{"id":4104,"date":"2022-05-27T10:20:05","date_gmt":"2022-05-27T17:20:05","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=4104"},"modified":"2023-11-09T17:24:22","modified_gmt":"2023-11-10T01:24:22","slug":"algebraic-expressions-lesson-4-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-4-teachers\/algebraic-expressions-lesson-4-episode-6-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 4 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=\"XBsc4FF5brk\"><\/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=\"t3TMM7xIba4\"><\/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\/L4E6_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><a rel=\"noreferrer noopener\" href=\"https:\/\/www.geogebra.org\/m\/jtvdrvtx\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-484\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/geogebra.jpg\" alt=\"Link to Geogebra applet\"><\/a><a rel=\"noreferrer noopener\" href=\"https:\/\/www.geogebra.org\/m\/junhxd3q\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-484\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/geogebra.jpg\" alt=\"Link to Geogebra applet\"><\/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><\/p>\n\n\n\n<p>ET and Haleemah reflect on their generalized algebraic expression and think about what would happen if their variable,&nbsp;<em>v<\/em>, was a negative number.<\/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='69f62bffe8b220071997717' value='69f62bffe8b220071997717'><input type='hidden' id='bg-show-more-text-69f62bffe8b220071997717' value=' '><input type='hidden' id='bg-show-less-text-69f62bffe8b220071997717' value=' '><button id='bg-showmore-action-69f62bffe8b220071997717' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f62bffe8b220071997717' ><\/p>\n\n\n\n<p>Haleemah and ET use the equation L = 3 \u2022 v + 4 to determine that the end location of the scooter ride will be 19 meters, when the velocity is 5. They then examine a new equation, L = 3 \u2022 (\u2212v) + 4. When asked to predict what L will be if v = 5, they quickly state \u221219\u00a0<strong>[3:57]<\/strong>. This suggests they are encountering a common challenge when working with negative numbers and algebraic expressions. While the negative symbol can be productively thought of as \u201cthe opposite of\u201d (e.g., \u22127 is the opposite of 7 and \u2212(\u22124) is the opposite of \u22124), the inclusion of a negative symbol does not necessarily mean the opposite of an entire expression or functional output.<\/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='69f62bffe8ce21000077624' value='69f62bffe8ce21000077624'><input type='hidden' id='bg-show-more-text-69f62bffe8ce21000077624' value=' '><input type='hidden' id='bg-show-less-text-69f62bffe8ce21000077624' value=' '><button id='bg-showmore-action-69f62bffe8ce21000077624' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f62bffe8ce21000077624' ><\/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 2:31]<\/strong>\u00a0If you plan to use Supporting Dialogue Prompt #1 below, ask that before using this Focus Question. Haleemah says both equations are good, depending on \u201cif you have a negative number or if you have a positive number.\u201d ET says just one equation will work, since v is a variable and it can be any number and \u201cit doesn\u2019t matter if it\u2019s positive or negative yet.\u201d Ask your students who they agree with and why.<\/li>\n\n\n\n<li><strong>[Pause the video at 3:57]<\/strong>\u00a0Remind your students that 19 was the end location that Haleemah and ET found when v = 5 and they used the equation L = 3 \u2022 v + 4. Ask your students to make their own prediction for what L will be, using the new equation\u00a0L = 3 \u2022 (\u2212v) + 4 when v is 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='69f62bffe8e017010947601' value='69f62bffe8e017010947601'><input type='hidden' id='bg-show-more-text-69f62bffe8e017010947601' value=' '><input type='hidden' id='bg-show-less-text-69f62bffe8e017010947601' value=' '><button id='bg-showmore-action-69f62bffe8e017010947601' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f62bffe8e017010947601' ><\/p>\n\n\n\n<ol class=\"wp-block-list\" style=\"list-style-type:1\">\n<li>Early in the video, Haleemah seems to claim that you need both equations, L = 3 \u2022 v + 4 and L = 3 \u2022 (\u2212v) + 4 depending on whether you use positive or negative values for v\u00a0<strong>[1:47]<\/strong>. In contrast, ET claims that one equation is sufficient, namely L = 3 \u2022 v + 4\u00a0<strong>[2:19]<\/strong>. Ask your students to rephrase both Haleemah\u2019s and ET\u2019s arguments in their own words.<\/li>\n\n\n\n<li>Ask your students to discuss with each other why they think ET and Haleemah initially guessed L = \u221219 when replacing v with 5 in the equation L = 3 \u2022 (\u2212v) + 4. Encourage them to make an argument for why \u221219 is either a reasonable or an unreasonable guess.<\/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-4-teachers\/algebraic-expressions-lesson-4-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-7-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-4-teachers\/\" style=\"background-color:#2d4059\">Lesson 4<\/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. ET and Haleemah reflect on their generalized algebraic expression and think about what would happen if their variable,&nbsp;v, was a negative number. Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":3934,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4104","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4104","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=4104"}],"version-history":[{"count":7,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4104\/revisions"}],"predecessor-version":[{"id":5311,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4104\/revisions\/5311"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3934"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=4104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}