{"id":155,"date":"2014-12-10T12:42:52","date_gmt":"2014-12-10T20:42:52","guid":{"rendered":"http:\/\/www.base-ten.com\/tm\/?p=155"},"modified":"2014-12-11T15:18:38","modified_gmt":"2014-12-11T23:18:38","slug":"shape-classification","status":"publish","type":"post","link":"http:\/\/www.base-ten.com\/tm\/shape-classification\/","title":{"rendered":"Shape Classification"},"content":{"rendered":"<p><a href=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/12\/image001.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-154\" src=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/12\/image001.png\" alt=\"image001\" width=\"366\" height=\"331\" srcset=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/12\/image001.png 366w, http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/12\/image001-300x271.png 300w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><\/a>This month we are working on classifying quadrilaterals. Creating these overlapping hierarchies is\u00a0 always a challenge. Relationships that work one way, don&#8217;t work the other way, and there is a lot of specific vocabulary that needs to be learned and applied in novel situations.<\/p>\n<p>It&#8217;s a little like this: everyone who lives in Olympia lives in Washington, but not everyone who lives in Washington lives in Olympia. Bringing it back to the shapes &#8211; all squares are rectangles, but not all rectangles are squares.<\/p>\n<p>To do this work, we need to know the defining characteristics of the quadrilaterals that we are classifying &#8211; and here we run into yet another difficulty&#8230; mathematicians don&#8217;t always agree on these! But the work of classification goes on. We just learn the specific characteristics and create the relationships accordingly. Here is a table that tries to communicate these overlapping relationships.<\/p>\n<p><a href=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/12\/quads-3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-165\" src=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/12\/quads-3.png\" alt=\"quads-3\" width=\"444\" height=\"412\" srcset=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/12\/quads-3.png 444w, http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/12\/quads-3-300x278.png 300w\" sizes=\"auto, (max-width: 444px) 100vw, 444px\" \/><\/a>Under the inclusive definition of trapezoids, all six shapes a the top of this post are trapezoids, under the exclusive definition only three of them are&#8230; can you spot them?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This month we are working on classifying quadrilaterals. Creating these overlapping hierarchies is\u00a0 always a challenge. Relationships that work one way, don&#8217;t work the other way, and there is a lot of specific vocabulary that needs to be learned and applied in novel situations. It&#8217;s a little like this: everyone who lives in Olympia lives &hellip; <a href=\"http:\/\/www.base-ten.com\/tm\/shape-classification\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Shape Classification<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4,8],"tags":[],"class_list":["post-155","post","type-post","status-publish","format-standard","hentry","category-math-content","category-curricula"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p59e30-2v","jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/posts\/155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/comments?post=155"}],"version-history":[{"count":3,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/posts\/155\/revisions"}],"predecessor-version":[{"id":167,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/posts\/155\/revisions\/167"}],"wp:attachment":[{"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/media?parent=155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/categories?post=155"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/tags?post=155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}