{"id":5312,"date":"2018-02-28T12:38:12","date_gmt":"2018-02-28T19:38:12","guid":{"rendered":"https:\/\/blogs.ubc.ca\/stem2018\/?p=5312"},"modified":"2018-02-28T12:38:12","modified_gmt":"2018-02-28T19:38:12","slug":"misconceptions-over-combining-non-like-terms","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/stem2018\/2018\/02\/28\/misconceptions-over-combining-non-like-terms\/","title":{"rendered":"Misconceptions over combining non-like terms."},"content":{"rendered":"

One of the most common misconceptions for students new to algebra occurs in simplifying and evaluating algebraic expressions, that is the idea that 5x+4 equals 9x. It is understandable how students might simplify this expression based on their prior knowledge of adding integers, but once again they fail to recognise x as a variable term. Since the second term only has a numeric part, 5x and 4 are not like terms, and so they cannot be combined into a single term. Even higher-level algebra students make this mistake, it is not uncommon to see the expression 3x2<\/sup>+4x3<\/sup> simplified to 7x5<\/sup> rather than recognising that these terms cannot be combined since they have different exponents. I came across a simulation on PhET<\/a> that would help to addressing this issue. Following is a suggested pedagogical approach using a graphic that depict the cyclical nature of GEM and its phases,<\/p>\n

\"\"<\/p>\n

Generate relationship<\/strong> \u2013 the students will generate pictorial representation of algebraic expressions using the simulation on PhET<\/a>. They will use different representation such as circles, triangles, and coins to generate graphical expressions. The aim is to have them categorise items and generate expressions such as \"\". Then generate the relationship between the variables in occurrence bananas and apples in this expression, the students should generate an idea on how to simplify it to \"\".<\/p>\n

Evaluate relationship<\/strong> \u2013 the students will replace variables in pictorial representations with variables such as x, y, or z. They will then evaluate the expression, comparing their results with the pictorial representation. They are expected to produce x+y+y+y+x+x+x equals 4x+3y and establish an analogy with what they have done in the previous step.<\/p>\n

Modify relationships<\/strong> \u2013 the students are also encouraged to substitute a random value in for any variables. In this case, x will have a random value, and y will have a different random value. They will evaluate and see whether the algebraic expressions are equivalent or not.<\/p>\n

Reference:<\/p>\n

Khan, S. (2011). New pedagogies on teaching science with computer simulations.\u00a0Journal of Science Education and Technology<\/em>,\u00a020<\/em>(3), 215-232.<\/p>\n

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One of the most common misconceptions for students new to algebra occurs in simplifying and evaluating algebraic expressions, that is the idea that 5x+4 equals 9x. It is understandable how students might simplify this expression based on their prior knowledge of adding integers, but once again they fail to recognise x as a variable term. […]<\/p>\n","protected":false},"author":53876,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1669392],"tags":[],"class_list":["post-5312","post","type-post","status-publish","format-standard","hentry","category-b-t-gem"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/5312","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/users\/53876"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/comments?post=5312"}],"version-history":[{"count":1,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/5312\/revisions"}],"predecessor-version":[{"id":5318,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/posts\/5312\/revisions\/5318"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/media?parent=5312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/categories?post=5312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2018\/wp-json\/wp\/v2\/tags?post=5312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}