# Sketching Transformations

I have come to recognize that many of my senior math students do not make a connection between transformations and algebraic processes.  They struggle to make the connection between physical movement and algebraic effect.  This activity is intended to assist these students in building connections in this area.

1. Step 1 – Review Cartesian planes and coordinate systems
1. Access prior knowledge
2. Identify any misconceptions or gaps in learning that should be addressed in these areas before moving forward.
2. Step 2 – Student Hypothesis
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)
2. While working on developing their hypotheses, students have access to a tabletop grid and shape cutouts to manipulate
3. Step 3 – Test hypothesis
1. Use Geometer’s Sketchpad to test hypothesis using prescribed “test” transformations
2. Students access transformations from a list within the Geometer’s Sketchpad file
3. Transformations will include confounding situations, such as a rotation in the opposite direction or a reflection in something other than an axis.
4. Step 4 – Refine rules/hypothesis in consultation with a small group
1. Students combine into groups of 3-5 students to discuss findings, inconsistencies, confirmations, etc
2. Groups come to an agreed upon set of rules by discussing and justifying their perspectives.
5. Step 5 – Use transformation rules to design a patterning activity for other groups in class
1. Each group will use Geometer’s Sketchpad to design a problem scenario involving transformations that will require other groups to apply their transformation rules.
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 “contexts allow the learner to reflect on and control for the meaning and reasonableness of their developing ideas” (Dixon, 1997, p. 140).

Dixon, J. K. (1997). Computer use and visualization in students’ construction of reflection and rotation concepts.School Science and Mathematics, 97(7), 352-358.