{"id":7077,"date":"2024-07-15T10:42:33","date_gmt":"2024-07-15T17:42:33","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7077"},"modified":"2025-07-15T10:31:31","modified_gmt":"2025-07-15T17:31:31","slug":"binomials-lesson-4-episode-7-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-4-teachers\/binomials-lesson-4-episode-7-teachers\/","title":{"rendered":"Binomials Lesson 4 Episode 7 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Reflecting<\/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=\"cP_hW_WxNEc\"><\/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=\"GxR_YiX5Uyg\"><\/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\/U5L4E7_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6222\" 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 class=\"wp-block-paragraph\">Mauricio and Emily&nbsp;reflect on the meaning of equivalence in another student\u2019s equation: (12 \u2212 y) \u2022 4 = 12 \u2022 9 \u2212 y \u2022 9. They identify what each symbol and term in the equation means in the garden context.<\/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='6a159ec9885143099675990' value='6a159ec9885143099675990'><input type='hidden' id='bg-show-more-text-6a159ec9885143099675990' value=' '><input type='hidden' id='bg-show-less-text-6a159ec9885143099675990' value=' '><button id='bg-showmore-action-6a159ec9885143099675990' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159ec9885143099675990' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This episode provides an example of a challenge that students commonly face when working with quantities in contexts, which is identifying the&nbsp;<em>value<\/em>&nbsp;of a quantity rather than the quantity itself. For example, the instructor asks where the students see any widths&nbsp;<strong>[1:30]<\/strong>. After they respond by stating \u201cJust the 9,\u201d they\u2019re asked to show that width in the garden and they circle the label of 9 ft, rather than showing the actual width along the side of the garden. If your students do the same, you can be explicit and ask them things like \u201cCan you use your pencil to draw the entire width?\u201d<\/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='6a159ec9885bb4076328730' value='6a159ec9885bb4076328730'><input type='hidden' id='bg-show-more-text-6a159ec9885bb4076328730' value=' '><input type='hidden' id='bg-show-less-text-6a159ec9885bb4076328730' value=' '><button id='bg-showmore-action-6a159ec9885bb4076328730' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159ec9885bb4076328730' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For use in a classroom, pause the video and ask this question:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[Pause the video at 3:39]<\/strong>&nbsp;The instructor asked Mauricio and Emily where they see the area of the new garden on the right side of the equation, which is 12 \u2022 9 \u2013 y \u2022 9. This question seems to stump Emily and Mauricio. Before watching further, try to identify where you see the area of the new garden in that expression.<\/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\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a159ec9886366062936086' value='6a159ec9886366062936086'><input type='hidden' id='bg-show-more-text-6a159ec9886366062936086' value=' '><input type='hidden' id='bg-show-less-text-6a159ec9886366062936086' value=' '><button id='bg-showmore-action-6a159ec9886366062936086' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159ec9886366062936086' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[Pause the video at 0:36]<\/strong>&nbsp;With a partner, take turns pointing out lengths you see in the drawing. As you do, connect the lengths you see in the drawing to parts of the equation (12 \u2013 y) \u2022 9 = 12 \u2022 9 \u2013 y \u2022 9. Then do the same with widths and areas.<\/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-4-teachers\/binomials-lesson-4-episode-6-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-5-teachers\/binomials-lesson-5-episode-1-teachers\/\">Lesson 5 Episode 1<\/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-4-teachers\/\" style=\"background-color:#2d4059\">Lesson 4<\/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>Reflecting 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;reflect on the meaning of equivalence in another student\u2019s equation: (12 \u2212 y) \u2022 4 = 12 \u2022 9 \u2212 y \u2022 9. They identify what each symbol and term [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":6867,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-7077","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7077","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=7077"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7077\/revisions"}],"predecessor-version":[{"id":8256,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7077\/revisions\/8256"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6867"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=7077"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}