Day Zero

Well lots more to do... still trying to pinpoint some of the things I want to try different this year.  As usual lots of great ideas that I have seen on the net, but refining them to fit me is always the challenge.   Anyhow, I have decided to arrange my room in groups of 3.  Here are a couple of photos showing how I labelled the desks, and how the room is arranged.  I have a total of 24 desks in groups of 3, plus one big table at the back of the room for another 3.  But my two PreAP Algebra II classes are packed, I have 32 in one and 35 in the other, so I have 3 groups of 3 sitting at each of 3 lab pods.

There are 12 pods, with each pod of 3 desks labelled with a number (A through L) as well as 1-3 for the desk position. Also I used different colors, but made 2 pods the same color.  That way if I decide to have two pods work together, I can tell them to work with the same color.

Here is a few of a portion of my room.

By the way one last thing I have done for years is that I arrange my room alphabetically BY FIRST NAME not last name.  This helps me remember their names.  As I can look at a particular part of the room, and know what part of the alphabet their name should start with.  A little different but it works for me.

Day Negative 2

Well it's Monday (Day - Negative 2)  Day 1 with kiddos is Thursday.  Time to panic (just kidding).  I've decided to rearrange my class room into groups of 3 instead of 4.  I think I read somewhere that this was slightly better, it probably was in the "Make It Stick" book.  Unfortunately I don't remember exactly where.  Anyhow, I kind of like it, because of the type of desks I have the 4th desk was always a bit tough to get into.    One another note, I'm in the process of trying to set up my new toy - the TI Navigator for the nspire.  I'm hoping to use this some for some of the additional quizzing I hope to do this year.  I have to admit, I'm really impressed with reading "Make It Stick" and hoping I can hone in some of the ideas to use in the classroom.  We shall see...

Hmm.... not sure why this isn't in my 180 Blog.  I guess I'm not clicking on something right.  Hopefully I will figure that out.

FIRST Robotics - Recycle Rush - The Rush is over! and the Teflon Moment.

After 6+ weeks of building our robot is now complete.  I hope to upload some photos and videos later, but just suffice to say, very tired. Need lots of rest, and looking forward to competition.  Also as you will see when I do show the video.  You will see sometimes some of your best designs are well thought about with lots of work, effort, and thought, and other time you get lucky and have what I call a "Teflon Moment"  the accidental discovery.  We had one of those that more than tripled our scoring capability.  I hope to reveal the Teflon Moment soon.

Introducing Logs by Inverse not Definition

Well as you can probably notice by the long dry spell, I haven't quite got into the Blogging thing yet.  Anyhow as I was introducing logs this week, I had kind of a "eureka" moment on how to introduce them.  In the past I sort of done the typical textbook approach here is the definition, now lets use it.  I took a slightly different approach in hopes of getting the kids to appreciate why we have logs.  I'm not sure how much they appreciated it, but I felt like it was a better way to introduce them than just stating the definition.  So here it goes....

I started off by talking about how to find an inverse for a function.   This is something we did earlier in the year.  So here are a couple of examples showing the process I use.  Write as y=, switch y & x variable, then solve for y..

s

Then I asked what operation did we have to use to find the inverse of the function for multiplying.  The answer was obviously division, and to find the inverse of the subtraction function became addition.  So they were able to see these as "inverse" operations to find the inverse functions.

Then we looked at 

Again, I' not sure how much the students appreciated this, but I like the idea of claiming we needed to have an "inverse" operator so we define the log to get this new operator.

After writing this I did happen to look in two other textbooks from different publishers than the one I am stuck with, both of them seem to do an approach similar to what I just showed.  So my approach isn't novel, but just another nail in the coffin that my textbook is pretty bad.  

Polynomial Rants

Sometimes teaching polynomials drive me nuts.   It seems like there are a number of “rules” textbooks want them to memorize, and a number of procedures that are kind of archaic in the age of graphing calculators.

So for starters:

Factoring the Sum of Cubes or Difference of Cubes. 

It seems like the books want them to memorize this formula for this, and normally I have fallen in line with this, in some respects it’s not that difficult.  But I tried a new plan yesterday – just kind of struck me as I started to cover this section in class.

I’ll do it here first with the general case then look at it for a specific case.  I decided to see what would happen if I used synthetic division,  granted you have to know the binomial factor but that is virtually staring you in the face. So here we go.

And yes I know I really should factor out the last term, but the purpose of this was to show how synthetic division could be use for this situation.  I don't know if this a better process or a more confusing process.  I guess I kind of would like feedback on what people think.

Now on with my continued rant teaching polynomials.  Is it really necessary in this day and age to talk about the Rational Zero Theorem (p/q rule), Descartes's Rule of signs?  I'm not convinced those are really important any more. 

I do believe End Behavior is important and understanding the essence of the Fundamental Theorem of Algebra, that polynomials have the same number solutions as the degree of the polynomial is important, and knowing that complex conjugates come in pairs is good to know.  While I can't say I have completely dissected Common Core, but I get the impression some of of these nitty-gritty details are not part of Common Core, and for the life of me, I'm not sure they are necessary. 

What do you think, are these skills necessary?  Or are there other skills we need to know with respect to polynomials, their zeros, local minimums and maximums, especially when these features can be found with a graphing calculator?  

Just curious.

3D Printers for FREE

Well, maybe not free, but pretty darn close.  The company MakerBot is offering 3D Printers for Public Schools, at virtually no cost.  All you have to do is set up a request through the DonorChoose.org organization and MakerBot will pay for all but about $96 or so of the cost.  The additional cost, comes from donations.  I set up my account last week, in two days the account was approved, and in less than 2 hours someone donated the additional $96, so we are now expecting to get a 3D printer for our robotics team sometime in December.  I'm not sure what all we will use if for, but you can't beat the price.

Although, they may be following the HP InkJet printer model --- Sell the printers dirt cheap, make it up with "ink" sales.   I don't have any idea how much the material costs, but I'm sure 3D printing is probably kind of addicting, so once you start down the path, it may be hard to stop finding things to print.  Thus more "ink" to buy.  Now  I'm not by any stretch complaining.  I'm looking forward to having to figure out what we should spend our printing capabilities on.

Interesting Quadratic Relationship - Tape Measurer

Spurred on by What can you do with this: Annuli by Dan Meyer,

I handed out tickets to the students as they entered my classroom on the first day of class in my Algebra II class, on each ticket, I write a number for their desk, that they have to find in the room.  After some of the obligatory first day stuff, I have them inquire about the roll of tickets and through a joint process we slowly come up with a plan of action on how to measure the ticket roll and estimate the number tickets.  The exercise goes fairly well, with the sole purpose to get them to start thinking of math as to answer questions of curiosity.   Anyhow as an extension, I was thinking about these big 30 meter tape measurers we have in our science department, and wondered if we could come up with a relationship between the number of turns it takes to roll in the tape and the reading on the tape measurer.   We collected the data a few days ago, but haven't done anything with the data yet.  However, I took a sneak peak  at the data and it provides a very strong quadratic relationship.

I plan to have the students plot the data and see if they can developed a quadratic function from data by choosing 3 points and solving a system of equations.  Obviously not quite as accurate as doing a full blown quadratic regression on the calculator, but hopefully it give them a feel for solving a system of equations as well as being able to make some predictions with their data.  Anyhow those are my thoughts at the moment.

In addition, I think I would like them to think about WHY this is a quadratic relation.  I'm not sure how well that exploration will go, but I am curious what they think.  Comments???