{"id":4169,"date":"2022-05-27T12:44:17","date_gmt":"2022-05-27T19:44:17","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=4169"},"modified":"2023-11-09T17:30:42","modified_gmt":"2023-11-10T01:30:42","slug":"algebraic-expressions-lesson-6-episode-1-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-1-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 6 Episode 1 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Making Sense<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n<div class=\"youtube-player\" data-id=\"8R7vNZsepF4\"><\/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=\"gGTidfb3HpM\"><\/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\/L6E1_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>ET and Haleemah make sense of Nicole\u2019s algebraic and arithmetic equations and create a drawing that they believe describes how she was seeing the pattern.<\/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='69f596b8d126d4050885275' value='69f596b8d126d4050885275'><input type='hidden' id='bg-show-more-text-69f596b8d126d4050885275' value=' '><input type='hidden' id='bg-show-less-text-69f596b8d126d4050885275' value=' '><button id='bg-showmore-action-69f596b8d126d4050885275' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b8d126d4050885275' ><\/p>\n\n\n\n<p>When analyzing a rectangular array of rows and columns of stones, the number of stones in one row also determines the number of columns in the array. ET and Haleemah seem to struggle with this idea, notably when ET describes one value in Amir\u2019s equation as representing the number of columns as being different from the same value in Nicole\u2019s equation, which he sees as representing the number of stones in a row&nbsp;<strong>[3:20]<\/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='69f596b8d12ff9045708842' value='69f596b8d12ff9045708842'><input type='hidden' id='bg-show-more-text-69f596b8d12ff9045708842' value=' '><input type='hidden' id='bg-show-less-text-69f596b8d12ff9045708842' value=' '><button id='bg-showmore-action-69f596b8d12ff9045708842' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b8d12ff9045708842' ><\/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 1:52]<\/strong>\u00a0Ask your students to examine Nicole\u2019s equation, x<sup>2<\/sup>\u00a0+ x \u2022 (x + 1) + x<sup>2<\/sup>\u00a0= T. Ask them what they think about this equation and how Nicole might have been viewing the picture of the cobblestone pattern when she created this equation.<\/li>\n\n\n\n<li><strong>[Pause the video at 3:50]<\/strong>&nbsp;ET describes the 3<sup>2<\/sup>&nbsp;as meaning \u201cthree times three\u201d and says the first three represents the three stones in one column while the second three represents the three stones in one row. Ask your students how they see the 3<sup>2<\/sup>&nbsp;in the diagram, and if they agree or disagree with how ET is seeing each 3.<\/li>\n\n\n\n<li><strong>[Pause the video at 5:28]<\/strong>&nbsp;Haleemah says that she sees 3 \u2022 4 by thinking about base times height. Ask your students what they think Haleemah means. Follow up this question by asking how thinking about base times height might help ET better see how the two methods (Amir\u2019s and Nicole\u2019s) are similar.<\/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='69f596b8d13e45098458662' value='69f596b8d13e45098458662'><input type='hidden' id='bg-show-more-text-69f596b8d13e45098458662' value=' '><input type='hidden' id='bg-show-less-text-69f596b8d13e45098458662' value=' '><button id='bg-showmore-action-69f596b8d13e45098458662' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69f596b8d13e45098458662' ><\/p>\n\n\n\n<p>After watching the episode, ask your students to use the \u201cgroups of\u201d language (featured at the end, starting at&nbsp;<strong>8:11<\/strong>), to describe the number of gray stones in the second section. You can anticipate that some students might see four groups of three by attending to the number of columns and stones per column, or they might see three groups of 4 by attending to the number of rows and stones per row. Encourage discussion by asking if these two ways of seeing the second section yield the same number of stones, which is a concrete way to discuss the commutative property of multiplication.<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><\/div><\/p>\n\n\n\n<p><\/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-5-teachers\/algebraic-expressions-lesson-5-episode-6-teachers\/\">Lesson 5 Episode 6<\/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-2-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>Making Sense 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 make sense of Nicole\u2019s algebraic and arithmetic equations and create a drawing that they believe describes how she was seeing the pattern. Episode Supports Students\u2019 Conceptual Challenges Focus [&hellip;]<\/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-4169","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4169","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=4169"}],"version-history":[{"count":9,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4169\/revisions"}],"predecessor-version":[{"id":5318,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4169\/revisions\/5318"}],"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=4169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}