{"id":3963,"date":"2022-05-16T16:12:50","date_gmt":"2022-05-16T23:12:50","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=3963"},"modified":"2023-11-09T17:07:45","modified_gmt":"2023-11-10T01:07:45","slug":"algebraic-expressions-lesson-1-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-1-teachers\/algebraic-expressions-lesson-1-episode-3-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 1 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=\"o7Fn70jvZhY\"><\/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=\"PITaX1O2qrc\"><\/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 href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2022\/04\/L1E3_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>Haleemah and ET generalize their method and write an algebraic equation that shows the relationship between a border with any number of tiles on one side and the total number of tiles in the border.&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='69e24b49d6e5e3037301443' value='69e24b49d6e5e3037301443'><input type='hidden' id='bg-show-more-text-69e24b49d6e5e3037301443' value=' '><input type='hidden' id='bg-show-less-text-69e24b49d6e5e3037301443' value=' '><button id='bg-showmore-action-69e24b49d6e5e3037301443' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e24b49d6e5e3037301443' ><\/p>\n\n\n\n<p>Haleemah and ET initially write an equation with three variables: (x \u2022 2) + (y \u2022 2) = B\u00a0<strong>[2:09]<\/strong>. It can be challenging for students to recognize when one quantity is related to another, which means fewer variables will suffice. Later, Haleemah and ET realize that y = x \u2013 2\u00a0<strong>[6:12]<\/strong>. Then they are able to express their equation with just two variables: (x \u2022 2) + (x \u2013 2) \u2022 2 = B<strong>\u00a0[9:34]<\/strong>.<\/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='69e24b49d6f154000409782' value='69e24b49d6f154000409782'><input type='hidden' id='bg-show-more-text-69e24b49d6f154000409782' value=' '><input type='hidden' id='bg-show-less-text-69e24b49d6f154000409782' value=' '><button id='bg-showmore-action-69e24b49d6f154000409782' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e24b49d6f154000409782' ><\/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 2:09]<\/strong>\u00a0Haleemah has written the equation (x \u2022 2) + (y \u2022 2) = B, which contains three variables: x, y, and B. What do you think each variable means in the pool context?<\/li>\n\n\n\n<li><strong>[Pause the video at 5:04]<\/strong>\u00a0Are the variables x and y related? If so, how are they related? Turn and talk with a partner about how you might express one variable in terms of the other.<\/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='69e24b49d6fec9033713153' value='69e24b49d6fec9033713153'><input type='hidden' id='bg-show-more-text-69e24b49d6fec9033713153' value=' '><input type='hidden' id='bg-show-less-text-69e24b49d6fec9033713153' value=' '><button id='bg-showmore-action-69e24b49d6fec9033713153' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69e24b49d6fec9033713153' ><\/p>\n\n\n\n<ol class=\"wp-block-list\" style=\"list-style-type:1\">\n<li>Ask students to generalize their own methods and encourage them to express their generalizations by using an algebraic expression or equation.<\/li>\n\n\n\n<li>As you monitor students working, look for opportunities to push students to make clear any relationships between quantities they are using in their equations, particularly if they have used two variables or defined two quantities to describe the number of tiles in the border. Ask \u201cI see you have two variables here. What can you tell me about the relationship between these?\u201d or \u201cI\u2019m wondering how you might write this equation using only one variable to describe the number of tiles in the border.\u201d<\/li>\n<\/ol>\n\n\n\n<p class=\"has-medium-font-size\"><\/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\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-1-teachers\/algebraic-expressions-lesson-1-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-1-teachers\/algebraic-expressions-lesson-1-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-1-teachers\/\" style=\"background-color:#2d4059\">Lesson 1<\/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 generalize their method and write an algebraic equation that shows the relationship between a border with any number of tiles on one side and the total number of tiles [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":3918,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3963","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3963","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=3963"}],"version-history":[{"count":8,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3963\/revisions"}],"predecessor-version":[{"id":5294,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3963\/revisions\/5294"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3918"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=3963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}