{"id":2201,"date":"2017-04-05T21:30:19","date_gmt":"2017-04-06T04:30:19","guid":{"rendered":"https:\/\/blogs.ubc.ca\/stem2017\/?p=2201"},"modified":"2017-04-05T21:32:58","modified_gmt":"2017-04-06T04:32:58","slug":"sketching-transformations","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/stem2017\/2017\/04\/05\/sketching-transformations\/","title":{"rendered":"Sketching Transformations"},"content":{"rendered":"

I have come to recognize that many of my senior math students do not make a connection between transformations and algebraic processes. \u00a0They struggle to make the connection between physical movement and algebraic effect. \u00a0This activity is intended to assist these students in building connections in this area.<\/p>\n

    \n
  1. Step 1 \u2013 Review Cartesian planes and coordinate systems <\/strong>\n
      \n
    1. Access prior knowledge<\/li>\n
    2. Identify any misconceptions or gaps in learning that should be addressed in these areas before moving forward.<\/li>\n<\/ol>\n<\/li>\n
    3. Step 2 \u2013 Student Hypothesis <\/strong>\n
        \n
      1. Working in pairs, students will create rules for translations, reflections, and rotations while working with coordinates (e.g. when translating horizontally, the x-coordinate of each point is adjusted accordingly)<\/li>\n
      2. While working on developing their hypotheses, students have access to a tabletop grid and shape cutouts to manipulate<\/li>\n<\/ol>\n<\/li>\n
      3. Step 3 \u2013 Test hypothesis <\/strong>\n
          \n
        1. Use Geometer\u2019s Sketchpad to test hypothesis using prescribed \u201ctest\u201d transformations<\/li>\n
        2. Students access transformations from a list within the Geometer\u2019s Sketchpad file<\/li>\n
        3. Transformations will include confounding situations, such as a rotation in the opposite direction or a reflection in something other than an axis.<\/li>\n<\/ol>\n<\/li>\n
        4. Step 4 \u2013 Refine rules\/hypothesis in consultation with a small group<\/strong>\n
            \n
          1. Students combine into groups of 3-5 students to discuss findings, inconsistencies, confirmations, etc<\/li>\n
          2. Groups come to an agreed upon set of rules by discussing and justifying their perspectives.<\/li>\n<\/ol>\n<\/li>\n
          3. Step 5 \u2013 Use transformation rules to design a patterning activity for other groups in class<\/strong>\n
              \n
            1. Each group will use Geometer\u2019s Sketchpad to design a problem scenario involving transformations that will require other groups to apply their transformation rules.<\/li>\n
            2. Examples of problem scenarios could include designing a quilt pattern, wall or floor tiling, yard landscaping, etc. The scenario context will be an essential component of the framing of the application because \u201ccontexts allow the learner to reflect on and control for the meaning and reasonableness of their developing ideas\u201d (Dixon, 1997, p. 140).<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

              Dixon, J. K. (1997). Computer use and visualization in students’ construction of reflection and rotation concepts.School Science and Mathematics, 97<\/em>(7), 352-358.<\/p>\n","protected":false},"excerpt":{"rendered":"

              I have come to recognize that many of my senior math students do not make a connection between transformations and algebraic processes. \u00a0They struggle to make the connection between physical movement and algebraic effect. \u00a0This activity is intended to assist these students in building connections in this area. Step 1 \u2013 Review Cartesian planes and […]<\/p>\n","protected":false},"author":47473,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1669400],"tags":[],"class_list":["post-2201","post","type-post","status-publish","format-standard","hentry","category-c-information-visualization"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/posts\/2201","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\/47473"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/comments?post=2201"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/posts\/2201\/revisions"}],"predecessor-version":[{"id":2203,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/posts\/2201\/revisions\/2203"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/media?parent=2201"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/categories?post=2201"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/stem2017\/wp-json\/wp\/v2\/tags?post=2201"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}