{"id":4012,"date":"2022-05-26T13:08:41","date_gmt":"2022-05-26T20:08:41","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=4012"},"modified":"2023-11-09T17:13:46","modified_gmt":"2023-11-10T01:13:46","slug":"algebraic-expressions-lesson-2-episode-4-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-4-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 2 Episode 4 (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=\"XfrubmnyY1g\"><\/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=\"LY7kZupz29M\"><\/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\/L2E4_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> <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The students work to explain what each symbol in their equation means in the pool context<strong>.&nbsp;<\/strong>&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='6a3c3c0b98d647049181566' value='6a3c3c0b98d647049181566'><input type='hidden' id='bg-show-more-text-6a3c3c0b98d647049181566' value=' '><input type='hidden' id='bg-show-less-text-6a3c3c0b98d647049181566' value=' '><button id='bg-showmore-action-6a3c3c0b98d647049181566' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3c3c0b98d647049181566' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Haleemah and ET seem to have slightly different ideas of what multiplication means. For example, when asked what 10 times 4 means, Haleemah says \u201cten groups of four\u201d and then \u201cor four groups of ten,\u201d <strong>[3:37]<\/strong>, but ET says he thinks it\u2019s the latter. At&nbsp;<strong>[5:04]<\/strong>&nbsp;Haleemah says that 40 (the result of 10 \u2022 4) is \u201cthe number of tiles on the border and the corners being&nbsp;<em>multiplied<\/em>&nbsp;twice\u201d while ET says he doesn\u2019t think they are multiplying them, instead they \u201care just&nbsp;<em>adding or counting<\/em>&nbsp;them one more time than we need to be.\u201d In both instances, both students are correct, but seem unsure of the other\u2019s ideas about multiplication.<\/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='6a3c3c0b98e026034764068' value='6a3c3c0b98e026034764068'><input type='hidden' id='bg-show-more-text-6a3c3c0b98e026034764068' value=' '><input type='hidden' id='bg-show-less-text-6a3c3c0b98e026034764068' value=' '><button id='bg-showmore-action-6a3c3c0b98e026034764068' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3c3c0b98e026034764068' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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 0:58]<\/strong>&nbsp;Before Haleemah and ET connect their equation to the diagram, ask students to do the same. Prompt students to visualize where they see (a) the 10, (b) the 10 \u2022 4, and (c) the \u20134. Ask for volunteers to circle or point out each of these on a pool diagram and ask the class if they agree or disagree and why.<\/li>\n\n\n\n<li><strong>[Pause the video at 3:36]<\/strong>&nbsp;Pose the same questions from the video to your students: What does multiplication means here in the pool context? What is 10 times 4? Press students to be explicit about this, and notice when both 10 groups of 4 and 4 groups of 10 are mentioned. You can have a discussion about if those are equal and if one or both are appropriate or not for this given context.<\/li>\n\n\n\n<li><strong>[Pause the video at 9:30]<\/strong>\u00a0Ask your students to consider the general case, in which there are x tiles on one side of the pool. Prompt them to discuss connections between the equation and the diagram, including where they see x, 4x, and the minus 4 from ET and Haleemah\u2019s equation.<\/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\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a3c3c0b98eb83033835802' value='6a3c3c0b98eb83033835802'><input type='hidden' id='bg-show-more-text-6a3c3c0b98eb83033835802' value=' '><input type='hidden' id='bg-show-less-text-6a3c3c0b98eb83033835802' value=' '><button id='bg-showmore-action-6a3c3c0b98eb83033835802' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a3c3c0b98eb83033835802' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you pose Focus Question 2, when students provide an explanation for what multiplication means, first ask \u201cWhy do you think that?\u201d Afterwards, ask for other students to restate what they heard in their own words.<\/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-2-teachers\/algebraic-expressions-lesson-2-episode-3-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-1-teachers\/\">Lesson 3 Episode 1<\/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>Reflecting No captions CaptionsStop the video above first if it is playing. No captions CaptionsStop the video above first if it is playing. The students work to explain what each symbol in their equation means in the pool context.&nbsp;&nbsp; Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/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-4012","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4012","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=4012"}],"version-history":[{"count":9,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4012\/revisions"}],"predecessor-version":[{"id":5300,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4012\/revisions\/5300"}],"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=4012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}