{"id":760,"date":"2024-07-25T01:52:04","date_gmt":"2024-07-25T01:52:04","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=760"},"modified":"2024-09-30T11:34:35","modified_gmt":"2024-09-30T11:34:35","slug":"esp-module-2-algebraic-equivalence","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-2-algebraic-equivalence\/","title":{"rendered":"ESP_AF Module 2-Algebraic Equivalence"},"content":{"rendered":"\n

Examining Students’ Practices in Algebra and Function<\/a> > Module 2<\/p>\n\n\n\n

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ESP_AF Module 2-Algebraic Equivalence<\/h2><\/div>\n<\/div>\n<\/div>\n\n\n\n
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This module uses two different technologies, polypad virtual algebra tiles and CAS, to explore completing the square. Teachers will examine students using both technologies to build a conceptual understanding of the procedure for completing the square and compare and contrast the affordances of each approach. Teachers will build on their understanding of noticing student thinking on technology-enhanced tasks and practice posing purposeful questions.<\/p>\n<\/div>

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This module could be used alongside a chapter from Teaching Algebra materials:<\/p>\n\n\n\n

Chapter 4:<\/strong><\/a> Equivalence and Equality<\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n

Overview Documents<\/strong><\/h3>\n\n\n\n
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Read the Overview Document<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n

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How to Read a Module Overview Document<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n

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Download All Materials<\/a><\/strong><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

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Module Elements<\/strong><\/h3>\n<\/div>\n\n\n\n
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2.1 Completing the Square with Algebra Tiles<\/strong>

Teachers will engage with a Desmos Activity in which they use virtual algebra tiles to determine a generalized procedure for completing the square
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Instructor Materials<\/strong><\/a>
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2.2 Completing the Square with CAS<\/strong>

Teachers will engage with an activity that uses Geogebra\u2019s CAS tools to determine a generalized procedure for completing the square<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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2.3 Noticing Student Thinking: Completing the Square with Virtual Algebra Tiles<\/strong>

Teachers engage with noticing one pair of students\u2019 mathematical thinking as they are making sense of completing the square with virtual algebra tiles.
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Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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2.4 Posing Purposeful Questions: Completing the Square with Virtual Algebra Tiles<\/strong>

Teachers practice posing purposeful assessing and advancing questions to pairs of students who have used virtual algebra tiles differently to model the same expression.<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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2.5 Noticing Student Thinking: Completing the Square with CAS<\/strong>

Teachers practice noticing student thinking and posing purposeful assessing and advancing questions, for a pair of students who are using a CAS to develop an understanding of completing the square.<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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Examining Students’ Practices in Algebra and Function > Module 2 This module uses two different technologies, polypad virtual algebra tiles and CAS, to explore completing the square. Teachers will examine students using both technologies to build a conceptual understanding of the procedure for completing the square and compare and contrast the affordances of each approach. […]<\/p>\n","protected":false},"author":66,"featured_media":230,"parent":313,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"test-blank-page","meta":{"_acf_changed":false,"ncst_custom_author":"","ncst_show_custom_author":false,"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-760","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/760","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/comments?post=760"}],"version-history":[{"count":19,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/760\/revisions"}],"predecessor-version":[{"id":1854,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/760\/revisions\/1854"}],"up":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/313"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media\/230"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}