{"id":3989,"date":"2022-05-26T12:25:17","date_gmt":"2022-05-26T19:25:17","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=3989"},"modified":"2023-11-07T10:39:37","modified_gmt":"2023-11-07T18:39:37","slug":"algebraic-expressions-lesson-2-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-2-teachers\/algebraic-expressions-lesson-2-episode-1-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 2 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=\"XhyqYSQWT7s\"><\/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=\"I1YJJHrtBpg\"><\/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\/L2E1_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\">ET and Haleemah make sense of their previous solution and think of a way to correct their answer, creating a new method for finding the number of tiles in the border of the pool.&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 wp-block-paragraph\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='6a1b0c5f40aa13095035039' value='6a1b0c5f40aa13095035039'><input type='hidden' id='bg-show-more-text-6a1b0c5f40aa13095035039' value=' '><input type='hidden' id='bg-show-less-text-6a1b0c5f40aa13095035039' value=' '><button id='bg-showmore-action-6a1b0c5f40aa13095035039' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b0c5f40aa13095035039' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Haleemah struggles to write a new equation for the number of tiles in the border of a pool with a side length of 10. Quantifying the information from the diagram can be tricky, and Haleemah initially writes 10 \u2022 10 to symbolize counting all four sides (with double counting of the corners)&nbsp;<strong>[2:11]<\/strong>. She also seems unsure about how to account for the double counting, and after writing \u201c\u2013 4\u201d she says she is confused about the equation<strong>&nbsp;[3:01]<\/strong>.<\/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\">Focus Questions <input type='hidden' bg_collapse_expand='6a1b0c5f40b718052858327' value='6a1b0c5f40b718052858327'><input type='hidden' id='bg-show-more-text-6a1b0c5f40b718052858327' value=' '><input type='hidden' id='bg-show-less-text-6a1b0c5f40b718052858327' value=' '><button id='bg-showmore-action-6a1b0c5f40b718052858327' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b0c5f40b718052858327' ><\/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 3:57]<\/strong>&nbsp;Recall from the first lesson that Haleemah and ET initially guessed that there would be 40 tiles in the border of the pool. Now, ET and Haleemah have written the equation (10 \u2022 4) \u2013&nbsp;4 = 36, which is the number of tiles in the border of a pool with 10 tiles on a side. Why does subtracting four work here? Would that always work for any pool? Why or why not?<\/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='6a1b0c5f40bf30003582606' value='6a1b0c5f40bf30003582606'><input type='hidden' id='bg-show-more-text-6a1b0c5f40bf30003582606' value=' '><input type='hidden' id='bg-show-less-text-6a1b0c5f40bf30003582606' value=' '><button id='bg-showmore-action-6a1b0c5f40bf30003582606' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a1b0c5f40bf30003582606' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ask students to compare their work with ET and Haleemah\u2019s work by talking with a partner. Encourage them to discuss what each part of their equation means, like Haleemah and ET did in this episode. For example, what in the diagram or context is represented by the 10 in the equation? The \u201ctimes four\u201d? The \u201cminus four\u201d? If there are differences in your students\u2019 work and the work of Haleemah and ET, ask your students to determine if each difference is mathematically significant. For example, are parentheses required in (10 \u2022 4) \u2013&nbsp;4? Does the order of these numbers matter, and if so, how?<\/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-1-teachers\/algebraic-expressions-lesson-1-episode-5-teachers\/\">Lesson 1 Episode 5<\/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-2-teachers\/algebraic-expressions-lesson-2-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-2-teachers\/\" style=\"background-color:#2d4059\">Lesson 2<\/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 their previous solution and think of a way to correct their answer, creating a new method for finding the number of tiles in the border [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":3925,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3989","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3989","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=3989"}],"version-history":[{"count":9,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3989\/revisions"}],"predecessor-version":[{"id":5238,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3989\/revisions\/5238"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3925"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=3989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}