{"id":7031,"date":"2024-07-15T09:49:39","date_gmt":"2024-07-15T16:49:39","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7031"},"modified":"2025-07-15T10:25:49","modified_gmt":"2025-07-15T17:25:49","slug":"binomials-lesson-3-episode-6-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-3-teachers\/binomials-lesson-3-episode-6-teachers\/","title":{"rendered":"Binomials Lesson 3 Episode 6 (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=\"wp-block-embed__wrapper\">\nhttps:\/\/www.youtube.com\/watch?v=RS9TXhMG-2Q\n<\/div>-->\n<div class=\"youtube-player\" data-id=\"tJ8SsggvbL0\"><\/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=\"m7ym3gf2dx4\"><\/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\/2024\/06\/U5L3E6_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6231\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"46\" class=\"wp-image-486\" style=\"width: 150px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/download_worksheets.jpg\" alt=\"Download Math Task\"><\/a> <a href=\"https:\/\/www.youtube.com\/watch?v=VZ0jG3W53nE\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/p>\n\n\n\n<p>Mauricio and Emily&nbsp;draw a picture of a new garden when the length of the original garden is increased by an unknown amount. They explore how to use symbols and letters to represent an unknown length and an unknown area.<\/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='69eb288c653187045565928' value='69eb288c653187045565928'><input type='hidden' id='bg-show-more-text-69eb288c653187045565928' value=' '><input type='hidden' id='bg-show-less-text-69eb288c653187045565928' value=' '><button id='bg-showmore-action-69eb288c653187045565928' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69eb288c653187045565928' ><\/p>\n\n\n\n<p>Emily has written \u201c?&nbsp;\u00d7&nbsp;4\u201d in the new portion of the garden. Mauricio argues that it should just be \u201c?\u201d that represents the area, while Emily argues that she wrote the area as \u201c? \u00d7 4\u201d because \u201c?\u201d and \u201c4\u201d are the dimensions of the new section. Mauricio seems to hold two different meanings for \u201c?\u201d in the drawing, as both the value of the one-dimensional measurement of the increase in length, and also as the value of the two-dimensional measurement for the increase in area of the new section. However, for a given context or problem, any symbol that represents a quantity must maintain the same value; so, this represents a challenge for Mauricio.<\/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='69eb288c653c07037647151' value='69eb288c653c07037647151'><input type='hidden' id='bg-show-more-text-69eb288c653c07037647151' value=' '><input type='hidden' id='bg-show-less-text-69eb288c653c07037647151' value=' '><button id='bg-showmore-action-69eb288c653c07037647151' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69eb288c653c07037647151' ><\/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 0:42]<\/strong>&nbsp;Before watching Mauricio and Emily create their own drawing, try making a drawing that shows an increase in length by an unknown number. How might you represent this mathematically?<\/li>\n\n\n\n<li><strong>[Pause the video at 9:39]&nbsp;<\/strong>Why does Emily think a new symbol is needed? Summarize her argument in your own words.<\/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='69eb288c6546d8029782368' value='69eb288c6546d8029782368'><input type='hidden' id='bg-show-more-text-69eb288c6546d8029782368' value=' '><input type='hidden' id='bg-show-less-text-69eb288c6546d8029782368' value=' '><button id='bg-showmore-action-69eb288c6546d8029782368' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69eb288c6546d8029782368' ><\/p>\n\n\n\n<p><strong>[Pause the video at 5:45]&nbsp;<\/strong>With a partner, take turns explaining the arguments made by both Emily and Mauricio. What does Mauricio think the \u201c?\u201d represents? What does Emily think the \u201c?\u201d represents? Who do you think is right and why? What do you make of the introduction of the new \u201c!\u201d symbol?<\/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\/multiplying-binomials-unit-teachers\/binomials-lesson-3-teachers\/binomials-lesson-3-episode-5-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\/multiplying-binomials-unit-teachers\/binomials-lesson-3-teachers\/binomials-lesson-3-episode-7-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\/multiplying-binomials-unit-teachers\/\" style=\"background-color:#2d4059\">Binomials<\/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\/multiplying-binomials-unit-teachers\/binomials-lesson-3-teachers\/\" style=\"background-color:#2d4059\">Lesson 3<\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/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. Mauricio and Emily&nbsp;draw a picture of a new garden when the length of the original garden is increased by an unknown amount. They explore how to use symbols and letters to represent [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":6864,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7031","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7031","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=7031"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7031\/revisions"}],"predecessor-version":[{"id":8247,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7031\/revisions\/8247"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6864"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=7031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}