Tuesday, August 30, 2011

Precalc box project

What's the biggest box you can make out of an 8 1/2 x 11 piece of paper?  Go.

That's the question I posed to my precalc classes yesterday.  The first class kind of just stared at me for a minute, then thought of some questions.
1.  What does biggest mean?  (we decided volume, not surface area)
2.  What's a box? (um....)
3.  Does it have a lid? (we decided no for simplicity's sake... but today figured it out with a lid)
4.  What shape?  (we went with a rectangular prism, but one boy wanted to do a cylinder, so he did!  love him.)

As a class we came up with a net of the box on the board, labeled some values, and came up with a formula for its volume.  But how do you find the maximum volume?  Someone suggested graphing the volume equation... but then what?  What does a cubic look like?  How does it have a maximum if it goes up forever?

That lead us to a discussion on the domain of our volume.  The polynomial itself will go to all reals, but that's not applicable for our box.  Once we had a good window, we talked about how to find the maximum value (without tracing on the calculator) and what that ordered pair represented for our box.

At this point, everyone grabbed a piece of cardstock (cut in different sizes so they had to work independently), measured, and proceeded to maximize their box.  (Question - what do I do with 90+ small open-lidded boxes?)

Today I had them do some checking for me.  Everyone grabbed a constructed box from yesterday, measured it, and entered their values into a google spreadsheet that I'd set up.  It was a little crazy with 14 people trying to enter their numbers all at the same time (because they kept typing over each other) but it was fun to see all of the data come in.  Then they were to come up with the maximum volume for a lidded box (after we drew a net and found a volume formula together)... though I'm not sure the net we came up with would maximize the paper, it was fun to see them think through what it would need to look like!

I actually did this project at the end of last year when we were doing limits and derivatives in precalc.  They then had to find the derivative of their volume function and determine where it would have a maximum (by setting = 0).  I'm going to keep one of the pages they filled out leading them through the process and give it back to them in May so we can do the limit and see that it's magically the same value that the calculator gave us!  Crazy how that works.

(Much thanks to Luajean Bryan, who showed us this project at NCTM!)

Thursday, August 25, 2011

Two down... how many to go?!

Two days down, and I think my body's in shock.

Ok, so maybe I'm exaggerating.  I'm feeling my feet and legs ache... I'm feeling my tummy rumble (lunch was at 10:15!)... and I'm feeling my body all yucky and covered in sweat - gotta love having no a/c when it's 90+ outside!  I literally was dripping around 7:45 this morning (but it actually got a little better as the day progressed because the humidity subsided a bit).  And did I mention that I could totally go home and go to bed?  5:20 am is inhumane.

But my first two days back have gone pretty well.  The kids seem nice (except one boy in a precalc class who I can already tell is super annoying... and I knew that after the first 10 minutes in my room!) and have been working for the most part. I assigned summer work for precalc and it was nice to jump right into factoring, solving, graphing, etc. without the normal foray into "here's what you should know" stuff.  I'm giving a quiz tomorrow which could be interesting (especially after grading all of the kids' summer work!)... honestly, what kind of "honors" kid doesn't do half of their assigned work? Or just writes answers (which I posted online for them)?  Maybe this will help my classes decrease in size a bit - I've got 32 in two of the classes and 27 in the other.

One thing that hasn't gone well is the technology component.  (I know - shocker!)  I had a wireless hub in my room which didn't seem to be working well except for the 5 minutes after I unplugged and replugged it.  Our tech people came in and determined that the hub was causing problems all around me, so it's now gone.  Yesterday was actually ok without it, but today's been a disaster.  I wasn't able to wirelessly connect to my projector and have lost my connection to the network numerous times (which means I haven't been able to print or get online). The tech guy was just back in the room and tried a new hub to no avail.  He said the engineer is supposed to come in on Monday and hopefully will get things back up like they're supposed to be... but I'm sure we all know that that's doubtful!

I'm a little at a loss with my Algebra 1 class.  There are only 22 kids and mostly girls and they all seem very sweet.  I gave them a fun problem to start class today (there are so many girls with cats and backpacks, etc. How many legs?) that they seemed to enjoy, then I handed out a skills review page just to see where they're at.  It had adding and subtracting with negatives, order of ops, and some simplifying/distributing with variables. We got through most of the first two sections without a whole lot of problems although there was some surprise that yes, sometimes you will need to divide before multiplying, but what I heard from them with the algebra section let me know that we'll basically be starting from square one with variables.  At least I know where they're at!  Kinda.

I'm done rambling and I want to find some a/c.  And a snack.

Saturday, August 20, 2011

Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.

Tuesday, August 16, 2011

Ask and you shall receive

It amazes me how generous people can be when you just take the time to ask.

Case #1.  My previously-mentioned paper folding escapade with my Algebra 2 kids last year. All it took for me to get 2 large (!) pieces of paper was an email and a special trip to pick them up. For free.

Case #2. I've been doing some searching this summer to find new projects I can use in Precalc. I've had a little luck finding stuff online and have run across a book called Projects for Precalculus every time I search.  Unfortunately, this book doesn't seem to exist in any stores.  I did, however, find the email address of one of the authors of the book and decided to write. I said I was a precalculus teacher and was interested in his book but wasn't able to find it for sale anywhere. He responded back today and said that it was out of print and then he sent me a copy of the book on pdf.  Can you imagine?!  Twenty-six precalc projects now at my fingertips. For free.

Case #3. One of my twitter friends sent me some files today that I'll be able to use in precalc to help the kids get ready for the AP Calc format.  Twitter.  I can't say enough.  If you're not on twitter, get on it. If you're not hooked up with a good group of teachers to help you, let me know.  You're seriously missing out.  And you know what? It's free.

Sunday, August 14, 2011

Memory loss

With opening day just a little over a week away, I'm trying to get a little more specific with what I want to do starting out in each class... and yet when I sat down to do that, I couldn't remember exactly how I'd opened last year.  Thank goodness for this blog!  Just checked out the archives and found my description of what I did last year (it's here).  Whatever did I do before blogging? :)


I typed that a few hours ago with the best of intentions to get some work done tonight for Algebra 1 (my kinda new prep). And then I got distracted with my first day stuff.  Last year @lmhenry9 made up a prezi to show the kids the answers to her Quiz about her and I thought about doing that but it would've taken me forever to make (I'm not the most proficient with prezi).  So I fell back on the good old powerpoint.  And 3 hours later, it's done!  (Seriously?!  Obsess much?!)

It was fun to make, though, and hopefully the kids will enjoy it. :)

Saturday, August 13, 2011

Things I've Tagged (weekly)

Posted from Diigo. The rest of my favorite links are here.

When will I ever use this?

@druinok sent me a formula the other day on Twitter that predicted the amount of time between insurgent attacks in battle.  She asked me when I thought we'd be able to use this in Algebra 2.  I thought that it looked more like a precalculus application (when dealing with sequences) and may show it then, but it also got me thinking that I'd like to find some formulas that people actually use outside the classroom.

I did a little bit of research online and this is what I came up with.  If you have any more, please pass them on! :)

Friday, August 12, 2011

One more week...

I'm currently sitting at home looking out the window at a beautiful sunny (yet awesomely pleasant!) day. Sigh.

I'm also sitting with three computers open in front of me.  How times have changed!

My husband doesn't work on Fridays (they work long hours Mon - Thurs) so my plan was to spend a childless morning at school today starting to get ready to go back.  That plan changed around 7 this morning when he received a phone call asking if he could work.  So much for having no kids around!  I would have put off going into school but I'd planned on meeting with one of the guidance counselors at school to talk about a student I'd had last year in precalc and not recommended for AP Calc who now wants to take it. Bleh.

So the kids and I got ready and headed down the road (with a stop at Dunkin' Donuts for a healthy breakfast!). They were really good, but it's really hard to do any work with a 4- and 7-year old around, even when they have their Nintendo DS and a tv tuned into Nick.  We made it a couple of hours and I got a few things done but still would like to get back to school sometime to finish things up - I hate waiting until our "work day" before school starts because something else always comes up!

A couple of weeks ago I thought about giving the kids labels with a QR code and the address of the class blog on it (read it here) so after the kids and I left school we went to Staples to see what kind of labels they had. I ended up picking up a pack of Shipping Labels (2" x 4") that I think will do the job. It turns out that there's a sit online (www.avery.com/templates) where you can design your label without downloading anything and they even have a QR Code generator!  Perfect.

I guess I should try out the code, though, before I print a bunch of them (which I'm going to wait to do until I get back to school) and have it not work.  It was super nice and easy! :)

Or you can play with some of their options... I just made this one (inserted an image I'd saved of a QR code previously set up).  Cute, right?  Even if printed in black and white?  Does the QR code need to be a certain size?  I'll need to check that out...

Wednesday, August 3, 2011

Getting down to business...

It was rainy this morning, so the kids and I stayed home to hang out (instead of our planned trip to the pool). What better time to get some work done?!  The kids were amazingly good and have played together nicely ... while making a mess of the house, of course!  But beggars can't be choosers!

Anyway, I've been trying to finalize what I'd like to do in Algebra 2.  I'm going to go with the re-quiz option for them (if they sign up and do some review work beforehand).  Now I'm going to have to go through my quizzes and tests and make sure that all of the learning topics are addressed, which is a great check for me!  Am I really assessing what I want to?

Last year I put together a list of topics and assignments for each section in each chapter, so all I had to do was tweak it a little bit to fit my needs.  Here's the Chapter 1 sheet:

Alg 2 Ch 1 Assignments

After trying to figure out how to format quizzes, this is what I came up with.

Quiz 1

Now I just need to decide if I quiz over the last half of the chapter, too, in addition to a chapter test.  I wasn't planning on letting them redo tests... but if I don't just quiz the last half then they won't get that chance.  Maybe just let them reassess the topics that hadn't been quizzes yet?

So much to think about.

Ideas and opinions welcome!