{"id":6935,"date":"2024-07-12T14:03:48","date_gmt":"2024-07-12T21:03:48","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=6935"},"modified":"2025-07-15T10:18:20","modified_gmt":"2025-07-15T17:18:20","slug":"binomials-lesson-2-episode-3-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/multiplying-binomials-unit-teachers\/binomials-lesson-2-teachers\/binomials-lesson-2-episode-3-teachers\/","title":{"rendered":"Binomials Lesson 2 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=\"afZRfjuPHVQ\"><\/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=\"bhNQQIhbuaM\"><\/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\/U5L2E3_Student_Worksheet.pdf\" data-type=\"attachment\" data-id=\"6242\" 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><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Emily and Mauricio reflect on the meaning of multiplication when finding the area of a rectangular room. They show multiplication as \u201cgroups of\u201d in their drawing.<\/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='6a40cd73c2d9b2007159150' value='6a40cd73c2d9b2007159150'><input type='hidden' id='bg-show-more-text-6a40cd73c2d9b2007159150' value=' '><input type='hidden' id='bg-show-less-text-6a40cd73c2d9b2007159150' value=' '><button id='bg-showmore-action-6a40cd73c2d9b2007159150' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a40cd73c2d9b2007159150' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The area formula utilizes a&nbsp;<em>groups of<\/em>&nbsp;interpretation of multiplication. The dimensions of a rectangle can be interpreted as some number of groups (one dimension), each comprised of a number (equal to the other dimension) of square units. For example, a rectangle with a width of 8 ft and length of 10 ft can be partitioned into 8 groups, each of which is made up of 10 square feet. This is readily seen in a grid by imagining the groups as vertical strips taking up the entire length of the rectangle and having a width of 1 foot. In other words, the groups can be seen as the columns of the array. However, in the previous lesson, as well as in this video, Mauricio and Emily create differently shaped groups (for example, by circling an array that is 2 ft wide and 5 ft long,&nbsp;<strong>[3:21]<\/strong>). This might mean that the pair haven\u2019t yet fully understood why multiplication is used to measure two-dimensional objects.<\/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='6a40cd73c2e2d1012872355' value='6a40cd73c2e2d1012872355'><input type='hidden' id='bg-show-more-text-6a40cd73c2e2d1012872355' value=' '><input type='hidden' id='bg-show-less-text-6a40cd73c2e2d1012872355' value=' '><button id='bg-showmore-action-6a40cd73c2e2d1012872355' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a40cd73c2e2d1012872355' ><\/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 3:24]&nbsp;<\/strong>How would you indicate more groups of 10 in this drawing? How do you think Emily and Mauricio will show more groups of 10?<\/li>\n\n\n\n<li><strong>[Pause the video at 4:55]&nbsp;<\/strong>How would you show 10 groups of eight in this drawing?<\/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='6a40cd73c2e950095431910' value='6a40cd73c2e950095431910'><input type='hidden' id='bg-show-more-text-6a40cd73c2e950095431910' value=' '><input type='hidden' id='bg-show-less-text-6a40cd73c2e950095431910' value=' '><button id='bg-showmore-action-6a40cd73c2e950095431910' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a40cd73c2e950095431910' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[Pause the video at 1:36]&nbsp;<\/strong>Talk with a partner and explain why multiplication works to find the area of the rectangle? What does&nbsp;<em>10 times 8&nbsp;<\/em>(or&nbsp;<em>8 times 10<\/em>) mean in this context? Can you use a&nbsp;<em>groups of<\/em>&nbsp;interpretation of multiplication in your explanation?<\/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-2-teachers\/binomials-lesson-2-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-2-teachers\/binomials-lesson-2-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-2-teachers\/\" style=\"background-color:#2d4059\">Lesson 2<\/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 the meaning of multiplication when finding the area of a rectangular room. They show multiplication as \u201cgroups of\u201d in their drawing. Episode Supports Students\u2019 Conceptual Challenges Focus [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":6860,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6935","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6935","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=6935"}],"version-history":[{"count":4,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6935\/revisions"}],"predecessor-version":[{"id":8236,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6935\/revisions\/8236"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/6860"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=6935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}