How do you make the surface area of cylinders captivating? "Do more of what you love," rings in my ears. (thanks Christopher ) I had to stop looking for approval and go with what is important to me. I had just been through two social justice minded nights of Seder, so I had a lot on my mind. As I was looking around my classroom, I noticed how many students had cylindrical shaped vessels with them. I gathered them all up and put them on display. I had an agenda that was both mathematical and much broader. My underlying goal was to expand student thinking, get some critical evaluation going, and apply a simple notion to having a voice (and maybe sneak in some talk about branding, economics, and consumerism)
The first day I lead a conversation, it looked like this:
The conversation was loud, and active, and thoughtful. The students came up with cylinder-shaped right away. I loved getting thick into their vocabulary, "girth, coney, purpose, mass, volume, recyclable, durable." I got to give them a new word, "ergonomics," and we talked about product placement in movies and tv, why some were "coney" and some straight up and down (right), and I even got to sneak in some SJ with branding which led to tribes, acceptable tribes and not acceptable tribes. (reusable, that is my tribe, tree hugging dirt worshipers, Starbucks, that is my tribe, etc...(we are in the San Francisco Bay Area, so our sports are very tribal) 
I realized that I could include more students if the next day, (we are on a block schedule so I hadn't seen 2 of my 4 sets of Geometry kids yet) I started smaller. I was thinking YOU, WE, ME. 

The next day, I gathered up all the cylindrical vessels, and handed groups of 4 some large paper. I had them do a brain dump.  When the students figured out what we doing, MORE bottles came out of backpacks and book bags, including a glittery one! Their's looked like this:












I had them then get up, and move around to read what others had written. Back at their seats I gave them a few more minutes to be inspired. to write down anything they wanted to remember or add. 

This time, when I called them together, I asked each person to share something that their team wrote, something they heard, or something they saw. More voices, and a much more delighted me. It now felt more okay for me to ask the following questions:
1. What is the net of a right cylinder? (I love the surprise when students recognize the length of the rectangle part of the next is actually the circumference of the circle)
2. What is its surface area--I found a student's bottle, asked for the measurements of the diameter and height. 
3. What is the volume?
4. and most importantly, can you find another set of dimensions for the cylinder that has the same volume? 

We will see what I get on Tuesday and Wednesday. I am curious to know if the different set of classes will have more enthusiasm, more of their assignments completed, and/or more investment in the task. 

I have been gathering evidence for my fantasy "Don't go it alone," series. We all work so hard, it is crazy that we feel so compelled to do so much ON OUR OWN. I subbed for a colleague teaching Algebra 1. She is so dang creative! Her class was working on graphing quadratics in factored form.
Unfortunately, working solo, she missed an entire page of graphing written as quadratic  = 0 (instead of y = or f(x) =)


I have done this too many times myself. Would this teacher have caught her mistake if I did not happen to cover for her? Sometimes we find 'em, sometimes we don't. With 15 sections of Algebra taught at our HS, the going it alone is too common place. I believe this because I am guilty of going it alone and I know the benefits of collaboration.






Mr. H. My BTSA Participating 1st year teacher is a systematic guy. He cares so much that the students get what they need step by step. He is careful not to overwhelm them with too much information.
Here is his pool problem for our unit on solids:



I had all these cool ideas for exploring circles in Geometry. Circles are a great bridge topic between Geometry and Algebra.
I have lots of good ideas, I am just not the most organized person in the world. Lucky for me, I have colleagues that are. Here was my lesson:
Me: Multiply  (x+1)^2
                      (x+2)^2
                          .
                          .
                         
                          .
                      (x+12)^2      Stop when you find the pattern and just write the product.

Me: What did you notice?
       How would it change if all the sums were differences?
Me: Can we work backwards? Can we find a magic number that makes a perfect square trinomial, etc...
Me: How are these equations related to the circles we have been graphing?
Me: Can you find the center and radius of this circle in standard form? x^2 + 8x +y^2 = 9?

My students were happy enough and there were "oh, I get its." We got into fractions, and even radii whose lengths were square roots.

My lovely colleague asked me how I was approaching complete the square for circles. And I shared the above. Here is how she interpreted my lesson:


To see her entire development get the file here: file

I just love how she saw the whole thing. How she was able to put the lesson into a form I could not.

I have many things I want to do with my students that I am not sure how to structure, so I shy away. The more I share with colleagues, the more we create rich and inviting experiences for the students.

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!

#tmc15 Experiencing Community
     
     Truly I don't know where to start this post. Partly an ode FOR all the MTBoSers, partly that experience where you just process and download. I did wrtite this all on paper first, just to get the thoughts out, hoping the sensation of pen to paper would help get the flow going.
(Also, I haven't read anyone else's posts yet, because I wanted to share my authentic experience of attending Twitter Math Camp 2015. Fancy that.)

Twitter Math Camp is literaly camp for math educators to gather, be a community, share, encourage, figure out, laugh, sing, and get their Geek on.  It is sponsored by us, paid for by us, and no one is getting any money for participating. The Keynotes are speaking from their hearts, the organizers are donating time and passion. That is what this is all about. And it. is. AMAZING.

     Starting with Gratitudes is always a good strategy. To Lisa Henry, her DH, her folks, and her kids, and all the tweeps who laid the ground for this amazing community, and it is about COMMUNITY.

It was one the few times in my professional life that I felt like I was in the right place. Sure I wish I had more of Fawn's consistency, and Matt's general hipness, and Michael F's mad computer skills, and Rachel's spunk, and Julie's infectious personality, and Sam's "take no prisoners" risk taking, and Chris' synapse stickers, and a thimbleful of the brainpower, energy, and creativity in that auditorium, AND stll, I felt cherished, valued, and believed in because I was there with the communal knowledge that it was our collective endgame to leave becoming better teachers, reaching more students, and grow more learning.

A few gems from the conference for you to use:

Christopher Danielson asked us to find what we love and do more of it in our classrooms. I love curiousity, I love helping students find their capabilities, I love  listening to NPR...

Fawn Nguyen said a lot, and had many of us in tears, and what I needed to hear most was, "Share ALL the lessons." Why? Because it is not about us, it is about growing learning for students. Mind Blown. Fuck the popularity contest.  (I get permission to say that from Fawn). Sure, give credit where credit is due and do please let the author know how you used the material, what tweaks you made, and how it went. And time to bring what works out of hiding.

* Do this cup rolling activity that Lisa and Jim shared with us: http://mathforum.org/pcmi/hstp/resources/papercup/papercup.pdf

Curtesy of PCMI

Add the extension: what formula could you come up with to generate the circle made by any cup?


* Ask Rachel's  two questions:
--What is the best question you asked a student today?
--What the best question a student asked you?

(Keep track and tweet or post them!)

* Google these for inspiration (thanks Fawn): Estimation180, Global Math, Mathtalks, Visual Patterns, WODB, MTBoS

* If you get stuck looking for the best way to make a lesson student centered look for the backwards version of the question (thanks Brendan and Sam)

* Get the students "Butts up," and use VNPS (Thanks Brian and Alex) to engage students in talking about math.

* So, so, so much more!

This is round one.


 
If I have left you out, please, like Sam says, don't take it personally. (I can't believe misscalcul8 was there and I didn't even know it. OMG, OMG.) I want to get this out, so you know you can do it too.

I wasn't in that great of shape Friday morning. An unsettled night sleep made for a potentially groggy day. Ever have one of those? And yet I managed quite well. Amazing what a brainstorm at 2am will do for a gal! (I did get home that afternoon to discover that I had my cami on backwards--ie--the skinny bra part in the back was in the front...good thing it was cold enough to wear my droopy scarf all day.)

I knew I needed a really good Hook to (re) teach percent problems. I looked through this really old POW book and found this problem for my warm up: 



So I did my happy dance because I felt like I had purpose. I let the kids wrestle with it for 3 or 4 minutes. Then I stopped them and told them this TRUE story: my brother is a Pilot for X airlines. Back in the late 80's, early 90's, his airline started to get into financial trouble. I asked the students, "who works for an airlines?" We brainstormed and came up with a list (good kiddos!) I erased all the low skill jobs from baggage handlers to air hostesses and hosts (yup, sorry you all, low skill). That left mechanics and pilots. Next question, who can work anywhere else and get a high paying job? No-brainer for most (yeah, there are some kids who think non-military pilots are in high demand), MECHANICS! Cars, Planes, Trains, and Automobiles. So when the company asked folks to make concessions, it was up to the pilots. Airline X asks the pilots to take a two year temporary pay cut of 25% of their annual salary, where at the end of the two years, the company would return the 25%. (you math folks know where this going!)
Boy were the kids mad and shaking their heads. "That's not fair." Of course not, had the lawyers and union reps had paid attention during ALGEBRA, this never would have happened. Then I asked them to do this:

Which is a better deal? Taking 25% off a $100 purchase then paying 10% tax, or paying the whole $100 including tax and then getting the discount? Go! Same, same...now go back and have another look at your Warm-up. Is there anything you want to change, add? You have 120 silent seconds to move your pencils across paper (and/or use your handy-dandy calculator).

I got "blah!" I got "blah-blah!" What is the answer Ms. Z.? Who's right? "I have no clue, I haven't done the problem and probably won't get to it for awhile." Go home and ask your parents. Ask your neighbors. Survey your whole block! Now put all that fun away, you have a Chapter test to take!

The most important part for me, was not giving the answer right away. I wanted them to hit it several times and rationalize/reason for themselves.

It is curious to me, that the most likely-to-not-do-their-homework, most squirrelly, students were the ones with the most insight into percent problems...could "suss" them out in their heads and had a high degree of accuracy.

It was a long day of directed teaching...of course there was another way to approach the whole enchilada, and sometimes the subject is just so much fun to go exactly the way you want it to go.

Next time I would put one of Dan Meyer's 101qs and ask what questions the students have, and sometimes you just gotta give them their Chapter tests with enough time to finish.

Do you have a favorite way to teach percent problems?

I am thrilled. I am hopeful that in the next 4 years I see the real movement that I voted for to come about 4 years ago. Let's move forward powerfully and courageously.

I have tried many ways from discovery, to begging straight up: "these are the rules" to help my Algebra students work through properties of exponents. I had some success with a process I called, "1 by 1." We did 12 problems in shadowed boxes:

1. 
   

You can capture what is on your screen, like a screen shot, and save it as a Jpeg to use in...your blog posts!

I made this Tarisa Puzzle:

It takes a 18 x 24 piece of construction paper to complete: Here is the first part:
The next thing will be for me to write Tarsia Puzzle and this will be live for you to download. Anyone? Anyone?

Happy Martin Luther King, Jr. Day!

Do you all know the Ipad Ap: Educreations? For all I know it is a program for Macs and PC's too, and, er, I am not the expert, yet...

So on Friday I promised my students that I would leave the Smart Board notes for them on the class website. Yeah, but guess who hit the "Don't Save" button before she left for the day? Yup, yo. So I recreated the main points on little video. Can't say it is the most watchable thing out there, yet it is me, and there is always the pause button for the kids.

The cousins from the previous Great Teaching Day got New Year's money again, however, this time, they got different amounts of money, but saved or spent at the same rate...and guess what? Wha-La! The students found out about parallel lines and I didn't "show" them anything. Phew!

This is a student with an IEP, who had a graph in last post, and this is a EVEN better!

Be sure to read his conclusion. Wow.

This next next student has about 28% in class...not anymore...well, okay, it is a step up.

And the last student I am showing off today is test-taking challenged. And her work is simply amazing.

The alternative that was given to me to me was a three page hand-out that began, "Now watch as I graph..."