{"id":1542,"date":"2017-02-22T18:00:57","date_gmt":"2017-02-23T01:00:57","guid":{"rendered":"https:\/\/blogs.ubc.ca\/stem2017\/?p=1542"},"modified":"2017-02-27T11:02:36","modified_gmt":"2017-02-27T18:02:36","slug":"1542","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/stem2017\/2017\/02\/22\/1542\/","title":{"rendered":"T-GEM"},"content":{"rendered":"

Challenging Concept: Integers<\/strong><\/span><\/p>\n

I teach grade 6s and 7s and integers is a common concept in math my students struggle with. Particularly, when dealing with negative integers. This includes adding, subtracting, multiplying and dividing with negative integers. Specifically, my students have had difficulties with understanding that adding a negative integer makes a number less positive and that subtracting a negative integer makes a number more positive. Though we go over the rules of integers, I have seen significant students experience difficulty with the concept. I have also utilized metaphors such as thinking of negative integers as \u201cunhappy things\u201d and positive integers as \u201chappy things\u201d and if we add more positive integers, we will be more happy and the number will be more positive and vice versa. However, if I subtract a negative number, I am metaphorically speaking taking away unhappy things, and therefore I will be more happy and the number will be more positive. <\/span><\/p>\n

3 Step T-GEM cycle<\/strong><\/span><\/p>\n\n\n\n\n\n\n\n
<\/td>\nTeacher Strategies<\/span><\/td>\nExamples<\/span><\/td>\nStudent Strategies<\/span><\/td>\n<\/tr>\n
<\/td>\nProvide background information on integers<\/span><\/td>\nIntroducing what \u201cpositive integers\u201d and \u201cnegative integers\u201d look like<\/span><\/td>\n<\/td>\n<\/tr>\n
Generate<\/span><\/td>\nShow examples of different types of integer equations, but starting only with adding of two positive and two negative integers.<\/span><\/td>\n(+2) + (+3) = +5<\/span>
\n<\/span>(-2) + (-3) = -5<\/span><\/td>\n		Try to generate relationship between positive and negative integers and operation. They also try to consider how this math concept is used in real life applications. <\/span><\/td>\n<\/tr>\n
Evaluate<\/span><\/td>\nEncourage students to evaluate their relationships to see if the integer equations will become true\/false.<\/span><\/td>\n\u201cWhat are some other examples?\u201d<\/span>
\n\u201cCreate your own examples and see if it follows your rules.\u201d<\/span><\/td>\n		Try out their theories and evaluate them.<\/span><\/td>\n<\/tr>\n
Modify<\/span><\/td>\nAsk students to modify original ideas of relationship between positive integers. <\/span><\/p>\n

Then, the teacher will introduce a new related concept such as adding a negative integer, then subtracting a negative integer, before moving on to multiplying and dividing. <\/span><\/td>\n

\u201cWhat changes can we make to your rule?\u201d <\/span><\/td>\nModify their relationships if it is false. <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Digital Technology<\/strong><\/span><\/p>\n

A digital technology that can be used to accompany the concept of integers is the use of coloured chips found at <\/span>http:\/\/nlvm.usu.edu\/en\/nav\/frames_asid_161_g_2_t_1.html?from=search.html<\/span><\/a> and <\/span>http:\/\/nlvm.usu.edu\/en\/nav\/frames_asid_162_g_3_t_1.html?from=search.html<\/span><\/a>. They allow students to visually represent the integers using different coloured chips (e.g. one for negative, one for positive). <\/span><\/p>\n

Index of Virtual Manipulatives<\/span><\/i>. (2017). <\/span>National Library of Virtual Manipulatives<\/span><\/i>. Retrieved 23 February 2017, from http:\/\/nlvm.usu.edu\/en\/nav\/search.html<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Challenging Concept: Integers I teach grade 6s and 7s and integers is a common concept in math my students struggle with. Particularly, when dealing with negative integers. This includes adding, subtracting, multiplying and dividing with negative integers. Specifically, my students have had difficulties with understanding that adding a negative integer makes a number less positive […]<\/p>\n","protected":false},"author":3635,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1669392],"tags":[],"class_list":["post-1542","post","type-post","status-publish","format-standard","hentry","category-b-t-gem"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/posts\/1542","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/users\/3635"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/comments?post=1542"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/posts\/1542\/revisions"}],"predecessor-version":[{"id":1620,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/posts\/1542\/revisions\/1620"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/media?parent=1542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/categories?post=1542"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/tags?post=1542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}