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Rigid Motions – Which Reflection?

23 Aug
Rigid Motions – Which Reflection?

We added to our introductory lesson on Rigid Motions this year. Sometime last year, I read Which Reflection is Best by Andrew Shauver.

Which_Reflection

I wondered what students would say without measuring and before studying reflections in depth. So I asked.

Screen Shot 2014-08-22 at 9.45.32 AM

And then I asked again, after students had the opportunity to use appropriate tools strategically (most used a ruler).

Screen Shot 2014-08-22 at 9.45.44 AM

Not very many changed their minds from their first glance.

 

Next we talked.

BK offered his argument as to why he chose B over D:

When I put the edges of one end of the ruler on A and A’, the line of reflection didn’t go down the middle of the ruler on D, but it did on B.

 

Screen Shot 2014-08-12 at 9.56.25 AM

Oh…so is there something significant about the line of reflection matching the middle of the ruler?

We made sense of the significance with the yellow-ish angles.

Screen Shot 2014-08-12 at 9.56.41 AM

Screen Shot 2014-08-12 at 9.56.54 AM

We developed the vocabulary as it arose, instead of having students write lists of definitions with no context (I cringe to think about how many of my former students suffered through writing geometry vocabulary each unit) – midpoint, bisector, distance from a point to a line, perpendicular bisector.

And we ultimately concluded that the line of reflection will be the perpendicular bisector of the segment that joins a pre-image point with its image.

What a great example of use appropriate tools strategically – BK was using his ruler both to measure distance and to measure for right angles. 

And so as the journey continues, I am thankful for students who are willing to share their thinking and for teachers like Andrew who are willing to share their lessons.

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5 Comments

Posted by on August 23, 2014 in Geometry, Rigid Motions

 

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5 responses to “Rigid Motions – Which Reflection?

  1. Andrew

    August 23, 2014 at 9:46 am

    If you want to make for an especially delicious sequel (time permitting), ask the students to decide as a group which of the four is second best. When you apply the same the criteria, it’s interesting to watch them realize that choice A (while sloppy), is actually a decent reflection.

     
    • jwilson828

      August 23, 2014 at 8:30 pm

      Thanks for the suggestion … and for all of the good ideas on your blog. The discussion that we had was well worth the time!

       
  2. howardat58

    August 23, 2014 at 10:12 am

    You could also try this without the line of reflection, and let them figure out which arrangement could be described as “reflection”. (I would say 3 of the four, after Andrew, above)

     
  3. howardat58

    August 23, 2014 at 10:15 am

    In passing, I have some difficulty in spotting the difference between “use appropriate tools strategically ” and “use appropriate tools”. If the tools are appropriate then how else are you going to use them?

     
    • jwilson828

      August 23, 2014 at 8:36 pm

      Jill (http://jplgough.wordpress.com) and I are in the process of writing leveled progressions for each SMP. We haven’t made it to SMP 5 yet … but thanks for giving us something to think about.

       

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