{"id":7061,"date":"2024-07-15T10:24:10","date_gmt":"2024-07-15T17:24:10","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=7061"},"modified":"2025-07-15T10:29:13","modified_gmt":"2025-07-15T17:29:13","slug":"binomials-lesson-4-episode-3-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-3-teachers\/","title":{"rendered":"Binomials Lesson 4 Episode 3 (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=\"Kw8HoSgjz08\"><\/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=\"PgSv7TOEXxo\"><\/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\/U5L4E3_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6226\" 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=xkfDSqbrjik\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"46\" class=\"wp-image-483\" style=\"width: 150px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/more_info.jpg\" alt=\"Link to more information\"><\/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\">Emily and Mauricio reflect on their drawing from Episode 2 and write equations&nbsp;to express different ways to find the area of the new garden. They explore whether or not they can&nbsp;<em>distribute<\/em> multiplication over subtraction.&nbsp;&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='6a1b2dc13e86d4070646115' value='6a1b2dc13e86d4070646115'><input type='hidden' id='bg-show-more-text-6a1b2dc13e86d4070646115' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc13e86d4070646115' value=' '><button id='bg-showmore-action-6a1b2dc13e86d4070646115' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc13e86d4070646115' ><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Early in the video&nbsp;<strong>[1:22]<\/strong>, Mauricio and Emily wonder if distributing (12&nbsp;\u2013&nbsp;4) \u00d7 9 would give the same answer as&nbsp;8&nbsp;\u00d7 9. They had to actually perform the distribution of 9 across 12 \u2013 4, which gave them 108 \u2013 36, and then calculate to see that the result would be 72 (which is the same as 8 \u00d7 9). This is an excellent example of how students often do not \u201ctrust\u201d a mathematical idea (e.g., the distributive property) until they have utilized it for themselves.&nbsp;<\/li>\n\n\n\n<li>Emily and Mauricio write the equation&nbsp;(12&nbsp;\u2013&nbsp;4)&nbsp;\u00d7&nbsp;9 = 4 \u2022 9&nbsp;\u2013&nbsp;9 \u2022 12&nbsp;<strong>[2:22]<\/strong>. When multiplication is distributed over a sum, the order in which you write the resulting pairs of products isn\u2019t important since addition is commutative. But where multiplication is distributed over a difference, the order matters. If you have students who do this, try asking them to evaluate each side of the equation to see how the equation isn\u2019t true. Then ask them how they might change it to make the equation true and have them discuss why the order matters in this case.<\/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\">Focus Questions <input type='hidden' bg_collapse_expand='6a1b2dc13e9c13063443902' value='6a1b2dc13e9c13063443902'><input type='hidden' id='bg-show-more-text-6a1b2dc13e9c13063443902' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc13e9c13063443902' value=' '><button id='bg-showmore-action-6a1b2dc13e9c13063443902' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc13e9c13063443902' ><\/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 0:34]<\/strong>&nbsp;Mauricio and Emily have written 9&nbsp;\u00d7&nbsp;8 = 72 ft<sup>2<\/sup>&nbsp;to represent the area of the new garden. Can you think of any other expressions or equations you could write that would also represent the area of the new garden?<\/li>\n\n\n\n<li><strong>[Pause the video at 3:25]&nbsp;<\/strong>Emily and Mauricio have created the equation (12&nbsp;\u2013&nbsp;4)&nbsp;\u00d7&nbsp;9 = 4 \u2022 9&nbsp;\u2013&nbsp;9 \u2022 12. Does the equation make sense? If so, explain why it makes sense, and if not, explain what is wrong with it.<\/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='6a1b2dc13ea550046247118' value='6a1b2dc13ea550046247118'><input type='hidden' id='bg-show-more-text-6a1b2dc13ea550046247118' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc13ea550046247118' value=' '><button id='bg-showmore-action-6a1b2dc13ea550046247118' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc13ea550046247118' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[Pause the video at 1:22]<\/strong>&nbsp;Emily and Mauricio wonder if (12 \u2013 4) \u00d7 9 will result in the same answer you get if you were to distribute first. Tell a partner what you think about this\u2014will you get the same answer either way? Why or why not?<\/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-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\/multiplying-binomials-unit-teachers\/binomials-lesson-4-teachers\/binomials-lesson-4-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\/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. Emily and Mauricio reflect on their drawing from Episode 2 and write equations&nbsp;to express different ways to find the area of the new garden. They explore whether or not they can&nbsp;distribute multiplication [&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-7061","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7061","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=7061"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7061\/revisions"}],"predecessor-version":[{"id":8252,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/7061\/revisions\/8252"}],"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=7061"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}