{"id":7027,"date":"2024-07-15T09:46:41","date_gmt":"2024-07-15T16:46:41","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7027"},"modified":"2025-07-15T10:25:09","modified_gmt":"2025-07-15T17:25:09","slug":"binomials-lesson-3-episode-5-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-5-teachers\/","title":{"rendered":"Binomials Lesson 3 Episode 5 (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=\"ga3U1ZC1fCY\"><\/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=\"HUVw4X_riwc\"><\/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\/2024\/06\/U5L3E5_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6232\" 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.geogebra.org\/m\/zd7nkqtr\" 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> <a href=\"https:\/\/www.youtube.com\/watch?v=VZ0jG3W53nE\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The students explore an applet to think about the area of a new garden when the length of the original garden is increased by 5 ft, 2 ft, and 3.5 ft. They provide a verbal explanation of a general method for finding the area.&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='6a152f83a291c8038663256' value='6a152f83a291c8038663256'><input type='hidden' id='bg-show-more-text-6a152f83a291c8038663256' value=' '><input type='hidden' id='bg-show-less-text-6a152f83a291c8038663256' value=' '><button id='bg-showmore-action-6a152f83a291c8038663256' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a152f83a291c8038663256' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this episode, Mauricio and Emily are asked to begin generalizing their method for finding the area of a garden after one dimension has been increased. Generalizing can be challenging for students, so provide plenty of opportunities for them to gather data from specific examples (for example, in this episode Emily and Mauricio find the area after increasing the length by 5 ft, 2 ft, and 3.5 ft before being asked to generalize). Notice how they are not asked to reason with variables, yet they still have some difficulty describing a method for finding the area of a garden with an unknown increase in length&nbsp;<strong>[7:00].<\/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='6a152f83a29ab1079317585' value='6a152f83a29ab1079317585'><input type='hidden' id='bg-show-more-text-6a152f83a29ab1079317585' value=' '><input type='hidden' id='bg-show-less-text-6a152f83a29ab1079317585' value=' '><button id='bg-showmore-action-6a152f83a29ab1079317585' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a152f83a29ab1079317585' ><\/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 6:25]&nbsp;<\/strong>The teacher has a number in mind for an increase in the length of the garden, but she isn\u2019t saying what that number is. How could you express the area of the new garden with the number she is thinking of, but not telling?<\/li>\n\n\n\n<li><strong>[Pause the video at 9:10]<\/strong>&nbsp;Compare your method from before with the one Mauricio and Emily just described. Are they the same? If not, how are they different?<\/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='6a152f83a2a111019008279' value='6a152f83a2a111019008279'><input type='hidden' id='bg-show-more-text-6a152f83a2a111019008279' value=' '><input type='hidden' id='bg-show-less-text-6a152f83a2a111019008279' value=' '><button id='bg-showmore-action-6a152f83a2a111019008279' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a152f83a2a111019008279' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[Pause the video at 4:07]&nbsp;<\/strong>Mauricio and Emily seem to have developed a method for finding the area of the new garden after any increase in its length. Talk with a partner about what seems to be the same each time they find the new area and what changes. Describe the method Emily and Mauricio seem to use in your own words. Do you think this method always works?<\/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\/multiplying-binomials-unit-teachers\/binomials-lesson-3-teachers\/binomials-lesson-3-episode-4-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-6-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 class=\"wp-block-paragraph\"><\/p>\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. The students explore an applet to think about the area of a new garden when the length of the original garden is increased by 5 ft, 2 ft, and 3.5 ft. They [&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-7027","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7027","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=7027"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7027\/revisions"}],"predecessor-version":[{"id":8246,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7027\/revisions\/8246"}],"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=7027"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}