Tuesday, March 2, 2010

More Motion Sketches

These sketches are to investigate the composition of motions, starting with reflections.  For a schema activation, I asked my preservice teachers to think about compositions.

Schema Activation:  What happens when you do two of a motion?  (Same type, not necessarily the same motion.)  Please guess if you don’t know.

Translation then a translation   K/G

Rotation then a rotation

Reflection then a reflection

Glide reflection then a glide reflection

This brings up the idea of orientation both in terms of turning and in terms of face-up/face-down.

For a focus we have the following:
Focus:  Today we’re just going to concentrate on reflections and their compositions.  We have three different sketches to consider, and will also consider the questions that could be asked about each.  A composition of motions is when you make one movement and then another.  The combination is still a motion, as the original and image are still congruent.

We're also going to consider using questions to move us forward.  The types of questions described by literacy instructors are:
  1. Literal - factual answer available or quickly available by recall, or can be found directly in the text.
  2. Application - answer found by applying known method or looking up with slight modification.  The method of getting the answer is known.
  3. Inference - answer requires prediction or extension from known information.  Can be an outright prediction or come from reading between the lines.
  4. Analysis/synthesis - answer requires combination or deduction from other known information, possibly requiring a method not currently known by the respondent.
In the three sketches, the students are asked to take more and more responsibility for the questions they are answering.

  Two Reflecting Lines:  webpage or geogebra file 

  Two Skew Lines:  webpage or geogebra file

   Two Parallel Lines:  webpage or geogebra file

We discussed these sketches together.  They asked about finding the center of rotation and saw a neat connection with the reflecting lines.  They also saw a neat connection between finding the center of a rotation and finding the center of a circle, but couldn't remember or figure out how.  They found a cool relationship between the direction and distance between parallel lines and the resulting direction and distance of the translation. 

Reflection:  What did you do during this workshop?  So what did you learn?  Now what would you want to consider next about motions or questioning?

Bonus: (or... extension)

Two Glide Reflections: webpage or geogebra file

Coming Soon:


  1. These sketches are fantastic! Thanks for sharing!! I wasn't able to open the first one though, either by webpage or by geogebra. I was able to open all the others though. Thanks again!

  2. Thanks for catching that. I just put the wrong filename in. I'm glad they're useful!