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I think transparency film is also a powerful tool for use with pattern blocks. For example, you could draw the perpendicular axes on the film and move it around over the blocks. You can trace pattern fragments onto a film to be manipulated (relative to axes, or rotated by 'pinning' down a point as a center of rotation, or you can literally flip the film, representing a reflection, etc.). After introductory presentation on cyclic (or dihedral, or linear or planar) patterns, students were to create their own patterns. These were exhibited in a gallery, and were used as samples for identifying classification codes. I've adopted the codification used by Kevin Lee in KaleidoMania! software from Key Curriculum Press. I also have students create Sketchpad scripts for the classic pattern block shapes, then use their scripts to generate virtual versions of patterns they create with the concrete manipulative. I am wondering how many teachers really teach transformations beyond the simplest level of reflection over a single mirror, or rotation about a centroid. What do you think?
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