### Matrices Experiment Debrief

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My daughter came home from London for a two week visit (She is a Junior at LSE), and asked, "What is the best lesson you've taught?" Whoa. Really? I can't say that one.thing. came. to. mind.

I don't think this is because I am a crappy teacher. I have a crappy memory. (Hitting 50 made things, oh, so much worse...) The best lessons come when you hear the students abuzz or the bursting bubbles of OH! Recently, I have had the students move from finding the center of a circle by construction to figuring out how to circumscribe a circle about three points. That got a lot of ohhs and ahhs. Especially when we talked about the extension of what that means. ALL triangles are cyclic polygons blew their minds and the students loved trying to prove or disprove the theorem. Moving on to quadrilaterals was fun too. When you see students hunkered down, and paper is flying, you know you've done a good thing.

Here's another way I know a lesson is going well, and I can thank Alex Overwijk at http://slamdunkmath.blogspot.com/, because now I know we're inspired when my students ask me, "Can we do that butts up Ms.Z?"

Here goes the debrief on Matrices:

I don't think this is because I am a crappy teacher. I have a crappy memory. (Hitting 50 made things, oh, so much worse...) The best lessons come when you hear the students abuzz or the bursting bubbles of OH! Recently, I have had the students move from finding the center of a circle by construction to figuring out how to circumscribe a circle about three points. That got a lot of ohhs and ahhs. Especially when we talked about the extension of what that means. ALL triangles are cyclic polygons blew their minds and the students loved trying to prove or disprove the theorem. Moving on to quadrilaterals was fun too. When you see students hunkered down, and paper is flying, you know you've done a good thing.

Here's another way I know a lesson is going well, and I can thank Alex Overwijk at http://slamdunkmath.blogspot.com/, because now I know we're inspired when my students ask me, "Can we do that butts up Ms.Z?"

Here goes the debrief on Matrices:

- Obviously I didn't meet my goal of blogging over time. I was so tired taking on an extra class!
- We had to decide ahead of time the entire unit...news for you...it isn't exactly how I roll. I don't like sticking to an unwavering plan. As I get into something, I find new and different journeys to take as I see what is inspirational and what is not.
- I opened with a classic system of two equation story problem:

I only showed the first one. This was Pre-Calculus, so I let them think they were oh, so smart.

For the second one, we laughed that anyone would besides a mom would buy a visor. I explained that my Girl rows, and

*rowers*wear visors. (She's 5' 9'' and she is about medium for her 8 boat, you do not make fun of those girls (or boys). The students had a good time remembering how to and finding the cost of Visors, Hoodies, and T-shirts. Woot. (Even asked if they could go VNPS)
Then I let them go at the Sale question for about two minutes and called for a time out! Don't you want a faster, easier, better way????

- The first day was a good review of lines in a plane, consistent, and inconsistent systems. We also got a good review of quadratic systems, how different conics interact with each other and lines.
- Students were very motivated to learn about augmented matrices and Gaussian elimination. There was a lot of grumbling and I was so happy!
- Next we did Gaussian-Jordan elimination. EVEN more grumbling (YAY!)
- A minute or two, okay, a whole period on Matrix operations. Mind blown about lack of commutative property for multiplication, and what in the heck would an identity matrix look like? When do we know a matrix doesn't have an inverse?
- Then we got to Matrix Inverses. They did not like the looks of this using Gaussian-Jordan elimination and were all over their calculators and Google looking for answers. (Yay them!)
- Motivation: a very secret message I encrypted with a 3 x 3 matrix. I didn't do anything special (a = 1, b = 2, etc...) But it was enough to be thoroughly entertaining and engaging. The idea of encryption and decoding was a favorite. (I wonder if I should have started with the secret message and let them try to crack it). (It was also super fun to give the students extra credit for deciphering a code I encrypted with a 4 x 4 matrix when we found out it was senior cut day--a test day for us...Can we have extra credit Ms. Z? YOU Bet!)
- Math Practices used: SMP 5: Use appropriate tools strategically. (I loved when students started Googling how to use their calculators!) SMP 2: Abstract, no duh!, SMP 6: Attend to precision. (oh boy, did we go down some rabbit holes!) SMP 6: Model with Mathematics. (So many geeks in one room thinking of encryption--so happy the Apple case and the FBI trying to subpoena Apple to break the San Bernadino shooters' phone was in the news!) SMP 7 and 8: Patterns and repeated reasoning (dear hearts, yes, you multiply AND add each row and column entry) Very satisfied with how many of the practices are utilized with Matrices.

That is where I ended. I did not go over determinants. I would love to extend next time with determinants and transformations in the plane. Also, I would do more with planes in 3D. Yeah, and how about writing a program that would decode these messages for us, all. at. once, cause doing 4 letters at time is tedious...

Anyone have any insights? Additions? Forgetaboutits?

I did make one Matrix Row Game for review. If anyone remembers who has the Row Game File, I will happily throw it in! File here: