{"id":5371,"date":"2024-01-19T13:34:25","date_gmt":"2024-01-19T21:34:25","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=5371"},"modified":"2024-01-22T17:52:44","modified_gmt":"2024-01-23T01:52:44","slug":"exponentials-lesson-1-episode-3-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/exponential-functions-unit-teachers\/exponentials-lesson-1-teachers\/exponentials-lesson-1-episode-3-teachers\/","title":{"rendered":"Exponentials Lesson 1 Episode 3 (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=\"z3qYnyRRjI0\"><\/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=\"cV9KTfndOKs\"><\/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 rel=\"noreferrer noopener\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2023\/01\/Exponents_L1E3_Student_Worksheet.pdf\" target=\"_blank\"><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\/ad4msrq6\" target=\"_blank\" rel=\"noreferrer noopener\"><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 class=\"wp-block-paragraph\">Arobindo and Joshua use an applet to determine how a new beanstalk is growing.&nbsp;<\/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='6a1c395c22fc37067185879' value='6a1c395c22fc37067185879'><input type='hidden' id='bg-show-more-text-6a1c395c22fc37067185879' value=' '><input type='hidden' id='bg-show-less-text-6a1c395c22fc37067185879' value=' '><button id='bg-showmore-action-6a1c395c22fc37067185879' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1c395c22fc37067185879' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The introduction of a new applet, one that displays tick marks corresponding to the height of the beanstalk on an earlier day, poses some new challenges for Josh and Arobindo. First, the students must interpret these new markings. Initially Arobindo and Josh count only the tick marks&nbsp;<em>above<\/em>&nbsp;the tick mark indicating the original height, which leads to them incorrectly guess that the growth rate is 2&nbsp;<strong>[3:14].<\/strong>&nbsp;Additionally, the students need to reinterpret the tick marks as quantifying distances or heights, in this case the number of distances equal to the height of the beanstalk on the earlier day. They resolve this challenge by calling each of those distances \u201cone unit\u201d and using circles to show those units, rather than just counting the tick marks&nbsp;<strong>[4:33].<\/strong><\/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='6a1c395c2307d9087374214' value='6a1c395c2307d9087374214'><input type='hidden' id='bg-show-more-text-6a1c395c2307d9087374214' value=' '><input type='hidden' id='bg-show-less-text-6a1c395c2307d9087374214' value=' '><button id='bg-showmore-action-6a1c395c2307d9087374214' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1c395c2307d9087374214' ><\/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><\/strong>[<strong>Pause the video at 1:10]<\/strong>&nbsp;Based on the observations of Day 0 and Day 1, what do you think is the growth factor of this new beanstalk? Can you provide evidence for your claim?<\/li>\n\n\n\n<li><strong><\/strong><strong>[Pause the video at 3:36]<\/strong>&nbsp;Tell a partner what you think Josh and Arobindo meant when they said they could count the first one. What does that first tick mark represent? What about the second and third tick marks?&nbsp;<em>(Push students to be precise with their language and highlight responses that discuss those tick marks in terms of the height of the beanstalk or as a distance.)<\/em><\/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='6a1c395c231001059520654' value='6a1c395c231001059520654'><input type='hidden' id='bg-show-more-text-6a1c395c231001059520654' value=' '><input type='hidden' id='bg-show-less-text-6a1c395c231001059520654' value=' '><button id='bg-showmore-action-6a1c395c231001059520654' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1c395c231001059520654' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong><\/strong>As students work to determine the growth rate for the new beanstalk, ask them to make note of what features of the context and the representation they are using to help them make their determination. At&nbsp;<strong>[1:36]<\/strong>, the students in the video claim they can check the heights of the beanstalk on any two consecutive days. Encourage your students to investigate this claim\u2014how does that help reveal the growth rate of the beanstalk?&nbsp;<\/li>\n\n\n\n<li><strong><\/strong>Later, Josh and Arobindo use non-integer days to check the growth rate. Ask your students to discuss this strategy and why it may or may not differ from checking two consecutive integer days.<\/li>\n<\/ol>\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-1-teachers\/exponentials-lesson-1-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-1-teachers\/exponentials-lesson-1-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-1-teachers\/\" style=\"background-color:#2d4059\">Lesson 1<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\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. Arobindo and Joshua use an applet to determine how a new beanstalk is growing.&nbsp; Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":4665,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5371","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5371","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=5371"}],"version-history":[{"count":3,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5371\/revisions"}],"predecessor-version":[{"id":5605,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/5371\/revisions\/5605"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4665"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=5371"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}