{"id":5424,"date":"2024-01-19T14:29:30","date_gmt":"2024-01-19T22:29:30","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5424"},"modified":"2024-01-23T09:59:27","modified_gmt":"2024-01-23T17:59:27","slug":"exponentials-lesson-5-episode-2-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-2-teachers\/","title":{"rendered":"Exponentials Lesson 5 Episode 2 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Exploring<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n<div class=\"youtube-player\" data-id=\"F0Mrdjc0PjA\"><\/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=\"btStpqIIbm4\"><\/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_L5E2_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>The students use their timeline to find the height of the beanstalk on Day \u00bd.<\/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='69f596b63dc1b9081477518' value='69f596b63dc1b9081477518'><input type='hidden' id='bg-show-more-text-69f596b63dc1b9081477518' value=' '><input type='hidden' id='bg-show-less-text-69f596b63dc1b9081477518' value=' '><button id='bg-showmore-action-69f596b63dc1b9081477518' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b63dc1b9081477518' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Early in the video, Arobindo introduces the idea of square roots, and Josh says \u201cthe square root of 3 times the square root of 3 equals 3\u201d&nbsp;<strong>[0:55]<\/strong>.The previous lessons have been building toward this moment\u2014linking fractional exponents with square roots. While Josh and Arobindo seemingly have made this connection, your students might not have done so yet. Consider using the focus questions and supporting dialogue prompts below to assess your students\u2019 understanding of square roots so they will also be ready to form this important connection.<\/li>\n\n\n\n<li>A hypothetical student, Jack, is convinced that the height of the beanstalk on Day \u00bd is 2 cm. His reasoning seems to be that since \u00bd is halfway between Day 0 and Day 1, the height should be halfway between the height of the beanstalk on Day 0 and on Day 1&nbsp;<strong>[2:20].<\/strong>&nbsp;This reflects additive reasoning for the heights, and is a common challenge for students. You may want to ask students if they agree with Jack or not before continuing the video.<\/li>\n<\/ol>\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='69f596b63df260009149595' value='69f596b63df260009149595'><input type='hidden' id='bg-show-more-text-69f596b63df260009149595' value=' '><input type='hidden' id='bg-show-less-text-69f596b63df260009149595' value=' '><button id='bg-showmore-action-69f596b63df260009149595' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b63df260009149595' ><\/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 1:46]<\/strong>&nbsp;Can you rephrase Josh\u2019s description of square roots? Remind a partner what a square root means. Have you worked with or seen square roots before?<\/li>\n\n\n\n<li><strong>[Pause the video at 1:46]<\/strong>&nbsp;Consider the expression Arobindo wrote: 1 \u2022 3<sup>\u00bd<\/sup>. Why did Arobindo substitute \u00bd for x in his expression for the height of the plant on Day \u00bd? Why does this make sense in the context of the growing beanstalk?<\/li>\n\n\n\n<li><strong>[Pause the video at 2:33]<\/strong>&nbsp;Jack suggests that the height on Day \u00bd is 2 cm. Does this makes sense given what Arobindo and Josh have discovered about this growing beanstalk?<\/li>\n\n\n\n<li><strong>[Pause the video at 7:08]<\/strong>\u00a0Arobindo claims that the height of the beanstalk on Day \u00bd will be 3<sup>\u00bd<\/sup>, and the height of the beanstalk on Day 1\u00bd will be 3<sup>1\u00bd<\/sup>. Do you agree or disagree with Arobindo? Why do you think\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"54\" class=\"wp-image-5333\" style=\"width: 32px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/sqrt-3.png\" alt=\"\">= 3<sup>\u00bd<\/sup>, and\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"152\" height=\"66\" class=\"wp-image-5572\" style=\"width: 65px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/3-times-sqrt-3.png\" alt=\"\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/3-times-sqrt-3.png 152w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/3-times-sqrt-3-150x66.png 150w\" sizes=\"auto, (max-width: 152px) 100vw, 152px\" \/>= 3<sup>1\u00bd<\/sup>?<\/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='69f596b63e0518055477342' value='69f596b63e0518055477342'><input type='hidden' id='bg-show-more-text-69f596b63e0518055477342' value=' '><input type='hidden' id='bg-show-less-text-69f596b63e0518055477342' value=' '><button id='bg-showmore-action-69f596b63e0518055477342' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b63e0518055477342' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Before watching the video, give your students time to reason about finding the height of the beanstalk on Day \u00bd. Encourage them to discuss with a partner their ideas about how they might represent this height. You can prompt them to make estimates, to draw a timeline, or to use any other representations they\u2019ve been working with, such as expressions or equations.<\/li>\n\n\n\n<li>Consider pausing the video at&nbsp;<strong>[4:47].<\/strong>&nbsp;Ask students to analyze Arobindo\u2019s argument for why the height of the beanstalk on Day \u00bd shouldn\u2019t be 2 cm. If need be, have them rewatch from&nbsp;<strong>3:00<\/strong>. You can prompt them to consider his argument that the&nbsp;<em>times 3<\/em>&nbsp;pattern seems to work from Day 0 to Day 1, Day 0.5 to Day 1.5, and Day 1 to Day 2, but that a doubling or&nbsp;<em>times 2<\/em>&nbsp;pattern doesn\u2019t seem to be consistent. Ask them to share with a partner why that consistency matters in this context.<\/li>\n\n\n\n<li>At the end of the video\u00a0<strong>[8:45]<\/strong>, Arobindo argues that the height is being multiplied by\u00a0<img loading=\"lazy\" decoding=\"async\" width=\"74\" height=\"54\" class=\"wp-image-5333\" style=\"width: 32px\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2024\/01\/sqrt-3.png\" alt=\"\"> every half day, and that this \u201cis constant.\u201d Ask your students what they think he means by that\u2014what is constant?<\/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\/exponential-functions-unit-teachers\/exponentials-lesson-5-teachers\/exponentials-lesson-5-episode-1-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\/exponential-functions-unit-teachers\/exponentials-lesson-5-teachers\/exponentials-lesson-5-episode-3-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>Exploring 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 timeline to find the height of the beanstalk on Day \u00bd. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/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-5424","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5424","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=5424"}],"version-history":[{"count":7,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5424\/revisions"}],"predecessor-version":[{"id":5618,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5424\/revisions\/5618"}],"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=5424"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}