{"id":4187,"date":"2022-05-27T12:56:06","date_gmt":"2022-05-27T19:56:06","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=4187"},"modified":"2023-11-09T17:33:57","modified_gmt":"2023-11-10T01:33:57","slug":"algebraic-expressions-lesson-6-episode-4-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-6-teachers\/algebraic-expressions-lesson-6-episode-4-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 6 Episode 4 (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\n<\/p><div class=\"youtube-player\" data-id=\"QGRUFkKjNlc\"><\/div>\n\n<p><\/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\n<\/div>\n\n<div id=\"video_hidden_first\" style=\"display:none\">\n<p>\n\n<\/p><div class=\"youtube-player\" data-id=\"hQ1PhjRn9NU\"><\/div>\n\n<p><\/p>\n\n<p style=\"text-align:center;\"><span style=\"font-size:90%\">No captions <a onclick=\"toggle_text('video_shown_first', 'video_hidden_first')\"><\/a><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 rel=\"noreferrer noopener\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2022\/04\/L6E4_Algebra_Student_Worksheet.pdf\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"46\" class=\"wp-image-486\" style=\"width: 150px;\" src=\"http:\/\/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\">Haleemah and ET explore the equality between Amir and Nicole\u2019s methods by discussing the similarities and resolving the differences between the two methods.<\/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='6a1b2dc2109ae2094838255' value='6a1b2dc2109ae2094838255'><input type='hidden' id='bg-show-more-text-6a1b2dc2109ae2094838255' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc2109ae2094838255' value=' '><button id='bg-showmore-action-6a1b2dc2109ae2094838255' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc2109ae2094838255' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This video presents another example of how challenging it can be to contextual symbolic expressions, especially algebraic ones. Both Haleemah and ET are able to explicitly link numerical expressions to features in the cobblestone diagram. For example, given the expression 5 \u2022 6, which comes from Nicole\u2019s method, Haleemah connects the five to the number of stones in one column and the 6 to the number of columns in the second section<strong>&nbsp;[7:11]<\/strong>. ET describes how he sees the expression 5 \u2022 5 + 5 by linking each five in that expression to features of the diagram&nbsp;<strong>[7:28]<\/strong>. However, making these connections with the algebraic expression x + 1 proves to be challenging, as ET shares it\u2019s \u201cvery hard to explain, so it\u2019s really hard to interpret that in Haleemah\u2019s drawing or in my drawing\u201d&nbsp;<strong>[8:32]<\/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='6a1b2dc210a5b6002754434' value='6a1b2dc210a5b6002754434'><input type='hidden' id='bg-show-more-text-6a1b2dc210a5b6002754434' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc210a5b6002754434' value=' '><button id='bg-showmore-action-6a1b2dc210a5b6002754434' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc210a5b6002754434' ><\/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\" style=\"list-style-type:1\">\n<li><strong>[Pause the video at 1:29]<\/strong>&nbsp;Ask students to compare Amir\u2019s method to Nicole\u2019s method. Encourage them to consider what they notice that is similar across both methods as well as what is different.<\/li>\n\n\n\n<li><strong>[Pause the video at 4:00]<\/strong>\u00a0Display the equation (x \u2022 x) + (x \u2022 x) + x + (x \u2022 x) = x<sup>2<\/sup>\u00a0+ x \u2022 (x + 1) + x<sup>2<\/sup>. Ask students to discuss why this equation is true (or rephrase the teacher\u2019s question about why we can set the left side of Amir\u2019s equation equal to the left side of Nicole\u2019s equation).<\/li>\n\n\n\n<li><strong>[Pause the video at 8:27]<\/strong>&nbsp;Haleemah and ET have taken turns annotating the cobblestone pattern and explaining where in the picture they see each expression. Ask your students to discuss what they notice is alike in the annotations and what is 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='6a1b2dc210b150051060013' value='6a1b2dc210b150051060013'><input type='hidden' id='bg-show-more-text-6a1b2dc210b150051060013' value=' '><input type='hidden' id='bg-show-less-text-6a1b2dc210b150051060013' value=' '><button id='bg-showmore-action-6a1b2dc210b150051060013' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b2dc210b150051060013' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At the end of the video, ET says interpreting the x + 1 is difficult for both his drawing and Haleemah\u2019s drawing\u00a0<strong>[8:27]<\/strong>. Ask your students how they see x + 1 in either or both of the drawings.<\/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\"><\/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\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-6-teachers\/algebraic-expressions-lesson-6-episode-3-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\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-6-teachers\/algebraic-expressions-lesson-6-episode-5-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\" 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\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/\" style=\"background-color:#2d4059\">Teachers Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/\" style=\"background-color:#2d4059\">AlGeBraiC Expressions<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-6-teachers\/\" style=\"background-color:#2d4059\">Lesson 6<\/a><\/div>\n<\/div>\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. Haleemah and ET explore the equality between Amir and Nicole\u2019s methods by discussing the similarities and resolving the differences between the two methods. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":3940,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4187","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4187","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=4187"}],"version-history":[{"count":6,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4187\/revisions"}],"predecessor-version":[{"id":5322,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4187\/revisions\/5322"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3940"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=4187"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}