{"id":37,"date":"2014-05-08T09:26:19","date_gmt":"2014-05-08T16:26:19","guid":{"rendered":"http:\/\/www.base-ten.com\/tm\/?p=37"},"modified":"2014-05-08T09:44:31","modified_gmt":"2014-05-08T16:44:31","slug":"algebraic-thinking","status":"publish","type":"post","link":"http:\/\/www.base-ten.com\/tm\/algebraic-thinking\/","title":{"rendered":"Algebraic Thinking"},"content":{"rendered":"<p><a href=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/05\/alh-1a.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-39\" src=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/05\/alh-1a.jpg\" alt=\"alh-1a\" width=\"400\" height=\"266\" srcset=\"http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/05\/alh-1a.jpg 400w, http:\/\/www.base-ten.com\/tm\/wp-content\/uploads\/2014\/05\/alh-1a-300x199.jpg 300w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/p>\n<p>One of the most exciting things for 5th grade students is learning about algebra. They have been anticipating this subject for some time. What&#8217;s interesting is that they have been working with abstract mathematics forever, but it just isn&#8217;t often called algebra.<\/p>\n<p>When we ask: 5 x 5 = ?, this could be written 5 * 5 = X sometime early on in elementary school. This introduction to variables can be a huge stumbling block for many students. It&#8217;s really important to get comfortable with variables in mathematics early on. We can make this problem slightly more difficult by asking it another way.<\/p>\n<p>5 * X = 25 or finally 5X = 25 &#8211; now we&#8217;re doing simple algebra.<\/p>\n<p>This week we have been looking at <strong>systems of equations<\/strong> and solving for all of the variables. These are wonderful problems that help students get familiar with variables in equations.<\/p>\n<p>Here is a sampling of some of the problems we have worked on. Feel free to create some on your own. As long as you have a unique equation for each variable, there will be one and only one answer.<\/p>\n<p>A + B + C = 36<\/p>\n<p>A + A + B = 26<\/p>\n<p>B + B + B = 18<\/p>\n<p>The next problem we tried was<\/p>\n<p>2A + B + C = 48<\/p>\n<p>A + B + C = 40<\/p>\n<p>2B + A = 18<\/p>\n<p>At least one class tried this one<\/p>\n<p>2\/5A + B = 17<\/p>\n<p>A + B = 20<\/p>\n<p>And most challengingly some attempted the following<\/p>\n<p>2A + B + C = 30<\/p>\n<p>A + 2B + C = 35<\/p>\n<p>A + B + 2C = 37<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One of the most exciting things for 5th grade students is learning about algebra. They have been anticipating this subject for some time. What&#8217;s interesting is that they have been working with abstract mathematics forever, but it just isn&#8217;t often called algebra. When we ask: 5 x 5 = ?, this could be written 5 &hellip; <a href=\"http:\/\/www.base-ten.com\/tm\/algebraic-thinking\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Algebraic Thinking<\/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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4,1],"tags":[],"class_list":["post-37","post","type-post","status-publish","format-standard","hentry","category-math-content","category-thoughts"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p59e30-B","jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/posts\/37","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=37"}],"version-history":[{"count":3,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/posts\/37\/revisions"}],"predecessor-version":[{"id":41,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/posts\/37\/revisions\/41"}],"wp:attachment":[{"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/media?parent=37"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/categories?post=37"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.base-ten.com\/tm\/wp-json\/wp\/v2\/tags?post=37"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}