Blogging On ... Blogging On Blogging!

( ^_^ ) Get it?! haha.

I guess it's about time to put some humor on this since we do have an audience. Hope everyone's enjoying it btw!

Here's my blog so I can put that "yes" on the first question on the page:

Probably everyone in the class knows, that I'm one of the people taking both Calculus and Pre-Cal 40S. I have to admit, that I was very intimidated, at first, as the first few weeks of calculus have started. For one, my summer was so full of memories that my mathematical knowledge somehow slipped away :S (very bad, I know). Second, everything seemed so new to me that my brain was crammed with so much new information each day. It's pretty hard to learn all these new terms such as logarithms when, pretty much, it's review for most of the people in the class. For example, logarithms. Last night, I remember doing my homework and attempted to catch up on some homework since my book went missing. I was doing the section on logarithms. The first couple of questions were pretty easy, but when I came to questions with the words "log" or "ln" everything became much more confusing. I kept telling myself, "A LOGARITHM IS AN EXPONENT!" But afterwards I told myself, "O.k. .... then what?!" (Now I feel like Mr. K, cramming that phrase into your head). I remember reading over the introduction a couple times but, based on my VARK test, I'm not that kind of learner. The next morning, I asked Mr.K for some help during lunch and of course, he agreed. I came right after third period and got ready to learn about logs. By the end of lunch, I finally understood it! *bows down* (Thanks Mr. K!) What helped me with logs are these properties:

1. log_b(xy) = log_bx + log_by
2. log_b(x/y) = log_bx - log_by
3.log_bx^r = rlog_bx

(Note: They're very helpful- trust me)

Maybe some of you didn't know this, but I was this close: → ← (see the space?) to dropping out the course :S. I found it hard and difficult to put all this new information in my head in such a short period of time. I guess I just wanted to give up and my brain was still in "summer mode". I really don't like giving up on anything that I know i could do. It's getting much easier though and a lot more helpful for pre-cal. I learn something new in calculus class and when I go to pre-cal, I'm learning the exact same thing, but more thoroughly! Unfortuanetly, it probably won't be like this the entire year, but I'm ready! So in conclusion, I'm staying in calculus!
I guess that wraps everything up for my blog.
-me :)

1000 Words

I love pictures! This applet will show you pictures of what sine, cosine, tangent, secant, cosecant and cotangent represent on a graph. Very cool! Play with it and we'll talk about it in class tomorrow.

BTW, do you know what they call a man who goes south for the winter?

A trig function! No, they call him a Tan Gent. ;-)

What does that picture have to do with this joke?

Glenney's Scribe-aler

^(Get it? Scribe-aler... scribbler?... not very funny I guess? hey, at least I tried :P)

This morning was better than it usually is. With more enthusiasm and energy, this year's going to be pretty good. I guess everyone's getting a lot more used to each other and it's not so quiet whenever Mr. K asks us if we get what he's saying. The morning started off with our usual challenging problems that sometimes makes us think until our head hurts :S. As soon as we all talk about the problems the first thing Mr. K always says:

"A LOGARITHM IS AN EXPONENT!"

Remember that :)

Mr. K's trying to plant that in our heads for the rest of lives! It'll be worth it though in the future. In university, the prof's going to ask what is a logarithm and you'll stand up, and say.. "A logarithm is an exponent!"

After a very interesting list of mascots, we finally made our decision with "The Prince of Calculand" featuring our very own Prince. I guess I'll be one of the first to say congrats! haha. It was pretty much a unanimous decision and I think our story plot's going to be very interesting.

Back on track with the problems, we learned that sometimes an extraneous root may appear. With this showing up, we had to remember to always check if our answer can fit the equation properly. In this case, -10 or any other negative number cannot be true because any number to any exponent cannot equal a negative number. The number must be positive and cannot equal 0 or be a negative number.

Near the end of class, we learned about the graph: f(x)=1/x and how it never touches the x or y axis'. No matter what number you substitute for x, whether it be a fraction or a large number, it'll never touch.

I guess this wraps up my daily blog, see you all tomorrow :)

Up next... Jay :D

Spikes and Spears

To refresh or enhance your understanding of rational functions I'd like you to work through the activities in this lab called "Spikes and Spears". Spikes are the vertical asymptotes and spears are the horizontal (or slant) asymptotes of rational functions.

Have fun with it!

Our Readership

I thought you might be interested to know about our readership. Our blog is being read by people all over the world. The graphic below shows where the last 88 visitors to our site have come from. Of course, this is constantly changing as more and more different people pop in to see what we're doing. While some of them visit only once a number of them do keep coming back. (The "unlisted" reader is from Belgium.) People are interested in what you have to say and what you are learning.

Ladies and gentlemen, you have an audience. It's worth your while to make a good impression by making sure your spelling and grammar are correct when you post. ;-)

More About Wooden Beats - Logarithms ;-)

Here is a good interactive review of logrithms and their properties. When you finish you can try the online exercise set.

Wood with a Beat - Logarithms!

Ouch, sorry about that title. ;-)

Several links to review logs:

    What on Earth is a Logarithm?

    Definition, Graphs and the Natural Logarithm

    Change of Base and other Logarithm Properties

We'll be talking more about logarithms tomorrow.

It's Invertable!

Today we talked about inverse functions. We've got lots of resources here if you need any help or extra practice:

To learn more (or review) about inverses follow the three links below. In each case you will need to have two windows open. In one, you'll be playing with an interactive graph -- it opens up when you click the button marked [click here to start] -- in the other are the directions to follow to learn the material. Have fun with it!

• Inverse Function Definition


• One-To-One function


• Inverse Function

You can practise applying your skill in these online quizzes:

• Finding simple inverse functions
  (5 questions)


• Look for the link: Chapter 4.1 Inverse Functions
  (10 questions)

After you click on the [submit quiz] button DO NOT click on the [email to instructor] button -- it won't get to me. ;-)

Remember also to have thought about:

(1) When is a good to to "meet" in the chatbox.
(2) We need a "character" for our year long project.
(3) Are you interested in creating an instructional video instead of the story project?

Cheers,
Mr. K.

Chatting and Study Groups

I noticed a lot of chatting going on in another blog so I installed a little chat window, it's called a Shoutbox. Give yourself a screen name and anyone can talk anytime you're here!

You may recall I talked about you all getting together in groups of 3 or 4 to create study groups. Meet once a week, say Wednesday's at lunch in the library or whatever works for you. Well, with the Chatbox you can set a time anytime when you call all meet online, chat and get whatever help you need with your homework in the Chatbox.

I think this will be a powerfull learning opportunity for all of you. It depends entirely on each of you individually. It's up to you whether or not you choose to get involved.

You'll find the AP Calculus Chatbox window down there at the bottom of the right hand sidebar.

Please leave me feedback in the comments to this post. Is this a good idea? Are you getting anything out of it? Should we keep it or delete the Chatbox? Leave your vote here. ;-)

Cheers,
Mr. K.

Exponents on Video!

Class time seems to just fly by! Sometimes we get hung up on a difficult problem and time seems to  d r a g  and sometimes we cover so much material in such a short time that it just seems to fly by.

I know some of us are still struggling with exponential functions. Well, help is here. I've got some brief video taped lectures you can watch to help you with this material over the weekend if you need it. The movies are of an instructor from the University of Idaho.

In order to watch the video you need to download the free realaudio player from here. (It's a little more than 11 Mb so if you have a slow internet connection this isn't a very good option for you.) After that, just click on the link below for help with the topic of your choice!

• A Review of the Laws of Exponents
  (4 min. 6 sec.)


• The Definition of an Exponential Function
  (7 min. 37 sec.)


• Sketching the Graphs of Exponential Functions
  (8 min. 34 sec.)


• The Definition of the Function e^x
  (5 min. 39 sec.)

Let me know what you thought of the video in the comments to this post. Did it help you learn? Is it clear and easy to follow? Should I post more of these? ;-)

If you still have trouble help each other through the comments to this post.

Have a great weekend!

Shifted Exponentials

We learned about the exponential function today. A quick review is over here and a review of problem solving with exponentials is over there.

A review of all the ways we can use transformations to move the graph around is just a click away ... right here. ;-)

Playing with Regression Lines

In tonight's homework you're working through the mechanics of generating a linear equation for a given set of data (points in the cartesian plane). It's easy to loose sight of what this all means or what it is exactly that we are supposed to be doing.

I'd like you to take a look at this online tool. It may take a moment or two to fully load in your browser. When it does you'll see a blank, white graph on the left and a horizontal line on a grey graph on the right. Clicking on the white graph will put a blue point at that spot. Add as many as you like. You'll also see a red line whose position changes as you add more points. Basically, this applet is drawing the "line of best fit" for the (random?) set of points you specify.

Play with it for a bit try to:

• get a line that has NONE of the points you create on it


• get a horizontal line that has none of the points on it


• get a vertical line using as few or as many points as you like

We'll talk about your results in tomorrow's class. We'll also talk about what we're looking at in the grey graph.

Have Fun!!

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 is can be quickly accesed 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.

Cycle 11

Prince ** (Don't choose me now, I'm getting better.) steve Chris* ara xun SarahS*

janet's scribe

Calculators are not that smart, sometimes! When graphing a calculator everything isn't always what they seem. That was one of the things I learned last class, I bet you didn't know that either. First exercise we did were the problem solving questions using our calculator, which really helped me refresh my memory. We wrote equations and sketched graphs to help us solve them. Also, we refreshed our memory on f(x) functions by doing reviews. Next we talked about most of the basic functions, Cubic, square root, reciprocal, absolute value, squaring and identity functions. In that lesson I learned to flip graphs over the y-axis instead of sliding them on the x-axis. It's always good learning different ways to solve problems as Mr. K's famous phrase goes, "There is more than one way to skin a cat, but don't really do that because it's cruel!"
So overall it was yet another productive class, for me that is, and I do apologize for not posting this sooner. I did try! I swear ... and I guess everyone knows who the scribe is for today's class, Sarah!! Have fun!

SCRIBE

Another productive class don't you think? Again, we got into groups and tried to create a graph representing our little story from Andover to Concord. I think that it was a bit too quiet... or maybe I just have bad hearing? During this activity, we all had different ideas on how we created our graphs- which is a good thing seeing how we can all learn from each other's mistakes. After some contemplation and discussion, we were able to understand how the graph was to be displayed. But hey, some of us might be in "summer mode" still and getting adjusting to the homework and the early morning wake ups.

It probably was a big refreshment to some of us on how to create graphs in our calculators- it was for me. We were taught how to determine if a graph was a line by using the calculator to create an equation and using it to draw a line through our points. We also learned about the r² function which determines how accurately it will go through our five points.

So, it's our first day of real calculus homework! And hopefully, no one struggles too much on it. As the next couple days go, we'll all remember work from s3 & s4 pre-cal! Don't let the forgetting curve get you during this course because it's something that would be very helpful in the future. Anyway, let's not have such a quiet class and start interacting! Let's have a fun year everyone :)

-Glenney


Next scribe. . . . Janet :)

Students Made This!

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.

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

One of them, Bud The Teacher, 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, 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.

SCRIBE

(scribe for Friday, September 9'05)

So yesterday was a productive class. We went into groups to discuss all the facts we knew about functions after doing it our selves. THAAAAAAAAT, was a great idea! I think you tend to get more when you have a conversation going on, and hearing things that either refresh your mind, or be like 'OH, i learned something new today =)' I mean, it is great to work independantly, but another way to learn is to have some sort of communication going on..

As Mr. K mentioned, there are three ways to present a function- numerically, symbolically and graphically.. It's kind of cool how one thing can be presented to you in different ways.. Just like how he showed us that block of wood.. Its kind of like for basketball, you can be told a play either, verbally, drawn on paper or see it demonstrated to you.. The same play, just presented in different ways.

We also tried to draw a graph of the lengths of our hair in a year... That was pretty difficult to draw.. But once we discussed how everyone's graph looked, and actually questioned; does this really look like how its supposed to be?, it turns out NO.. After seeing how it should be drawn, i was like OHHHHH! That makes so much sense!

-- Mary Ann

This is all for today folks..
( *glenney your next =D )

Blogging on Blogging

A good class today folks! You worked together really well in groups and gave good verbal feedback over the course of the lesson. Thank you. There's still a little more room for growth here though. When you find that everyone in your group is stuck and doesn't know how to proceed please let me know immediately. Don't wait until I come around to ask. Time is precious and we don't want to waste any of it.

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

• A reflection on a particular class (like the first paragraph above).


• 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.


• Respond to a Blogging Prompt I posted. (see below)

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

Blogging Prompt
To help us along our blogging journey I've decided that I will also occasionally post a Blogging Prompt. It will be easy to find because I'll always put it under a heading like the one above this paragraph. Feel free to create your own Blogging Prompt for the rest of us if you like. If it's a really good one (i.e. has rich possibilities for blogging) we'll count it as your post. ;-) Here's my first one:

We've learned about three different ways to represent a function; symbollically, numerically and graphically. Blog a brief paragraph identifying ways in which these three representations are similar. Blog a second paragraph outlining the ways in which they are different.

This sort of compare and contrast exercise can be made easier to do using Venn Diagrams. Draw three large overlapping circles. List the similarities in the appropriate overlapping sections and the differences in the non-overlapping sections. If you like, you can use this web tool to do it online. If you do blog about this prompt and want to post your diagram we'll talk about how to post pictures sometime in class. ;-)

Happy Blogging!

You're Here! Let's Begin ...

Hi There! You found our blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; to get copies of a handout you didn't get in class (here's the course outline); for parents to find out "How Was School Today;" to share your knowledge with other students;.... Most importantly it's a place to reflect on what we're learning.

Remember what I said about the Forgetting Curve? Well a big part of Learning and Remembering involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, or make your own blog and link it to this one, or....the sky's the limit...let your imagination soar and lets get down to some serious blogging!

Here's your first online assignment:

Do you see the Links list in the side bar over there on the right? Follow the Study Skills Resources link. Browse through the sites until you find one that you think has excellent suggestions on how to study math; then, on a piece of loose leaf paper (or this worksheet) to be handed in on Monday:

• Write the address and name of the site you most liked.


• Rate the site out of 100; i.e. give it a grade!


• Write a brief description (no more than 4 or 5 sentences) of the site.


• Include a comment on what it was about this site that made it stand out for you (no more than 1 or 2 sentences).

Repeat this exercise for the second link that deals with Test Taking, i.e. how to write a test.

If you take this assignment seriously now and invest some real time and energy into it, you'll probably do real well in my class this semester...who knows, it might even help you in your other classes too! ;-)

Have Fun!