{"id":4042,"date":"2022-05-27T09:36:59","date_gmt":"2022-05-27T16:36:59","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=4042"},"modified":"2023-11-09T17:17:50","modified_gmt":"2023-11-10T01:17:50","slug":"algebraic-expressions-lesson-3-episode-3-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-3-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 3 Episode 3 (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<div class=\"youtube-player\" data-id=\"mePVgewTHvw\"><\/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=\"_g2AyfEsRvc\"><\/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\/2022\/04\/L3E3_Algebra_Student_Worksheet.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><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> <a rel=\"noreferrer noopener\" href=\"https:\/\/www.online-calculator.com\/\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-485\" style=\"width: 150px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/calculator.jpg\" alt=\"Link to on-line calculator\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The students generalize their method and write an algebraic equation that shows the relationship between the cost per game and the total amount spent by the friends.&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='6a152f956140b2085839134' value='6a152f956140b2085839134'><input type='hidden' id='bg-show-more-text-6a152f956140b2085839134' value=' '><input type='hidden' id='bg-show-less-text-6a152f956140b2085839134' value=' '><button id='bg-showmore-action-6a152f956140b2085839134' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a152f956140b2085839134' ><\/p>\n\n\n\n<ol class=\"wp-block-list\" style=\"list-style-type:1\">\n<li>When asked to check their equation, ET replaces the variable <em>c<\/em> with the number 2, but initially writes 32 instead of 3 \u2022 2&nbsp;<strong>[5:40]<\/strong>. He resolves this challenge with seemingly little effort, but it points to a potential obstacle your students might need to overcome. The use of juxtaposition for multiplication with non-numerical symbols is a&nbsp;<em>convention<\/em> that&nbsp;is widely used in algebra and beyond. You may want to explain this convention to your students as you view this video.<\/li>\n\n\n\n<li>One challenge your students might encounter that ET and Haleemah did not, is using letters incorrectly as labels or abbreviations. For example, when trying to use algebraic symbols to quantify the total amount of money spent by Danyal, students might think \u201cDanyal bought 3 apps, and I need a variable in here, so it must be 3d, where d stands for Danyal.\u201d Be on the lookout for expressions that might indicate students are replacing words directly with letters (for example, 2s where s stands for Suado, rather than the cost per app). To help students overcome this challenge, ask them to be explicit, as ET and Haleemah are, with writing out exactly what each variable represents in the context.\u00a0<\/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='6a152f95614f88026573261' value='6a152f95614f88026573261'><input type='hidden' id='bg-show-more-text-6a152f95614f88026573261' value=' '><input type='hidden' id='bg-show-less-text-6a152f95614f88026573261' value=' '><button id='bg-showmore-action-6a152f95614f88026573261' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a152f95614f88026573261' ><\/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 3:45]<\/strong>&nbsp;Ask your students \u201cWhat do you think Haleemah means when she said she used the numbers they were given?\u201d Which numbers does she mean, and what might she mean by saying they were \u201cgiven those numbers?\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\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a152f95615533082193924' value='6a152f95615533082193924'><input type='hidden' id='bg-show-more-text-6a152f95615533082193924' value=' '><input type='hidden' id='bg-show-less-text-6a152f95615533082193924' value=' '><button id='bg-showmore-action-6a152f95615533082193924' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a152f95615533082193924' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>[Pause the video at 5:20]&nbsp;<\/strong>Say to your students, \u201cBefore we see how Haleemah and ET test their equation, how would you test their equation? Turn and tell your partner what you might to do to see if the equation works. After you each have shared, pick a testing method and try it.\u201d Afterwards, let them compare their work with the work of ET and Haleemah.<\/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-3-teachers\/algebraic-expressions-lesson-3-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\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-3-teachers\/algebraic-expressions-lesson-3-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\" 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>Exploring No captions CaptionsStop the video above first if it is playing. No captions CaptionsStop the video above first if it is playing. The students generalize their method and write an algebraic equation that shows the relationship between the cost per game and the total amount spent by the friends.&nbsp; Episode Supports Students\u2019 Conceptual Challenges [&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-4042","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4042","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=4042"}],"version-history":[{"count":10,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4042\/revisions"}],"predecessor-version":[{"id":5304,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4042\/revisions\/5304"}],"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=4042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}