Wednesday, February 20, 2008

Limits

Why hello there!



Kristin here - reporting the events that took place in todays' Calculus class.



The day started off with introductions to Mr.Rekrut- our substitute teacher for the class, with his first words being, "Looks like you have a quiz today" ....a little shocked, not going to lie.



Luckily, it was only four questions involving the simplifying of problems with exponents, factoring with exponents, finding the equation of a line in general form given the slope and a point on the line, and finding the equation of a line given a point and a parallel line.



Then we were assigned pages 45-58 in the orange and white booklet, as well as pages 6-8 in the blue booklet, which I'm assuming are due for next class, seeing as how we don't have one until next week..



If there is anything I forgot, please let me know....

The Scribe for next class is....SAMUS!!!

Monday, February 18, 2008

AsianTown.NET


Whoa! I can’t remember the last time I blogged for Math! But, yes, again, blogging is a very important instrument to enhance knowledge and develop self responsibility (remember the escalator video..). It is our utmost responsibility to do things ourselves even though we tend to lean on others – which means:
  • do our homework
  • try to blog as extensive as possible for it determines how well you know the material
  • read scribe post everyday
  • ask questions if necessary
  • always check for misinterpretation by peers so that no one else will be confused and eventually mess up a test or exam in the future.
So, have you read the blog-online rules? Have you watched the video? Have you finished your homework? If you haven’t done so, please do.

Talking about unlimited amount of math, Mr. K introduced a very interesting approach to

UNIT 1: LIMITS

What is a limit? The first time I heard it was when I watched “Mean Girls” back then. I didn’t know what it was. Yes, 5 years after… here it comes, slowly making sense. Yes, AP CALC people, you can laugh since we’re only at the threshold of the house you have already explored three times! Here it goes.

This notation is used to express LIMITS, which means if you do not have this in every line, the entire thing is incorrect!

PROBLEM #1:

What do we first notice about this equation?

  • a second degree function (x^2 : parabola) over a first degree (linear)
  • a difference of square in the numerator
  • if we graph this on our graphing calculator, it’s a straight line, opposing the fact that it should be some kind of a parabola. Hmmm, weird.

What happens if we factor the numerator?

  • the (x-1) reduce
  • we’re left with f(x) = x + 1
  • graphically, it is identical to the graph we had earlier when we graphed the original equation

What if x = 1?

  • Most of the students would say, “IT’S 2!” because of the equation: f(1) = 1 + 1 = 2
  • However, some might disagree and say, “It’s undefined, buddy!”

The question now is WHY? Well, f(x) = x + 1 isn’t the original equation.Therefore, substituting 1 for all x gives us:



This brought the discussion about the very round number called ZERO. Usually when we divide any number by zero, we say “YOU CAN’T!!!”. It’s very hard to explain. Actually it’s pretty simple. You can’t divide by NOTHING! This follows the same curvature of the ball of wax. Anything over ZERO is undefined… it’s not two… again, it’s undefined!

We also had a discussion about 0/0 is not 1, why is it so different from 2/2 = 1?, when both 0 and 2 are numbers? Isn’t a number divided by itself equal to 1? Why is zero such an exception? Well it could mean NOTHING, INFINITY, or ZERO. It all depends on the hwo you look at it. Interesting… Mr. K, took out his “block of wood” to further discuss how you can look at something at different ways but it still refers to the same thing.

Consider SLOPE. It can be represented in three ways:

  • m
  • y = rise / run
  • y = delta y / delta x

So, why do we have three ways to describe slope? ANSWER: because we have three ways to illustrate a function:

  • equation – where ‘m’ is present in the standard form of a line (y = mx +b)
  • numerically (table of values) – where we can take two ordered pairs and put them into the equation
  • graphically – where we can locate two a point and use y = to find the slope.

In this case, f(1) is in an indeterminate form, which means, when x = 1, it is undefined. To prove this, we can graph the equation one more time. But this time, hit ZOOM 4, which will provide you with a much closer scrutiny at the graph.




Look at the gap on the linear equation. Isn’t it weird? Well that’s exactly what we had earlier. f(1) ix not 2. Because the point missing on the graph. Try tracing any integer greater or less than 1. It will give you the y-value but will not do it so if you enter x = 1. This squeezes out the value of 2 from both sides - >2 and <2.>

Let's take a look at a very similar problem:

As the end of class approaches its LIMIT, Mr. K, very quickly went through the laws of limits with all the mathematical operations (addition, subtraction, multiplication, and division). They are on the slides posted of Friday! It's pretty simple. It's somehow like logarithms but not really! AND AGAIN, MAKE SURE TO INCLUDE THE PROPER NOTATION FOR LIMITS OR YOUR WORK WILL LOSE A VERY FRUSTRATING AMOUNT OF MARKS!

We had a glimpse of the graphs of limits at the end of the period but since I was not sure about how it goes, I chose not to include it here. I hope Mr. K further go into details about that one in class next next class (he won't be here on Wednesday, which is the only class we have this week). This concludes my scribe post and I hope everyone had a great 3-day weekend! If you didn't, don't worry, there IS another one! YES! Anyway the next scribe will be...

K r i s t i n !






Friday, February 15, 2008

Today's Slides: February 15

Here they are ...



The Scribe List

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post can be quickly accessed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

IMPORTANT: Make sure you label all your Scribe Posts properly or they will not be counted.


Cycle 1

m@rk
haiyan
1
SAMUS
MrSiwWy

Grey-M
John D.
«Craig»
vincentr
Dino

Tim_MATH_y
rusz.l
Kristin_R (update your posts)

Thursday, February 14, 2008

February 13 / 08 - Scribe

I will be taken Vincent's scribe duties as he requested.

Mr. K was not present in class today so we had a sub. This class was a working period to do the review booklets. (Blue, White/Orange)

The new assignments are: Read pages 30-45 (White/Orange book), Do page 5 (blue book).

That concluded the class of February 13!

The next scribe will be: Vincentr!

Monday, February 11, 2008

First Scribe!!!

Oh Boy! Here we go, I'm scribing again.

This is my fourth class with Mr. K., all of which I had to scribe for at least thrice, so I'm used to it.

Anyway, today's class was basically our first official class of learning. However, it ended up being a review of grades 10 through 12. Mr. K. went over the Review Test we had the previous class, touching on the questions we seemed to have the most trouble with.

These questions included the concepts of:
•Inequalities
•Fraction Operations
Factoring
Rational Functions
•Function Notation
•Trigonometry

As well, there is a list that may be seen here(slides 14 and 15) that goes over the things we should already know.

I believe Mr. K. did a sufficient job in discussing the problems we may have had in class, as no one seemed to ask questions.
***But remember, if you need any help in dealing with any of the content in the course, arrange a time with Mr.K. or even ask some other students to see if you can get the advice you need***

As well, I suggest if you got some questions wrong on this quiz that you should go back to the questions and try them again. It should help. Or, just open your booklets and do the homework; it provides tons of practice questions dealing with the above concepts and more.

Homework: All exercises up to page #30 in the ORANGE BOOK
•Pages 2, 3, 4, and 5 in the BLUE BOOK


Last but not least, Wednesday's Scribe will be:......


VINCENT!!! (he does awesome Scribes =D)

Today's Slides: February 11

Here they are ...



Thursday, February 7, 2008

Just for laughs

So.. this is what boredom does to you. Especially if you're LOLcat fan.



















I found it on http://icanhascheezburger.com/2008/01/22/funny-pictures-sisyphus-cat-tries-again/..

Today's Slides: February 7

Here they are ...



Blogging On Blogging (BOB)

We were talking about exactly what sort of post you're supposed to make to get that one blogging mark on your test. The kind of post I'd like you to make should have one or more of these characteristics:

  • Write about what you understand the least in the unit so far; your personal "Muddiest Point."

  • A reflection on a particular class.

  • A reflective comment on your progress in the course.

  • A comment on something that you've learned that you thought was "cool".

  • A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.

  • Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.


Your posts do not have to be long. I'm far more interested in the quality of what you write rather than the quantity.

Make certain you always use 3 labels on your post: [your name], [unit tag], BOB

When you share where you are in your learning a few days before the unit test I can address those issues in class so, hopefully, you will get much more than one extra mark on the test. ;-)

Happy Blogging!

Tuesday, February 5, 2008

Digital Ethics

Blogging is a very public activity. Anything that gets posted on the internet stays there. Forever. Deleting a post simply removes it from the blog it was posted to. Copies of the post may exist scattered all over the internet. I have come across posts from my students on blogs as far away as Sweden! That is why we are being so careful to respect your privacy and using first names only. We do not use pictures of ourselves. If you really want a graphic image associated with your posting use an avatar -- a picture of something that represents you but IS NOT of you.

Here are a few videos that illustrate some of what I want you to think about:



Two teachers in the U.S.A. worked with their classes to come up with a list of guidelines for student bloggers.

One of them, Bud Hunt, has these suggestions, among others:

  1. Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.


  2. Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.


  3. Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.


  4. Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.


Another teacher, Steve Lazar, developed a set of guidelines in consultation with his students. You can read them here.

Look over the guidelines and add the ones you like in the comments section below this post; either from one of Steve's students or one of your own. I think Bud's suggestions are excellent. We'll be using the one's I highlighted above as a basis for how we will use our blog.

Cheers,
Mr. K.

Today's Slides: February 5

Here they are ...