So Long ...

And so we begin where we left off ... don't let the sky be your limit. ;-)

I'm so glad we've had this time together,

Just to have a laugh or learn some math,

Seems we've just got started and before you know it,

Comes the time we have to say, "So Long!"

So long everybody! Watch this space for pointers to new blogs for each of my classes.

Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)

My very best wishes!

I am thinking that these days each of you, your family, and your friends are looking to your future. I'd like to do that too and wish for you all that Emerson describes--

Lani

Passing it forward!

Some 44 years ago (when I was about your age) my father who used to travel a lot, penned a letter to me and enclosed a short article clipped from a magazine. In that letter, he wished for me a life of purpose and joy. The enclosed clipping described such a life and quoted George Bernard Shaw whose words you can read above.

I carried that article with me for years; unfortunately, somewhere in the many moves, it was lost. But not the thought and the power of those words; they have become a part of who I am. I know that my career as a teacher, and my mentoring are but "drops in the ocean" in this often violent, globalized world of ours but they are a significant part of my life which has been filled with joy, happiness and love. I'm sure that my father's writing and sharing those thoughts adds to their meaning for me, especially now that Alzheimer's prevents him from recalling what occurred. His belief in me, in mankind in general,and his wish that I might find a life of purpose and joy shaped my world.

I'm passing that forward --my belief in you, my belief in mankind, and my wish that you find real purpose and joy in life!

You're in The News

I just stumbled across a couple of links where folks are talking about your work here on the blog and linking to it as an example of high quality blogging in mathematics ... thought you'd like to know ...

Website of the Week (05-28-07)

Wikis and blogs in senior secondary classrooms

I know I've mentioned this before but it's worth mentioning again ... I've very proud of you. All of you.

Cheers!
Mr. K.

You Should Know ...

As we wind down towards the end of the year and you finish your Take Home Exam, complete your Developing Expert Voices projects and look back on all you've learned using flickr, wikis and your blog (including various entries into The Hall of Fame) you may recall my telling you the world is watching and talking about you. Well, they really are. Look at this blog post by Dr. Paul Martin, an English professor at the University of Vermont. (Scroll down to Best Practices.)

Any time you want to see whose been talking about and linking to you can do that by clicking here.

Photo Source: Security

Happy

I am so happy to be done my DEV PROJECT and so proud of it too.. Anyway, hope you guys like it. http://liiinger.blogspot.com/

Today's Slides: May 16

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

Food For Thought

Watch this. It's only about a minute long. You really need to see this ... really ...

Research Assistants

How are Research Assistants Chosen?
Choosing to be a Research Assistant is entirely voluntary ... but if you do it you can get a bonus mark on the unit test for each unit you undertake to act as Research Assistant. A maximum of one bonus mark is available for each student that publishes as Research Assistant.

IMPORTANT: There can only be one Research Assistant for each scribe post.

What Does a Research Assistant Do?
The Research Assistant must search the internet to find a minimum of two links in support of one of our daily scribes.

(a) One link must be to a site that reviews the content we have been studying in class as described in the scribe post for which you are acting as Research Assistant.

(b) One link must be to a site that has one or more interactive quizzes (self correcting) that deals with the specific content covered by the scribe post for which you are acting as Research Assistant.

(c) The links you find cannot have been published by any previous Research Assistant.

(d) Tag your post with i) your name, ii) the unit ii) Research Assistant.

How Do I Know What Previous Research Assistants Have Done?
Below is a list of the units and Research Assistants to date. This list will be updated as each Research Assistant posts the results of their research. Each Research Assistant's name is linked to the post they made with the links they found. This post is your "one stop shop" to find out what has gone before and learn/review when you need it.

The Research Assistants List

Conics
MrSiwWy

Photo source: HoP Mad Science Fair: Jon and Natalie

heres a funny video =) about calculus

Today's Slides: May 8

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

Scribe Post

Hi, this is Christian! In our last class, the lovely Mrs. Stawski came to help us with prep stuff for our upcoming exam. It's on Wednesday everyone!!!

After that, we had to do questions. As soon as we go over those questions, and we get the answers (we haven't done either), I'll do a follow up on this scribe post. For now, hang in there!

And one more thing!!

On the day that I was to take my "big" test, I was just about to leave for the testing center when I asked my husband to wish me luck. "No," he said, "I won't do that." I was crestfallen. I felt like I needed one last boost before the "big" one.

Then he continued, "You don't need luck. You're smart. You're prepared. You're good. I believe in you. Go out there and just do it!!!! I'll be here when you get back."

It's time for me to pass that forward to you! You don't need luck. You're smart. You're good. You're well prepared (thanks to your hard work and Mr. K). I believe in you. Go out there and just do it!!!!

From ZZZZZ's to A's

The bottom line: Teens need 9.25 hours of sleep per night

from Do Teens Get Enough Sleep?

In experiments done at Harvard Medical School and Trent University in Canada, students go through a battery of tests and then sleep various lengths of time to determine how sleep affects learning. What these tests show is that the brain consolidates and practices what is learned during the day after the students (or adults, for that matter) go to sleep. Parents always intuitively knew that sleep helped learning, but few knew that learning actually continues to take place while a person is asleep. That means sleep after a lesson is learned is as important as getting a good night's rest before a test or exam.

from Adolescents and Sleep

At the risk of sounding "mom-ish", have you taken this into consideration in your preparation for your upcoming test? I know you mentioned it in a scribe as being discussed in class!

Asking only because, when I was sleep deprived, I know I wasn't fully aware of how much more difficult problem solving and remembering was. I never fully realized how sleep deprivation changed my abilities and me until after I started getting adequate sleep.

Another factor in your preparation to be your very best for your test??

Visualize Success on Your Test!!

SCribe post

The Calculus exam is in seven days and seven nights.

Things to remember:
- Bring food
- Sleep early the night before
- Bring water
- Stretch when it is break during the exam

The wiki assignment is due at midnight tonight. Remember to log in with your first name on the wiki. Constructive assignment starts tomorrow.

AP MINI EXAM ANSWERS
1) A


2) B


3) D


4) D


Free Response question
A) Using a mdpt sum we get 43.1 multiply it by six which is equal to 258.6

B) Yes there is a a value where r'(t) = 0 because if you look at the table, there is a maximum value between 9 and 15 hours.

The next scribe is christian

Scribe Post

Here are the answers for the exam review quiz. Just click on the images to make them bigger.

Developing Expert Voices Rubric v1.1

Here is the updated version 1.1 of our rubric ...

---

Teaching mathematical concepts is the main focus of this project; so we can teach other people and learn at the same time.

Achievement Descriptors
Instead of levels 1-4 (lowest to highest) we use these descriptors. They better describe what this project is all about.

Novice: A person who is new to the circumstances, work, etc., in which he or she is placed; a beginner.
Apprentice: One who works for an expert for instruction or to learn a skill or trade.
Journeyperson: Any experienced, competent but routine worker or performer.
Expert: One who possesses special skill or knowledge; trained by practice; skillful and skilled.

Achievement	Mathematical Challenge (25%)	Annotation (40%)	Solutions (15%)	Presentation (20%)
Novice	Problems illustrate only an introductory knowledge of the subject. They may be unsolvable or the solutions to the problems are obvious and/or easy to find. They do not demonstrate mastery of the subject matter.	Explanation does not "flow," may not be in sequential order and does not adequately explain the problem(s). May also have improper mathematical notation.	One or more solutions contain several errors with insufficient detail to understand what's going on.	Presentation may or may not include visual or other digital enhancements. Overall, a rather uninspired presentation. Doesn't really stand out. It is clear that the student has invested little effort into planning their presentation.
Apprentice	Problems are routine, requiring only modest effort or knowledge. The scope of the problems does not demonstrate the breadth of knowledge the student should have acquired at this stage of their learning.	Explanation may "flow" well but only vaguely explains one or more problems. Some parts of one or more solutions are difficult to follow. May include improper use of mathematical notation.	One or more solutions have a few errors but are understandable.	The presentation style is attractive but doesn't enhance the content; more flashy than functional. It is clear that the student has invested some effort into planning their presentation.
Journeyperson	Problems showcase the writer's skill in solving routine mathematical problems. They span an appropriate breadth of material. One or more problems may require careful thought such as consideration of a special case or combine concepts from more than one unit but not necessarily.	Explanation "flows" well and explains the problems step by step. Solution is broken down well and explained in a way that makes it easy to follow. May have minor use of improper mathematical notation. May point out other ways of solving one or more problems as well.	All solutions are correct and easy to understand. Very few or no minor errors.	The presentation may use multiple media tools. The presentation style is attractive and maintains interest. Some of the underlying message may be lost by some aspects that are more flashy than functional. It is clear that the student has given some forethought and planning to their presentation.
Expert	Problems span more than one unit worth of material. All problems are non-routine. Every problem includes content from at least two different units. Problems created demonstrate mastery of the subject matter. Showcases the writer's skill in solving challenging mathematical problems.	Explanation "flows" well, explains the problems thoroughly and points out other ways of solving at least two of them.	All solutions correct, understandable and highly detailed. No errors.	The presentation displays use of multiple media tools. The presentation style grabs the viewer's or reader's attention and compliments the content in a way that aids understanding and maintains interest. An "eye opening" display from which it is evident the student invested significant effort.

Creativity (up to 5% bonus)
The maximum possible mark for this assignment is 105%. You can earn up to 5% bonus marks for being creative in the way you approach this assignment. This is not a rigidly defined category and is open to interpretation. You can earn this bonus if your work can be described in one or more of these ways:

• unique and creative way of sharing student's expertise, not something you'd usually think of;


• work as a whole makes unexpected connections to real world applications;


• original and expressive;


• imaginative;


• fresh and unusual;


• a truly original approach; presentation method is unique, presented in a way no one would expect, e.g. song, movie, etc.

Today's Slides: April 30

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

A thought--

Exam Prep Wiki Solution Manual

As we gear up for the exam two short weeks away I want to push your thinking to yet a higher level. To a level commensurate with what will be required of you on the AP Exam. Towards that end here is your final major assignment (other than the take home exam in May) for the course.

You will collectively create a solutions manual for this course, one question each. Actually, there are two parts to this assignment: A Significant Contribution and a Constructive Modification. Here's what you have to do:

Part 1: A Significant Contribution
to be completed no later than May 2, 2007.
(1) Go to your Solutions Manual wiki (also linked in the side bar right under the Scribe List) and pick one question in the Side Bar list.

(2) Solve the problem completely. Show all work and annotate it as if you were explaining it to a classmate who was having trouble with it. (Similar to the way you write up your scribe posts.)

Part 2: A Constructive Modification
to be completed no later than May 6, 2007.
(1) Scan through the solved problems your classmates have written up. Find one with an error and fix it or correct a diagram or improve on what they wrote if it is unclear in any way or ... there's more about this on the front page of the wiki.

IMPORTANT
Make certain you always log in to the wiki using your first name. If you don't I won't know what work you have done and will be unable to assign you the marks you earned. Not logging in with your name is the same thing as handing in a paper assignment without putting your name on it. Also, if you've forgotten the password email me and I'll email it back to you.

Photo source: no solution

BOB

The course has concluded... This unit has been very interesting. I remember when Mr.K said we will learn how CSI people do their investigations. I saw it in the homework assignment. For me, Newton's Law of Cooling is a very interesting lesson. We learned how to calculate how long it would take for a certain object to cool down. I've learned a lot for the past couple of months in this course, even though the past things are just starting to make sense (since I'm just taking PreCal 40S). I still have to worry about my DEV in calculus. Some people say it's not fair for me to do 8 questions for DEV. I'm not usually the kind of person that "complains" about what my teachers give. Yeah, its a lot of work, but I'm up for anything the teacher throws at me.

I hope everyone did well on the test! =D

BOB

WOW it's the last unit test. I'm amazed by how quickly the time passed... anyway, I think I'm ok for this unit for the most part. We'll see how the test goes though. I'm more concerned about the DEV project right now though so I don't really have time to study. I guess it's a good lesson though, I should have thought more carefully about the due date I picked. I really wanted to hand it in earlier so my life wouldn't be so stressful after the AP exams, but now it's really REALLY hectic :S Right now I'm starting to feel like I don't even care anymore. One of my teachers said that it's because we're so close to the end we can see the light at the end of the tunnel, and we're just looking towards that and hoping to get there on momentum alone... and another thing I want to mention, all the people who write math textbooks and come up with problems, my respect for them has increased by about a billion percent. Coming up with questions is a lot harder than I thought it would be. Even if you can solve a certain type of question, creating one in a way that works seems to me like pulling a rabbit out of a hat. an enormous rabbit. :)

BOB

Differential Equations is the final unit. It was short and I guess a bit difficult in the beginning, but what chapter isn't. During the beginnning it's mostly mechanical. Near the end there's more thinking, especially for the word problems. The day we did all those word problems really helped me out. Practice makes perfect. Those problems were practically the same, only the story was different. The assembly today really got to me especially about the attendance. When one of the guidance councillors discussed about the statistic or math problem he took about relations between attendance and marks it was kind of interesting for me. Even more when it was only for DMCI students not national or overall. We completed this unit, but I still have to study the previous units to get ready for that crazy exam coming up. Work hard everyone =)

Blogon the Blog #9

This unit in Calculus is fun to me. Even though I did pretty horrible on the pre-test, I think I have the right process of thinking to go about the problems. Had I remembered the antiderivative of e^-x was -e^-x, and not the same positive number, I'd have a perfect paper. Well near perfect paper, because I forgot to cube a number in the last part of the long answer question. But I'm pretty happy because it was just a mechanical error, or spelling error as Mr.K would like to call it. Going into this test I feel pretty confident in myself. Like I said this unit is pretty enjoyable. Once you grasp the idea of it, everything seems to flow easily. Good luck everyone.

BOB

omg... i almost for about BOB.. ok .. this unit is finally our last...but still we have the exam we have to study for... i really need to study for the exam.. because yes.. i don't want to waste this school year that I did calculus, all for nothing. =) test is tomm.. eventually it was going to come sonner or later.. I feel as if I didn't study as hard as I usually do... I guess i just thought in my head, "last chapter, 4 chapters, won't be as hard." Now as I study, I realized that its almost equally diffilcult/easy as the other units...It's really late, I should sleep now.. btw...I'm glad i didn't forget about bobbing. =D

BOB

Believe it or not, we've covered everything in the course!! I'm honestly proud of everyone!! First, Calculus isn't a class that everyone in high school takes. Second, even for the ones who can take it, it's not an easy course to get through. It takes patience and hard work. I'm lucky to be among people who actually care about their education and care about their peers. Thanks you guys for a great year.

The AP Exam is 15 days away. Anyone getting panic attacks yet? Well no one should, haha, we all deserve peace of mind. It boils down to choice, don't you think? This exam doesn't affect our marks after all, so why should we worry about it? Well, this is how I justified the put off homework and lack of prep for quizzes and tests. It wasn't a wise choice.

The reason why I took Calculus was to prepare for University. I've made up my mind even before taking the course that I'd take Calculus in University again. Like Mr. K said, we won't write an exam like this in our lives again. If we get through the AP Exam, it'd help us with our post-high-school education, and that's worth something. Why would anyone take this course in the first place if s/he is not willing to work for it?

We are all aware that we're busy and there are so much things going on in our lives. Honestly, my life doesn't revolve around Calculus. Throughout my high school career, I've worked my butt off. The only time I had a spare, in my almost 4 years at Daniel, is this semester, and even then I'm still having a hard time juggling everything. I'm sure all of us experience this. But we're almost there! Never give up, yeah? It would've been so easy to just drop this course altogether. But we're still here. What might be possible strategies to get through the course? Personally, I like working with other people. Might we do those study groups? Should we have "classes" where we're just having a conversation about Calculus topics, very casual, non-threatening? I think those work.

I'm starting to go through the Scribe Posts throughout the year. Haha, good times. Just before I leave this off, a reminder to everyone that we shouldn't get stressed out. Haha, someone once said, "one has achieved success, he who has lived well, laughed often and loved much". That, for me, is success. Recipe for success is passion + hardwork... then the money starts pouring in.. hurray!

Good night everyone.

BOB

Wow our last unit. This unit is alright. I think that the hardest part is figuring out what to do in the beginning. I think I did alright on the pre-test. I keep on forgetting the "C" and it's annoying! That is where I messed up on the last question on the pre-test. it's something that should have been avoided. I really like having the smart board in class. I can go back to check what we did in class. It's a big help. It's too bad we didn't have it at the beginning of the year. Although I find that it takes a little bit longer.

I liked questions like these:



But I'm not so hot with question like these:


because it is so easy for me to mess up on the question. It's just figuring out how to start.

My bio teacher has this thing he calls his students. He calls us all "Dr. Yeah Buts." They think of reasons not to do something like calculus homework. I don't want to be a "Dr. Yeah but," but sadly I am. I think its a very very bad habit to get into since we'll be in university next year. If I can't handle a busy workload in high school, well imagine university.... bahh!

I've started reviewing for the exam last week. It's frustrating because... well it's frustrating. I'm very glad I've stuck with this class. There were countless times where I wanted to drop this class, but I chose not to... plus my mom's a bit scary =S ... in a good way though =P Mom's are good at making you feel guilty....

bob

Well yeah this is theunit is over. well i guess this unit is pretty short compared to others and should be simple. i know that i shouldn't have missed those classes i have missed in the past few weeks and i am holding myself totally accountable. i guess its just becuase ive just been so busy with everything going on in my life that i just needed a break from everything and to just relax. anyways well the test is coming and i guess i can say that i am somewhat ready. ive just been ready the text book today and i think i understand most of it. well good luck to me cause i know ill need it.

BOB

We're done, done, done!!!! So the last unit was short... and that should have made it easier to learn, easier to understand, easier to do homework, etc, etc. Truth is, it hasn't gotten any easier for me. This is not the place to complain and I only have myself to blame. I haven't attempted to do all of the homework, or completely read the blog for this unit. I'm pretty clueless. I know if I did the homework, I would have a better understanding and idea of how to go about solving the problems. The exam is in two weeks. My project is due before that. We may be done the unit, but I am far from where I want to be in this class. I'm glad we're done the unit, I'm just not looking forward to the test =/

BOB

Hm the last unit! Our exam is coming up...and half of us will be in Banff this week. Chapter 9 was short and mostly mechanical. I think the hardest part is finding what to do first. After you know what to do, you can do the rest easily. The Pre-test wasn't that difficult but I still have some things to relearn. The only thing I'm worried about is Euler's method but I'll read about it in the textbook. I also have to practice those problems on those worksheets on Mr.K's post.

Scribe Post

Hello guys, it's Christian. 16 days left 'til the exam!!

Today we had the pre-test in class. The solutions can be found in the day's slides. The questions we worked on today were applications of ideas we learned this chapter. Not surprisingly, they were pretty much the same questions we've done before. That's all for me..

The next scribe is Suzanne.

Today's Slides: April 20

I was expecting you all to show up at lunch hour ... only Christian came ... and that was an accident!

19 Days Left until the exam.

Anyway here are the slides I filled out for you ... read them ... understand them ... ask questions if you don't ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

Scribe

Well we were supposed to have the pre-test today, but as a class we were not that ready. So instead we went into three different groups and worked on word problems. All the problems were practically the same, the steps were: 1) finding two points on the parent, 2)seperating varibles, 3) integrating, and 4) creating an equation. However we still had some difficulties or maybe it was just an off day. I don't know. But the more practice the better.

Remember everyone to keep up with the assigned homework. The AP exam is just around the corner. I also have to catch up and review. There's a homework sheet below for more practice.

The next scribe is Christian.

Today's Slides and Homework: April 18

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

Here is your homework ...



and the answers ...

Scribe Post

Ahoy everyone! This is Jann, and I'll be your scribe for today.

We have finally finished the whole course. Today, we looked at some word problems on Differential Equations.

Here we go... (Note: I will be using Mr. K's slides... )

In order to solve this problem, we need to find the parent function. dy/dx is some constant multiplied by the parent function. We know that the temperature, T, varies with respect to time. (Basically, the temperature of the roast decreases over time) We need to find 2 points on the parent function...

At time, t=0, the initial temperature of the roast, which is 68 degrees F. Therefore, we have our first point, (0,68). For our second point, at time, t=2 hours, the temperature of the roast is down to 40 degrees F. This is our second point, (2,40).
Then, after acquiring the 2 points in the parent function, we integrate the formula. The Red Line shows that the calculus part of the problem ends. The following line is all Pre Calculus stuff. If we can recall our natural law from Grade 12 PreCal, "kt + C" is an exponent. Therefore, it is an exponent of the base "e". "e^C1" can be substituted into "C" because it is a constant. Then, we isolate the "T" in order to obtain the Parent Function.















Now that we have the structure of the parent function, we can solve for the missing terms such as "C" and "k".


Now that we have the parent function. We are ready to solve the problem...Then, we looked at one more example...


That's all we did today in class. We were suppose to look at another example, but we ran out of time. Good day everyone! XD

Oh yeah... next scribe is Crystal.

Today's Slides: April 16

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

Scribe Post

So during Calculus class today we opened up the class reviewing Newton's method, which is used for approximating a nearby value using the slope of a tangent line on a differiential equation. e.g. approximating √(37) from using tangent line at √(36)

Then after that we programed our calculator with Euler's Method, which is just a mechanical process and is explained in the slides below. When you have a function that tells you the rate of change, we'd use this method to solve the differentiable equation. And a diffentiable equation is when one of the variables is a derivative. These problems can also be called initial value problems.

There's not much to explain for what we did in class, as you can see below in the slides.

Homework is chapter 9.3. Next class we'll tackle the newton's law of cooling question.

Next scribe will be Jann.

Perseverance

Do you think? Where does calculus fit into this?

Today's Slides: April 12

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

Scribe Post

THIS IS LINDSAY =)

In class, we learned how to draw slope fields.

Let's review from our previous calculus class:


The order of a differential equation is the highest-order derivative.

y'=y is a first order differential equation.
y"=-y is a second order differential equation.

The solution to a differential equation is any function that fits the eqatuion.

For example, to find the differential equation to y'=y you find that you have to find a function that is its own derivative. We know that y=e^x is a solution.

When we think about derivatives, we think about slopes! For every input x, f''(x) is the slope of f(x) at (x,y). This is a first order differential equation: when it describes the slopes at a specific point.


Example: y'=y is a differential equation. At any point (x,y), the slope of the solution curve is the same as the y coordinate. If we use the point (1,2), the slope of the curve is 2. Whenever the y coordinate is y=3, the slope will be 3.


We were given a handout with some examples. We did this in class and the solutions are in the slide post.

1) y'=y; you would use y=e^x because it is its own derivative.

2) y'=2x; the parent function is x²

3) y'=-x/y;
x² + y² = k
2x + 2yy' = 0
y'= -x/y

*parent function is a circle

4) y'=x+y

For homework, we need to create a new program to create slope fields. You can find how to create it in 9.2 or you can ask a calculus buddy to send it to your calculator! Also do all the odd questions!

Euler's Method Solutions and Answers

Here is a copy of the assignment you had today showing the answers and solutions. The second page below shows two spreadsheets that you may find helpful.

Today's Slides: April 5

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

First Things First? Again??

Linger mentioned in a comment:

"These challenges that we're faced with everyday only make us stronger and better people. I know that there's been times when I wanted to give up... but then I think about how far I've come. My classmates are great and so is Mr. K... and yes, it gets frustrating sometimes, but it's always worth it at the end of the day. I think that these challenges are just oppurtunities for us to learn more about ourselves and each other, so whatever comes our way, we can and will defeat it =)"

So very good to remember now that May 9 is not far away!

I’m hoping that in my sharing one of my experiences, you can find some bit to help guarantee your success that day! In early 2003, I too faced an important test date and I too appreciated the opportunity and felt I had to find a way to defeat it as Linger says. Achieving this goal was too important to me and my test if I passed would lead to a national teacher certification (only 40% of test takers passed). I was really trying to be superwoman—just as I imagine many of you work at being superteens. I thought I was prioritizing but ooohh---a to-do list with 20 items all the time!!! Urgent “stuff” kept happening and I was always responding to that. Does that sound familiar?

I was overwhelmed!!!! I sat down and broke my test review into manageable chunks (I had 2 months until the test) and put them into my planner. I did that first because the goal to pass the test was so important. And I planned to turn off instant message, not answer the phone, or have the TV on during the review sessions. I had tried before but was always interrupted by the phone or my students on instant message with questions about our studies.

Then I looked at my other “stuff”, and categorized it: vital, important, or nice. Then I took the vital “stuff” and categorized them again: vital, important, or nice. And I let go the nice. So my house wasn’t very clean during the process, and we didn’t have gourmet dinners. But the laundry was done and we had quickie suppers. My students’ work was graded but I didn’t plan any big field trips or projects during that time. I set aside a time every second night to evaluate their work. As I look back now, I prioritized, and then prioritized again. I did a mental daily check of my goals and made every effort not to be dragged down by urgent if it didn’t help me achieve my goal. Of course, I had to be flexible at times. I couldn’t always follow the plan exactly. But since I knew where I was going and I had planned for time to get there, my review was accomplished by “the day”.

I truly believe, that with good preparation and putting first things first, you'll too feel that great rush of a job well done, and a goal achieved when you learn your scores. I share these experiences, knowing that you are planning and reviewing, but wondering is there one little piece here you could use to help you on your way? Or can you point us to some tips that are really helping you manage to put first things first?

Hey math buddies...

This is not math related, but I need your help. In my jounalism class and also for the school paper, I'm writing a story on downloading music and I need your opinions! ... I also don't have much time :

Most people don't think of downloading music as stealing. Do you? I've certainly never thought of it that way. I just thought of it as a way of listening to music. If I really like the song then go out and buy it. You don't want to be stuck with an album that sucks and your stuck with it. I mean how much is a CD, like $15 to $20. Most people think "why spend the money when you can get it for free?" Therefore, saving that money for something else. I mean what about libraries. Is there a difference between borrowing a book and reading it for free and listening to a song for free?

There are copyright laws that need to be respected but most people don't think about it. In the states you here about people, even as young as 12, being sued by RIAA for downloading. I mean imagine being a 12 year old and recieving a letter saying your being sued. Does the same thin happen in Canada.

I think the music industry needs to discover a new approach. Internet is obviously here to stay and we have access to sooo much, including free music, to millions of people.

You're opinions will be greatly appreciated, it wouldn't be fair to include only my opinion since this topic has so many other views.

By the way, have you guys checked out the new school paper?? =D

I don't know what to label this... BOB? Yes I'll call it BOB

Developing Expert Voices - Invitation to the Blog

As promised, I built a unique blog for your Developing Expert Voices projects. Email me and I will send you an invitation to the new blog. When you publish your projects on the DEV blog tag them with the name of your class (AP Calculus) and the topics covered by the problems you created.

You can take a sneak peak at the new blog here.

Click that picture ... there's a great article at the other end of that link.

BOB

Hi! My BOB's a bit late, because I haven't done the test yet. It's 11pm of Monday, March 26th right now, and I just finished a couple of calculus questions. That tells you how boring my life is when it's the first day of Spring Break, and of all things, cALcuLus is in my head. Well, it's because of the anxiety some people have expressed on Friday by the people who have taken the test. They said it was very difficult and they had a hard time doing it. I thought I had the main ideas down, but according to a few classmates, that wouldn't be enough.

This is my gameplan:

I'll try to come up with a step-by-step method in solving these problems. These are integral questions still right, but see, I still have problems with integrals. I'm not super duper comfortable with them yet. If there's a step-by-step method with the problems, I think it'll help me. Sometime when we come back to school, I'll probably stop by Mr. K's room to ask for help. Til then!

Developing Expert Voices Rubric out of beta v.1.0

This is the final version of the document we built together.

---

Developing Expert Voices Rubric

The teaching of mathematical concepts is the main focus of this project; so we can teach other people and learn at the same time.

Acheivement Descriptors
Instead of levels 1-4 (lowest to highest) we use these descriptors. They better describe what this project is all about.
Novice: a person who is new to the circumstances, work, etc., in which he or she is placed; a beginner.
Apprentice: to bind to or place with a master craftsman, or the like, for instruction in a trade.
Journeyperson: any experienced, competent but routine worker or performer.
Expert: possessing special skill or knowledge; trained by practice; skillful or skilled.

Acheivement	Mathematical Challenge (25%)	Solutions (55%)	Presentation (20%)
Novice	Problems illustrate only an introductory knowledge of the subject. They may be unsolvable or the solutions to the problems are obvious and/or easy to find. They do not demonstrate mastery of the subject matter.	One or more solutions contain several errors with insufficient detail to understand what's going on. Explanation does not "flow," may not be in sequential order and does not adequately explain the problem(s). May also have improper mathematical notation.	Presentation may or may not include visual or other digital enhancements. Overall, a rather uninspired presentation. Doesn't really stand out. It is clear that the student has invested little effort into planning their presentation.
Apprentice	Problems are routine, requiring only modest effort or knowledge. The scope of the problems does not demonstrate the breadth of knowledge the student should have acquired at this stage of their learning.	One or more solutions have a few errors but are understandable. Explanation may "flow" well but only vaguely explains one or more problems. Some parts of one or more solutions are difficult to follow. May include improper use of mathematical notation.	The presentation style is attractive but doesn't enhance the content; more flashy than functional. It is clear that the student has invested some effort into planning their presentation.
Journeyperson	Not all the problems are "routine" in nature. They span an appropriate breadth of material. At least one problem requires careful thought such as consideration of a special case or combines concepts from more than one unit. Showcases the writer's skill in solving routine mathematical problems.	All solutions are correct and easy to understand. Very few or no minor errors. Explanation "flows" well and explains the problems step by step. Solution is broken down well and explained in a way that makes it easy to follow. May have minor use of improper mathematical notation. May point out other ways of solving one or more problems as well.	The presentation may use multiple media tools. The presentation style is attractive and maintains interest. Some of the underlying message may be lost by some aspects that are more flashy than functional. It is clear that the student has given some forethought and planning to their presentation.
Expert	Problems span more than one unit worth of material. All problems are non-routine. Every problem includes content from at least two different units. Problems created demonstrate mastery of the subject matter. Showcases the writer's skill in solving challenging mathematical problems.	All solutions correct, understandable and highly detailed. No errors. Explanation "flows" well, explains the problems thoroughly and points out other ways of solving at least two of them.	The presentation displays use of multiple media tools. The presentation style grabs the viewer's or reader's attention and compliments the content in a way aids understanding and maintains interest. An "eye opening" display from which it is evident that the student invested significant effort.

Creativity (up to 5% bonus)

The maximum possible mark for this assignment is 105%. You can earn up to 5% bonus marks for being creative in the way you approach this assignment. This is not a rigidly defined category and is open to interpretation. You can earn this bonus if your work can be described in one or more of these ways:

• unique and creative way of sharing student's expertise, not something you'd usually think of;
• work as a whole makes unexpected connections to real world applications;
• original and expressive;
  
• imaginative;
• fresh and unusual;
• a truly original approach; presentation method is unique, presented in a way no one would expect, e.g. song, movie, etc.
  

BOB

This unit was about finding the definite integral. I understood most of it in the beginning, but then I started getting confused near the end. I should have went to class more, but that was my fault. I crammed all night and attempted some of the questions. But I'm still not confident in how well I'll do the test this morning. Well hopefully the lunch classes will help me for the big exam. Good luck everyone!

BOB

This unit was pretty quick. I understood most of what we were learning in class. The only thing I have trouble with if figuring out the image with the shells and all. The picture is what I get mixed up on, then my answer's wrong. In class today, I understood it, so I was happy. I liked this unit. I don't really like the word problems, again because of picturing the problem and the graph. I don't like the density problems I get confused easily. I didn't do very well on the pre-test. It was a lot of guessing. When Mr. K explained it all, it seem so simple. I usually think that it's more complicated than it really is. So I end up doing all this funky complicated stuff. This week was very, very busy. I had four other tests (this one's the last =D!), essays, and articles to do. So, that didn't really help. I'm soooo glad Spring Break is coming up!!

BOB

Right now I'm working on the supplementary problems for this chapter, and so far so good. I had some trouble on the pretest yesterday, I think mainly because I didn't practice the different types of problems as much as I should have, so I forgot how to solve them after a few days. But yesterday and today has refreshed the basics of this chapter a little, so I think I can manage tomorrow. I was a bit confused by the density problems, and haven't really tried any outside of class yet, so that's my plan for the immediate future. And I want to work on the average value and mean value stuff too. (Though we didn't do much with the mean value thing, so I don't know if it'll even be on the test.) I have three tests tomorrow though and I still have to study for one of them... but hey, get through tomorrow and it's spring break :) Good luck everyone! Have a nice spring break, preferably homework-free.. preferably somewhere with sandy beaches and no snow.

BOB the Snail

Hi everyone! Our unit on Integral Applications is done and we're going to have a test. This unit has been really short. I found this unit easier to understand than the unit before this. The applications are fairly straight forward. We just need to practice these problems. Why BOB the Snail? A snail is a very slow creature. It's having difficulty in crawling from one place to another; but it never gives up. Like us, we should never give up on our studies. Even though I feel like falling behind, I still think about "going for it".

Good luck on the test everyone! XD

BOB

BOB,

To be completely honest, I do not understand this unit. I hear everything that's being said in class, and during that time, I think I understand. When I leave the class, WHOOSH, it's all gone. Why? Maybe it's because in calculus class, you have to think about it, so you understand it. It's fresh in my mind. When I leave the room, I walk into a world where you have to think about many other things and all that calculus knowledge is pushed back into the dark corner of a filing cabinet...which MAY or MAY NOT come back. This unit is supposed to be the fun part of calculus but I'm really not enjoying it. It could be because I don't understand it, I can't picture what the graphs look like. The paper towel and washer analogies are helpful, but to me, it doesn't have a purpose.

I wish, like many of my fellow classmates, that we had more time to study. It's late in the year, we're tired. We need to recharge our batteries. Tomorrow is the test and honest to goodness, I am more afraid of this test than the AP exam. I really am. There are bits and pieces that I do understand, but I just can't use them to get the whole picture.

Good luck to my classmates. After this test, we could relax, Spring Break is so near, I can feel it. I wish we had more time to study x 2. Tests are supposed to show how well you understand a topic...but if we really don't understand, I don't think it's beneficial to have one. If we don't understand this unit, we will struggle in the next unit. Spring break, spring break, spring break.

Ohhh my BOB

Dear Bob,

As you may already know, we've been having lunch hour classes, because we're behind in the curriculum. The exam is in the beginning of May, which is really just around the corner. Hmm.. you see, I took AP Calc for the experience and as a challenge. And so far, it really has been a challenge.

This unit was really easy to follow and understand in the beginning. But as we progressed, I had diffuculty in picturing what the arbitrary slice would look like when taken from the solid. They come in disks, washers, and prisms depending where you rotate them. To find the volume, you need to find the volume of one slice by finding its area. The only thing that varies is the radius, and I think its true, how knowing what the radius represents is the tricky part of it. Once you have the integral, the rest is just a matter of punching into the calculator. I don't know why, but I understand things when we do it in class... when it came to the pretest, I thought too hard about it. It was simpler than I thought. It sometimes frustrates me, because I should know better... I do know better.

I wish I had more time to study. I have another test to study for, a pile of homework to do, a book to finish reading, and other things to take care of. Nonetheless, don't we all wish we had more time? If we could rewind and do it better, put more effort, DO not some, but ALL of the homework, would we not? Yes, the test is tomorrow.. but that is the beauty of AP Calc.. because now, if and when we take it in University, we can remember what it felt like when we weren't prepared and we can laugh... because by then, we'll have learned our lesson and know better.

Biiig siiiigh.. the test is tomorrow!!! But you know what that means.. SPRING BREAK is on its way.. and it's getting nice out! WOOHOO... one more unit and we're done, done, done. When you think of giving up, just remember Sisyphus. Good luck to all and to all a good night =)

BOB #8

This unit started off easy and towards the end it got harder. I think that's the way all the units were. At the beginning I did the homework and then stopped because I thought I already knew what I was doing. When the pretest came, it hit me that I didn't quite know what I was doing and right now I feel like I need to do the last chapters so that for the test tom. I feel confident enough to complete the questions. I think its going to be tough for me but I'm still going to try. I need to do more questions about when the function spins around the y-axis and at different values. I'm not quite sure about those. Good luck to everyone and be happy b/c remember it's spring break next week! =)

Today's Slides, Review and Worksheet: March 22

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

And here is the worksheet ...



and (some of) the answers ...

BOB

well, im not sure this unit is kind of weird. i am having a hard time seeing how a function would look like if we spin it around an axis. on the multiple choice, i noticed they were questions similar to what we did in the beginning of the unit. For example, the first question that dealt with wrapping the function around y= -1. i actually found the rate multiple question easier (last question on first page). must be careful with those itty bitty pieces.

Blogon the Blog #8

The pre-test was hard. This unit is pretty tough! But once you get around how to find the integral, which pretty much is the hard part, then it becomes mechanical from there. I think my biggest problem is deciding whether or not the solid volume produce spinning a function around the y or x axis is going to be a cylindrical shells, or round discs.. when the y or x axis you're spinning it about is translated units. But I think by doing more problems like these, I could surely get it. I've been focusing my attention to another subject that is of much greater value to me and resulted in less time for calculus. After spring break, everything should be fine.

Today's Slides: March 21

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

Scribe Post 90

First off, i would like to remind everyone to go and add to the marking rubric for our project. Rubric is due this Friday.

1) Oil is leaking at a rate of R(t) = 2000e^-0.2t
, where t is measured in hours, how much oil has spilled in 10 hours?


We want to end up in gallons, so we multiply gallons per hour (which we are given) by some change in time. We want to find the total sum over the ten hours.
*When we are given a rate, such as the one above, we are trying to find a unit related to the rate. I.e. (gallons/hour)x(hour) = gallons.*


A) Density of an oil slick on a body of water is defined by

Suppose the oil slick is extends from 0 to 1000 m. Determine the mass of the slick.
We have Kg/m² and we want to get kg, so we have to get rid of the m²

We cut a piece from the oil slick. If we drill down, the density of the oil slick is the same throughout.

Here we have cut a piece out of the oil slick. The ends of the strips (triangles) become smaller. So we take the triangle and move it to one side to form a rectangle. The area of the rectangle is what we need to find. Going back to our equation we can now get rid of m²

With our our information and our missing piece found, we can create an integral to solve for the mass of the oil slick. We take the limit of n as it approaches infinite and it becomes smaller. We can then take the sum, where n equals one. p(a) is our given equation so we multiply that by the rectangle piece we cut out, Am². Then we get the integral from 0 to 1000 meters. 100/(1+r²) is kg/m² multiplied by 2pi r dr m², which will give us the mass of the oil slick 1000 m out. 2pi r is multiplied by dr because dr becomes infinitely smaller.
*check the slide for march 19 to view the solution to the integral*

B)What is the smallest radius that contains 75% of the oil slicks mass?
With our solution from A, all we do is take seventy percent of the value we found. We can then pull out 200pi. From here we just solve for r, by expanding the bracket notation first.

For the last part of class, we talked about how our physics formula can be derived. We also did a quick question before the bell rang. We were given an amount of cars per kilometer. instead of trying to cancel out a unit area we had to cancel a length to get the number of cars.


URGH, i got a cold.... next scribe is Suzanne... pre test tmrw?

Today's Slides and Homework: March 20

Here they are ...





To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

A Second Wind?

"Most people never run far enough on their first wind to find out they've got a second. Give your dreams all you've got and you'll be amazed at the energy that comes out of you." --William James

I wonder, would this apply to calculus too?