Kaneka,
You are hitting me right in my gut and heart! I fear I am not smart enough to play, AND I just let my enthusiasm and age wisdom push open that door!
I am a member of MTBoS, I made myself so. That is the thing about the MTBoS, it is one of those leaps of faith. You don’t have to be the brightest, funniest, smartest, newest, greatest, rockin’-est. You just have to have FAITH that you want to be better, that there is someone to who will listen, that you have peeps that care about your mathy well-being, and your person well-being. YOU ARE SOMEBODY! And the MTBoS is here to support you. Only thing is, no one is going to beg. That is what I mean about faith. And we are patient. And we want you to be with us. There are the amazing folks who started the ball rolling, and they have HUGE hearts. Come and play! Twitter is the same way. I was so overwhelmed, I felt like I was left out of the inside of everything, and guess what, I usually am, and there is always, always, always SOMEONE who is listening and will “like” a tweet, or respond to a plea, or feel compelled to tell you about a great resource. Because that is what we do for each other.
I didn’t believe it at first. (well first of all, I didn’t even know that I who I was really contacting and commenting on) Then you comment and get a reply from Matt Vaundry, or Fawn, or Dan…and then we are just all the MTBoS and so what?
The best way to handle twitter is Tweetdeck. Just have a column for #MTBoS, or for #Geomchat or whatever, and that really helps limit all the middle of stuff that makes you feel, well, out of it.
I hope I have given you some ideas and made MTBoS and twitter less intimidating. I am listening and reading!

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:

  • 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:

Matrix Row Game

Next Posts: When you are brave and ask for help and How a new course was born




My lovely colleague is out with hand surgery. Ouch! No writing for 6 weeks! Being the manly mother hen that he is, he figured he would get surgery a few days before spring break, get 10 days rest, take two weeks after that, and stroll on back to the classroom! We all know how hard it is to leave our kiddos, and worse to make lesson plans that work with a sub--now translate that into Pre-Calculus! We have a math sub thankfully, but still...so we have decided to try a Matrices Unit. (I cannot find the topic in the common core state standards, can you?--I could most definitely make the argument that the math practices strongly come into to play teaching the topic, and geez, they are so pretty and fun.)

My intention here is to blog a bit everyday about what I do, what I would do again, what I wouldn't do again, and giant, HELP! if I need it. I am excited to blog about something over time, which I have never done before. With our lovely calculators, do we really need to talk about Cramer's Rule? Determinants? Can we just go with row operations and Inverses to solve?

If you have any pre-emptive advise, please chime in!
Thanks Randall Munroe




First Period: Well, what do you think? Anybody, anybody? I can wait you out...OY VEY!

By second and third (we are on block schedule, so we are now from 10am to 2pm) Things are oh, so much better!

Mostly I learn from try, try, try again. My favorite question go to is: How are they alike? How are they different?

Some examples:

Similar Triangles vs. Congruent Triangles
Similar Triangles vs. Dilated Triangles
Solving Equaliites vs. Solving Inequalities
atrigb(x-c) +d vs afcnb-c) + d

Other favorite questions are:
Harold says, Emilia says, who's correct? Are they both correct?

What is another way?

How do you know your solution makes sense?

How do you know?

When did you know you were on the correct path to a solution?

Where did you fall off the ramp? When did you stop understanding?

What was so and so thinking when they took the next step?

I am determined to start writing more of my questions ahead of time, and write them HUGE so I will remember to ask. I would also like to be in the habit of answering more questions with another question, even if it is only, "What do you think?"

As I have been thinking about this prompt, I am reminded about how much you learn when ask students super straight forward questions.

When you write SinA/a what does it mean exactly?
What does proportional mean?
If the scale factor is 5/4 is the image bigger or smaller?
Is the answer going to be more than or less than?

My favorite new technique is inspired by Kate Nowak, simply, "What is the Question?"

29 years and so much room for improvement...Thanks MTBoS



%math %blog %education %learn %cool
Week 2
My Favorite Things:

Favorite Geometry Activities: Too Much Trash. Guess I am a proportional reasoning kick. "If everyone in Windsor lined up their recycled papers for a year it would reach 249, 289 miles! That is 4,000 miles shy of the Earth to the Moon!" Says Casey M. a ninth grader in my Geometry class that took the amount of paper his family uses in a day, and extrapolated the data based on Windsor, California. *Just found out cannot link to document on Blogger, so just message me for copy of project and Rubric. 

Off the Quadrilateral Island: This is a simple little sort we did with Quadrilaterals. I gave groups of 3-4 students one line of this hand-out: (Not mine, got it from Google, can't find my original source, does anyone recognize it?
%math %blog %education %learn %cool


The directions are for students to use the proper marks to show your assumptions about each figure in their row. Then decide which quadrilateral doesn't belong and explain why. The product is a poster that explains the attributes of the survivors and why the quadrilateral they choose was kicked off the island. We did a gallery walk. The students only got 20 minutes to decide, plan and make the poster. 


Favorite Ice Breakers:
From Dinner Party Download Podcast: The hosts, Chuck and Josh, ask all their guests two questions: What question are you tired of being asked and what is something that we don't know about you. 
Another is: Uncommon Commonalities. In a group of 3-4 (preferably 4), one student, say the oldest, draws a pair of concentric circles. 
Have students divide up outer ring with the number of students in group. Each person has to find something unique about him/herself to put in outer ring. In the center ring, they have to find something they have in common, can't be about school, the town they live in, or gender. Some pretty interesting facts come up. My favorite was a group of two boys and two girls, where all had at least two pierces in their ears. You get unique allergies, folks who play instruments, black belts, people who were born in other countries, all kinds of cool people tricks. 

Favorite Places to Get Insight:
Twitter: #MTBoS
Desmos
Geogebra
Wolfram Alpha

Favorite New Source for Mathematical Thinking:
If you teach any kind of proportional thinking, you have to check this site out! 
Example:
%math %blog %education %learn %cool

Love!