# 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

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:

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!

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?