{"id":4062,"date":"2022-05-27T09:48:23","date_gmt":"2022-05-27T16:48:23","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=4062"},"modified":"2023-11-09T17:20:02","modified_gmt":"2023-11-10T01:20:02","slug":"algebraic-expressions-lesson-3-episode-6-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-3-teachers\/algebraic-expressions-lesson-3-episode-6-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 3 Episode 6 (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=\"youtube-player\" data-id=\"k8iAoTh5zOw\"><\/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=\"youtube-player\" data-id=\"RvmJVAgs4wo\"><\/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><a rel=\"noreferrer noopener\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2022\/04\/L3E6_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>Haleemah and ET work to explain why the two methods are equal by explaining what each part of their equations mean in the gaming app context.&nbsp;&nbsp;&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\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='69e222bbb7f855027057104' value='69e222bbb7f855027057104'><input type='hidden' id='bg-show-more-text-69e222bbb7f855027057104' value=' '><input type='hidden' id='bg-show-less-text-69e222bbb7f855027057104' value=' '><button id='bg-showmore-action-69e222bbb7f855027057104' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e222bbb7f855027057104' ><\/p>\n\n\n\n<p>In this episode, we see evidence of a conceptual challenge that ET has worked to overcome. Extending one\u2019s understanding of arithmetic to algebraic expressions is challenging, and ET gives voice to this challenge when he says \u201cWhen you think of addition, you think of a total sum; you don\u2019t think of a total sum with a variable with all possible outcomes\u201d&nbsp;<strong>[7:48]<\/strong>. This is similar to when Haleemah was working to see (3 \u2022 2) simultaneously as something to compute and as an entity in Episode 1 of this lesson.<\/p>\n\n\n\n<p><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Focus Questions <input type='hidden' bg_collapse_expand='69e222bbb804a0043896062' value='69e222bbb804a0043896062'><input type='hidden' id='bg-show-more-text-69e222bbb804a0043896062' value=' '><input type='hidden' id='bg-show-less-text-69e222bbb804a0043896062' value=' '><button id='bg-showmore-action-69e222bbb804a0043896062' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e222bbb804a0043896062' ><\/p>\n\n\n\n<p>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 1:15 and again at 4:36]<\/strong>&nbsp;Haleemah and ET will describe what various parts of their equations represent in the context of the apps. This is the work of reasoning abstractly and quantitatively\u2014they are contextualizing the symbols in the equation by describing the quantities those symbols represent and the relationships between them. Before your students watch these clips, ask them to contextualize the same symbols and then compare their answers with ET and Haleemah\u2019s.&nbsp;<\/li>\n\n\n\n<li><strong>[Pause the video at 3:47]<\/strong>\u00a0ET and Haleemah have shown that when the cost of an app is $5, both expressions, (3 \u2022 5) + (2 \u2022 5) + (4 \u2022 5) and 9 \u2022 5, yield the same total cost, $45. Ask students to discuss how that might help them see why the two expressions are equal, that is (3 \u2022 5) + (2 \u2022 5) + (4 \u2022 5) = 9 \u2022 5. Follow up by asking them if the expressions are equal even if they don\u2019t calculate each of the expressions. Push them to explain their reasoning. Highlight any comments that include ideas about the distributive property or that utilize\u00a0<em>groups of<\/em>\u00a0language (e.g., 3 groups of 5 and 2 groups of 5 and 4 groups of 5 is really just 9 groups of 5).<\/li>\n<\/ol>\n\n\n\n<p><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Supporting Dialogue <input type='hidden' bg_collapse_expand='69e222bbb817a1052432512' value='69e222bbb817a1052432512'><input type='hidden' id='bg-show-more-text-69e222bbb817a1052432512' value=' '><input type='hidden' id='bg-show-less-text-69e222bbb817a1052432512' value=' '><button id='bg-showmore-action-69e222bbb817a1052432512' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e222bbb817a1052432512' ><\/p>\n\n\n\n<ol class=\"wp-block-list\" style=\"list-style-type:1\">\n<li>To interpret 3 \u2022 5 as an entity, Haleemah says \u201c15 is the amount of money spent\u201d and asks ET if he agrees. He says he does, but then pushes for specificity by suggesting that they add \u201cit\u2019s the amount spent by Danyal\u201d&nbsp;<strong>[1:35<\/strong>]. Ask your students to review each other\u2019s descriptions of the symbols in their equation and give suggestions for making them more precise.<\/li>\n\n\n\n<li>After ET explains why contextualizing each equation helps him understand why they are equivalent, pause the video&nbsp;<strong>[8:25].<\/strong>&nbsp;Ask your students to consider what ET said and try to put it into their own words. Ask them what else they would like to add, or if they are thinking about it differently from ET.&nbsp;<\/li>\n<\/ol>\n\n\n\n<p> <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><\/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-3-teachers\/algebraic-expressions-lesson-3-episode-5-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-4-teachers\/algebraic-expressions-lesson-4-episode-1-teachers\/\">Lesson 4 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\" 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-3-teachers\/\" style=\"background-color:#2d4059\">Lesson 3<\/a><\/div>\n<\/div>\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. Haleemah and ET work to explain why the two methods are equal by explaining what each part of their equations mean in the gaming app context.&nbsp;&nbsp;&nbsp;&nbsp; Episode Supports Students\u2019 Conceptual Challenges Focus [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":3929,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4062","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4062","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=4062"}],"version-history":[{"count":9,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4062\/revisions"}],"predecessor-version":[{"id":5307,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4062\/revisions\/5307"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3929"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=4062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}