' value='69f63f77bed289075663424'><input type='hidden' id='bg-show-more-text-69f63f77bed289075663424' value=' '><input type='hidden' id='bg-show-less-text-69f63f77bed289075663424' value=' '><button id='bg-showmore-action-69f63f77bed289075663424' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f63f77bed289075663424' ><\/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 4:36]<\/strong>&nbsp;Consider the explanation given by Josh for why the beanstalk grows by a factor of 9 over any two-day period. Do you agree or disagree with his argument? How do multiplicative growth factors over individual days contribute to the overall growth?<\/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='69f63f77bed6c1018338258' value='69f63f77bed6c1018338258'><input type='hidden' id='bg-show-more-text-69f63f77bed6c1018338258' value=' '><input type='hidden' id='bg-show-less-text-69f63f77bed6c1018338258' value=' '><button id='bg-showmore-action-69f63f77bed6c1018338258' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f63f77bed6c1018338258' ><\/p>\n\n\n\n<p>After watching the video, ask your students to talk with each other to summarize the discussion about\u00a0<em>groups of groups of\u2026<\/em>. In the video, Josh and Arobindo use this language to argue about how they know the growth factor over a given time period. For example, you might ask students to argue about the growth factor for the height of the plant from Day 3 to Day 6 and ask them to try to use the\u00a0<em>groups of<\/em>\u00a0framing in their argument.<\/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\/exponential-functions-unit-teachers\/exponentials-lesson-4-teachers\/exponentials-lesson-4-episode-6-teachers\/\">Lesson 4 EPisode 6<\/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\/exponential-functions-unit-teachers\/exponentials-lesson-5-teachers\/exponentials-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\/exponential-functions-unit-teachers\/\" style=\"background-color:#2d4059\">Exponentials<\/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\/exponential-functions-unit-teachers\/exponentials-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. Josh and Arobindo review the mathematical relationships on a timeline that represents the growth of a beanstalk that represents the growth of a beanstalk that triples in height each day and [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":4689,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5421","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5421","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=5421"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5421\/revisions"}],"predecessor-version":[{"id":5566,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5421\/revisions\/5566"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4689"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5421"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}