{"id":5401,"date":"2024-01-19T14:07:54","date_gmt":"2024-01-19T22:07:54","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5401"},"modified":"2024-01-22T13:47:27","modified_gmt":"2024-01-22T21:47:27","slug":"exponentials-lesson-3-episode-3-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/exponential-functions-unit-teachers\/exponentials-lesson-3-teachers\/exponentials-lesson-3-episode-3-teachers\/","title":{"rendered":"Exponentials Lesson 3 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=\"youtube-player\" data-id=\"p1UFJ38C6Ro\"><\/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=\"zcg_Sa3sZto\"><\/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 class=\"wp-block-paragraph\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2023\/01\/Exponents_L3E3_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><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Josh and Arobindo&nbsp;use their timeline to create an expression that represents the height of the beanstalk on Day 100.<\/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 wp-block-paragraph\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='6a1cf11de5a323026723087' value='6a1cf11de5a323026723087'><input type='hidden' id='bg-show-more-text-6a1cf11de5a323026723087' value=' '><input type='hidden' id='bg-show-less-text-6a1cf11de5a323026723087' value=' '><button id='bg-showmore-action-6a1cf11de5a323026723087' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1cf11de5a323026723087' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Josh and Arobindo do not seem to struggle much with creating an equation to represent the height of the beanstalk on Day 100, though they do not use a symbol to indicate the height of the beanstalk and choose instead to write out the words \u201cheight of the plant on Day 100.\u201d Some students may struggle to link the various quantities in this context (starting height, growth rate, and number of days) using appropriate mathematical operations. For example, they might not know whether to add 1 (the starting height) to the expression 3<sup>100<\/sup>\u00a0or to multiply it. Since the starting height is 1, they might not even include it, which can be problematic when the starting height is not the multiplicative identity element.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a1cf11de5ad87001561403' value='6a1cf11de5ad87001561403'><input type='hidden' id='bg-show-more-text-6a1cf11de5ad87001561403' value=' '><input type='hidden' id='bg-show-less-text-6a1cf11de5ad87001561403' value=' '><button id='bg-showmore-action-6a1cf11de5ad87001561403' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1cf11de5ad87001561403' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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 0:14]<\/strong>&nbsp;Make a prediction for how tall the beanstalk will be on Day 100. Discuss with a partner how you could represent this number. Which quantities from the beanstalk context are important for your representation?<\/li>\n\n\n\n<li><strong>[Pause the video at 3:03]<\/strong><em> <\/em><em>Ask your students the following questions, providing time for them to discuss their ideas with a partner for each question before you pose the next one:\u00a0<\/em>\n<ul class=\"wp-block-list\">\n<li>What does the 1 represent in the expression 1 \u00d7 3<sup>100<\/sup>?\u00a0\u00a0<\/li>\n\n\n\n<li>What does the 3 represent in the expression 1 \u00d7 3<sup>100<\/sup>?\u00a0\u00a0<\/li>\n\n\n\n<li>What does the 100 represent in the expression 1 \u00d7 3<sup>100<\/sup>?\u00a0\u00a0<\/li>\n\n\n\n<li>What does the 3<sup>100<\/sup>\u00a0represent in the expression 1 \u00d7 3<sup>100<\/sup>?\u00a0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>[Pause the video at 4:33]<\/strong>\u00a0Consider Arobindo\u2019s description of the little bumps representing 100 days and his utterance, \u201ctimes 3, 100 times.\u201d Can you rephrase Arobindo\u2019s explanation and describe how that explanation relates to the expression 3<sup>100<\/sup>?<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a1cf11de5b8e1007985523' value='6a1cf11de5b8e1007985523'><input type='hidden' id='bg-show-more-text-6a1cf11de5b8e1007985523' value=' '><input type='hidden' id='bg-show-less-text-6a1cf11de5b8e1007985523' value=' '><button id='bg-showmore-action-6a1cf11de5b8e1007985523' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1cf11de5b8e1007985523' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Josh and Arobindo provide two different explanations for what the 3<sup>100<\/sup>\u00a0represents in their diagram. First, they say it represents the height of the beanstalk on Day 100, and then they say it also represents the growth factor from Day 0 to Day 100. Ask your students to discuss these two different meanings for the expression 3<sup>100<\/sup>. You might consider introducing a new timeline that begins on a day that is not zero, say Day 5, and extends past Day 105. Ask them if they can see any place in the diagram that would also represent the expression 3<sup>100<\/sup>.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"> <\/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-3-teachers\/exponentials-lesson-3-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\/exponential-functions-unit-teachers\/exponentials-lesson-3-teachers\/exponentials-lesson-3-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\/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-3-teachers\/\" style=\"background-color:#2d4059\">Lesson 3<\/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. Josh and Arobindo&nbsp;use their timeline to create an expression that represents the height of the beanstalk on Day 100. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":4678,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5401","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5401","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=5401"}],"version-history":[{"count":3,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5401\/revisions"}],"predecessor-version":[{"id":5549,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5401\/revisions\/5549"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4678"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}