{"id":642,"date":"2017-05-01T08:57:45","date_gmt":"2017-05-01T15:57:45","guid":{"rendered":"http:\/\/blogs.bend.k12.or.us\/blspd\/?p=642"},"modified":"2017-06-19T20:09:13","modified_gmt":"2017-06-20T03:09:13","slug":"equivalence-through-properties-of-operations","status":"publish","type":"post","link":"https:\/\/blogs.bend.k12.or.us\/blspd\/equivalence-through-properties-of-operations\/","title":{"rendered":"Equivalence Through Properties of Operations"},"content":{"rendered":"<div class=\"page\" title=\"Page 1\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p><strong>Equivalence Through Properties of Operations<\/strong><\/p>\n<p><strong>August 7-9, 2017, 8:30-4:00<\/strong><\/p>\n<p>This seminar focuses on equivalence through properties of operations \u2013 mathematical ideas that are a foundation for algebraic thinking in elementary school mathematics.As a participant, you will deepen your knowledge of these mathematical ideas, their trajectory across time, and the pedagogy that supports student understanding of the ideas.<\/p>\n<p>For example, you will explore:<\/p>\n<div class=\"page\" title=\"Page 1\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<ul>\n<li>\u0084 the meanings of the properties of operations, the role the properties play in the creation of equivalent expressions, and the use of those expressions to invent and understand computational strategies<\/li>\n<li>\u0084 the concept of equivalence and its progression from numerical expressions to algebraic expressions to representing situations and solving equations<\/li>\n<li>\u0084instructional approaches that focus on \u2013\n<ul>\n<li>understanding students\u2019 mathematical thinking (their unique and common conceptions)<\/li>\n<li>developing conceptual understanding (to enable uency, retention, and continued learning)<\/li>\n<li>eliciting and analyzing student justifications and generalizations, and key other mathematical habits of mind that enable justifying and generalizing<\/li>\n<li>facilitating productive struggle (a central element of high-cognitive engagement and learning)<\/li>\n<\/ul>\n<\/li>\n<li>Your mathematical explorations of equivalence through the properties of operations will be situated in the mathematical work of teaching and will emphasize the content teachers need to know.You and colleagues will:\u0084\n<ul>\n<li>&#8220;Do Math&#8221; together<\/li>\n<li>Analyze short professional readings<\/li>\n<li>Create, critique, and debate different representations<\/li>\n<li>Consider ways that specific representations enable student understanding<\/li>\n<li>Experience research-based, mathematically productive teaching practice.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><em>Portland State Graduate Credits will be available.<\/em><\/p>\n<p><em>Contact Kerry Morton at kerry.morton@bend.k12.or.us with any questions.<\/em><\/p>\n<p><em>Register on PD Place:<\/em><\/p>\n<p><a href=\"https:\/\/pdplace.bend.k12.or.us\/index.php?page=course\/class_detail.php&amp;zk_class_p=1455&amp;search=0\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-16 size-full\" src=\"http:\/\/blogs.bend.k12.or.us\/blspd\/files\/2016\/05\/PD-Place.png\" alt=\"\" width=\"236\" height=\"85\" \/><\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><span style=\"text-indent: 20px;width: auto;padding: 0px 4px 0px 0px;text-align: center;font: bold 11px\/20px 'Helvetica Neue',Helvetica,sans-serif;color: #ffffff;background: #bd081c no-repeat scroll 3px 50% \/ 14px 14px;cursor: pointer\">Save<\/span><\/p>\n<p><span style=\"text-indent: 20px;width: auto;padding: 0px 4px 0px 0px;text-align: center;font: bold 11px\/20px 'Helvetica Neue',Helvetica,sans-serif;color: #ffffff;background: #bd081c  no-repeat scroll 3px 50% \/ 14px 14px;cursor: pointer\">Save<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Equivalence Through Properties of Operations August 7-9, 2017, 8:30-4:00 This seminar focuses on equivalence through properties of operations \u2013 mathematical ideas that are a foundation for algebraic thinking in elementary school mathematics.As a participant, you will deepen your knowledge of &hellip; <a href=\"https:\/\/blogs.bend.k12.or.us\/blspd\/equivalence-through-properties-of-operations\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":425,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[33757,32812,3852,34997],"tags":[],"class_list":["post-642","post","type-post","status-publish","format-standard","hentry","category-elementary-k-5","category-mathematics","category-middle-school","category-summer-2017"],"_links":{"self":[{"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/posts\/642","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/users\/425"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/comments?post=642"}],"version-history":[{"count":3,"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/posts\/642\/revisions"}],"predecessor-version":[{"id":735,"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/posts\/642\/revisions\/735"}],"wp:attachment":[{"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/media?parent=642"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/categories?post=642"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.bend.k12.or.us\/blspd\/wp-json\/wp\/v2\/tags?post=642"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}