Transformations: One at a Time or All at Once?

Great post form Tina C on her upcoming transformation unit. I’m doing transformations right after winter break. Really like her general principles:

  • translate
  • rotate about the origin multiples of 90 degrees
  • reflect over a variety of horizontal and vertical lines, not just the axes
  • wait to dilate until we get to similarity, for now rigid transformations only
  • use the phrase rigid transformations
  • use the prime notation P -> P’
  • incorporate language about congruence, including corresponding parts
  • one of our textbooks emphasizes coordinate rules, we will not emphasize them, in fact we will encourage students to physically rotate the paper rather than memorize a rule

Although our curriculum emphasizes motion rules, so I will try to get my students there. Nervous about that one. My question is–should I introduce all four transformations at the same time and have students get some intuition for rigid motions in general, or go one by one looking at reflections, translations and rotations a day at a time before composing.

One principle I would love to get at is that rigid motions imply congruence–if you can use a series of rigid motions to map one figure to another, they are congruent. Moreover, if two figures are congruent there must exist a series of transformations to map one to the other. Then parity, orientation, etc. All really useful ideas that extend beyond transformations for the sake of transformations, which is what this unit can really easily become.

Not sure how to teach for understanding with any of this.

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