Day 143: Matrices and Geometry

It is time to explore another, different, interesting use of matrices….this time in the field of transformational geometry!  A few years ago, when I first decided I wanted, no needed!, to have a unit on Matrices in precalculus (since the topic was not part of our Algebra 1 nor Algebra 2 curriculum), I hunted for interesting and engaging uses of matrices.  I found a pre-made activity with student and teacher handouts on the TI Math Nspired website called Matrix Transformations

Nspire Matrix Site

The handout needed almost not tweaking!  Always a plus since I am forever changing activities to do just exactly what I want it to do.  An example of an exploration question is:

Grab and move the sliders for each element of the multiplication matrix until the polygon in Quadrant I is a reflection of the polygon in Quadrant II.

  1. What 2 x 2 matrix results in a reflection over the y-axis?
  2. Why does this matrix multiplication result in a reflection over the y-axis?

Here is a progression of motions for the question:

04-21-2015 Image005 04-21-2015 Image00604-21-2015 Image007

I like how the activity is a nice marriage of Action-Consequence theory (moving sliders to see what happens) and multiple representations of the mathematical idea (numeric-matrix, visual-graph, and abstract-matrix calculation in green).  Here are my “giggling boys” exploring, giggling, discussing, giggling, solidifying their observations, giggling…. You get the idea!

20150421_145623

How do you give your students experiences where they make sense of the mathematics by trying things and adjusting their thinking as they go along?

 

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Posted on April 21, 2015, in Uncategorized and tagged , , , , , . Bookmark the permalink. Leave a comment.

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