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Monday, February 28, 2005

Inverse

Blogging Prompt
This photograph is called "inverse;" it's the inverse of the picture that was originally taken. Look carefully at the picture and recall what we were saying about inverses in class today:
  • What time of day was the picture taken?
  • Can you tell what season is illustrated in the picture? Explain how.
  • Since it's the "inverse" of the original picture can you explain the colour scheme we see?

A Clarification
The Posting π activity is just a fun thing to do as we approach π Day. It is not worth a Blogging Mark. Posting pictures in and of themselves won't earn you a Blogging Mark either unless you blog something that underscores how it relates to what we are learning in class. To earn your Blogging Mark reread Blogging on Blogging or reply to a designated Blogging Prompt like the one above.

My Reflections

Yah, I guess it's been awhile since I've blogged also before the first test. So here's some more pictures that I've found on reflections. hope you all enjoy them.
Mountain
town
river
river
another
These are just a few of images I've found on the internet. Also, if you want to listen to a song about "Reflections", you can download or listen to the song "My Reflections" by Christina Aguilera.

pi anyone?

well since i didn't blog before the first test, i thought it's probably best if i do it now. i found some pictures of pi and hopefully it's good enough for a mark =)
i found this picture pretty neat cause the legs of this bench actually looks like the symbol for pi. neat eh?
i also came across this photo while i was searching; not much info was given and lastly my favourite picture of "pi" is: haha got you didn't i? i thought so. well if i find anymore i'll be sure to post them up and let you all know. this was fun!

Sunday, February 27, 2005

Reflections





In tomorrow's class we'll be studying vertical reflections









Go here to learn how to write the HTML code to post pictures. Here you can learn the HTML code to embed hyperlinks in your posts.

A fun place to find lots of really cool pics: Flickr.

I Have Encountered Pi

I've found only two pictures that resemble Pi:


I have to admit, i never knew that pi is found everywhere we go. We just have to look a little closer to the things around us.

Saturday, February 26, 2005

The Expanding Classroom

I'm really loving this blogging thing; on many levels.

On a personal level I've subscribed to several blogs of outstanding educators from whom I'm learning so much that each week I feel as though my head is spinning. I get all sorts of teaching ideas just from reading about the educational growth and projects of the folks out there in the "edublogosphere."

On a professional level I have found that blogging has had a profound and positive impact on our class. It has given voice to some of you who don't always get a chance to express yourself in class; it has encouraged some of you to raise your voices and ask questions in class you were reluctant to before; I've seen you grow into courageous learners by asking questions, posting your thoughts, difficulties, confusions, moments of clarity and more! Our classroom has expanded to include the entire internet in the guise of previewing learning material and accessing interactive review material online. Now I have to admit that some of this is by design; I had hoped that all this would happen. But I never imagined just how well you all would take to this learning format nor to what depth you would "get into it!"

Now it seems that our class has expanded to yet another (unanticipated) level. You should know that we're getting read. By the folks here in our own DMCI community, including teachers and our admistrators, and by the folks out in the "edublogosphere." Check it out here. Although Mrs. Davis singles out Adrien's post as exemplary (and it is) you've all impressed me to a degree I can't begin to describe. I'm so proud of all of you!

Keep learning and keep blogging!

Friday, February 25, 2005

I found Pi's

Here are some of the links I found with Pi: www.gfii.org/facts_ about_india.htm www.internetbookshop.it/ame/ser/serdsp.asp?z=z&e=1591022002 cosmetics.365daysshopping.com/ Givenchy2.html www.bensons-world.co.uk/.../ 5/7000000054136.as I'm sorry I can't show the images because I don't know how. But will just discribe the image I found so that when you look at the link, you can easily see it. The first link shows an image of flags with pi shape and they are surrounding the Earth. The second link shows an image of a book cover with pi in the middle. The third link shows an image of a cosmetic with pi as its design. And the fourth link shows a cover of a DVD which is entitled PI. I hope I did what you asking us to do Mr. K.

π π Everywhere π

Wow! It's everywhere!

OK folks, now it's your turn. Everybody post π!

Hmmm...do you think there's such a thing as a π dance?

Have a great weekend and don't forget to watch NUMB3RS tonight! Imagine, a TV show where the hero is a mathematician and the show actually gets the math right!

Thursday, February 24, 2005

π Day Is Coming!

Ok, let's have some fun with this.....can you find and post pictures of π? This one is an actual sculpture in Seattle. Can you find π in nature? Lets see how many pictures we can find. ;-)





Wednesday, February 23, 2005

Where did I put that graph?

That's the "Title" of tomorrow's class. We'll be studying how rewriting the equation of any function can shift its' graph vertically or horizontally, or both. Following those links will give you a preview of what we'll be talking about. BTW, I don't like the way they describe the equation of a "horizontal shift;" read about it and compare it to the standard forms of quadratic and trig functions. See if you can figure out why I'll change the plus sign into a negative. ;-)

Something interesting I read today at math.about.com:

The Best Way To Teach Math Is.......
In no other subject does the pendulum swing as much as it does in math. Currently another wave is occuring (math reform) about the way children learn math. Is math a spectator sport? Is it better to teach math using hands on, engaging, authentic strategies? Is math about thinking or memory? You decide which side of the fence you sit on with the 'math wars'. See what teachers in Arizona are doing.

The two styles of teaching are described as a "constructivist" or a "focused, guided" approach. Some of you folks have been studying with me for a little while now; which side of the fence do you think I fall on? ;-)

Circular functions

We have spent hours on this subject. I have found that this blog has helped alot with my learning compared to last semesters blogless course. It has allowed me to get another perspective to a subject that I have never really understood. The extra help given from websites that revolve around pre-cal is invaluable knowledge. These sites have helped me see what we are talking about in a more pictoral environment. Which is were I feel i can learn alot as i can rember pictures alot better then words. The first blog dealing with study habits has given me insight on ways to break my habits. Hasn't broken all of them but has helped me improve my study habits and help me learn this difficult subject. Also i have tryed and proven to myself that some of these things do work. example today I was discussing some questions with another classmate and we both had problems with the same problem and both went to you for help . Allowing your explination to be explained to me froma different point of view. Also letting me know that i'm not the only one having trouble with some things. Simple things like having the answers to the excersices done in more detail then just answers has allowes me to see where exactly i'm making my mistakes and what needs to be done to correct the problem. I also have found that this unit is largley based on topics learned in pre-cal 30s and reviewing some of my old notes has helped with the graphing of circular functions. This has been somewhat difficult for me as the complete change from degrees to radians is very new and something I'm not used to ,plus I despise root signs. In the end it really depends on how much effort a person is willing to put into something and thats got to do with being interested in a course or what the course really means besides entrance to university.

Tuesday, February 22, 2005

Test Mark

The past couple of classes really helped me out a lot. Everything we've learned so far, i have a good understanding of it, except graphing trigonometric functions. At first, I wasn't all too sure about how to graph the equation of both sin and cos, but Mr. K clearly showed us how to graph it in a step-by-step process. Afterwards, it made so much sense. I agree with what the others have said about regretting not asking questions and with Kevin's comment on "being in front of the class makes you learn even more." Also, I think my "fear" of answering questions is almost gone. I've already answered some questions, hoping it wouldnt be wrong, and even though it was right for the most part, it felt good to be able to speak up. It made me realize that i actually knew what i was doing. Oh yeah, just to let Mr. K know, i've been reviewing my notes everday since that disheartening moment on thursday. Anyways I hope this should be enough to receive my mark.

Hooray For Mr.K

Is it just me or does anybody else think that Mr.K is a really good teacher. I know what you’re thinking and no, I’m not posting this for any more than my one mark. I really do think he is one of the best teachers that I’ve ever had. Here are some reasons why. One reason is that little book called your bible…I mean math dictionary that he makes everybody keep. Did I mention that the math dictionary is worth marks? I think that this is one of the main reasons that I actually passed math last semester. If you’ve never taken his class before, believe me, he is doing everybody a favor by doing this. Another thing is that Mr.K introduced our class to this web site. I doubt I’m the only person that thinks this is helping us out a lot. Even if you hate blogging, you have to admit that it is helping you out at least a little bit. Lastly, the main reason is Pi Day =P Just saying it makes me hungry. Can you name any other teacher that brings in about 30 pies in one class? What more can you ask for in a teacher? He tells great stories and jokes, makes you carry around an answer key, and promotes eating pies in class. Well that’s my two cents.

Practice makes perfect =)

Taking pre cal 40s for the first time was very difficult, I passed but didn't get my desired mark. Maybe it was because I didn't ask enough questions in class or review my notes as often. The one thing that i didn't underdstand was the other trig functions such as cosecant, secant and cotangent. No matter how many times i asked classmates, friends or even Mr. K i had no clue how these trig funcitons worked. And finally it got to me just a few weeks before the exam. and still during the first few days of classes (taking pre cal a second time), i was a bit iffy (..is that a word =/). But all it took for me was those little questions on the board at the beggining of class. This time i had no help, i don't even know how i figured it out myself =) but i did. The reason why i couldn't understand the other trig functions was because i needed a diagram to help me out, which i found easier. Flipping fractions around, also known as reciprocals was the main problem. Example: sec[(21(pi))/(6)], how understood this question was to do it all in one step. But when i looked at it, i figured what 21(pi)/6 was and then took the secant of it. it seemed easier for me that way and it still works out. As mr.k says, to be good in math, you need to practice and do it over and over again. it would of been great to understand this just before semester one ended, but a second chance is worth it. And probably all the things i couldn't get before will just make sense more easily now.

The Tower of Hanoi: Where's the Math in this Game?

The Tower of Hanoi..... one of the puzzles for tomorrows booth. I'm really interested about this puzzle, and it hit my attention when Mr K. told us about the monks solving the tower with 64 discs and the end of the world.. I did some research and here's what I found....

The Tower of Hanoi (sometimes referred to as the Tower of Brahma or the End of the World Puzzle) was invented by the French mathematician, Edouard Lucas, in 1883.

The number of separate transfers of single disks the priests must make to transfer the tower is 2 to the 64th minus 1, or 18,446,744,073,709,551,615 moves! If the priests worked day and night, making one move every second it would take slightly more than 580 billion years to accomplish the job!

I also found some neat site about the tower.. and it has a mathematical solution for solving the puzzle and they even derived some general formula for solving it. Where's the Math in this Game? Click this link to check it out. http://www.cut-the-knot.com/recurrence/hanoi.shtml

Now, I see the point. .IT is really the end of our world when the puzzle is solved or maybe.. the world has ended million years ago before they finsihed it. With no disrespect to Edouard Lucas, but we should change the puzzle from the Tower of Hanoi to the Tower of Annoy .. because it is really annoying.... (^_^) hehehe!

Monday, February 21, 2005

Really This Time, The Test is on Wednesday

Tomorrow we have the Pre-Test and Wednesday IS the test.

As promised here is where you can find some excellent interactive review exercises. Try Topics #30, 31, 32 and 34. Omit Topic #33; we'll be covering that material in our next unit.

I'm really impressed with the quality of the last couple of posts/comments. (Yes, Liezl, Kevin and Calvin, you've all got your blog mark for this test. ;-) ) Being a math nut I can't help noticing patterns and I've noticed a distinct pattern in the content of several posts over the last little while. Can you find the pattern? I'll give you a hint; it's excellent advice! ;-)

My One Mark

So, it's the day before the big test. In the beginning of this course, I thought that we'd be the doing same rubric as I was in Ms. A's class last semester. I was quite shocked we were doing trig first because I didn't quite understand trig very well. Then, Mr. K. explained it very well in class and I was able to do the problems very well in my homework. I guess doing math a second time is very easy, but math is still hard. I also learned that being in front of the class makes you learn even more because I did not enjoy sitting at the front in other classes before. I also regret not asking questions because I was shy and didn't have the confidence to ask for help. The only weakness I have in this course is graphing sine and cosine. Everything was doing well, until the graphing stuff came and started haunting me. But, i'll try my best to work with that also. I hope this is long enough to receive me ONE mark.

Sunday, February 20, 2005

Going for the mark =)

Let's see, well, I don't know if it's the night before the test because I'm being confused by two different dates, but I might as well be on the safe side. I think that the class that I can reflect on most would probably be when we started doing the transformations on the trig functions. I even remembered when Mr. K asked what they all had in common, it took a few seconds for me to get it, and I wanted to answer, but the fear of being wrong took over! TIP:DO NOT BE AFRAID TO ANSWER IN CLASS! OR TO ASK QUESTIONS! I knew the answer and I regret not answering. But the past is the past, yes? Greats. Well, seeing transformations for I guess a second time has helped a lot. I have understood what to do better and with a greater depth of understanding. The way Mr. K taught the transformations helped a lot as well. To me, it was thorough enough and just always remember DABC and you should do fine. I think that my progress in the course is actually progressing. haha. I can actually do most of my homework now with ease and the questions that I didn't get I can always post on the board. Although, there are the moments where I have not being doing the homework. YES! I admit it. I feel bad, and I know that I'll be the one in the end losing because of it. But, I am going to change that habit! I want to get a mark WAAAAY! higher than before, and I am going to change many habits just to get it that way. But you have to admit, there should be more hours in a day! I think that doing things more than once helps, eventually, with practise and use of the material that you have, it will become easier to do things and you'll feel really good that you have accomplished something. When Mr. K posts those questions on the board for us to do, some of them are challenging, but if you attempt to do them and get them wrong, at least you tried right? And it's not wrong to ask someone for help because both of you will be learning at the same time. hmmmm, I hope that this is enough for the one mark. If not, then I'll keep trying for future marks!

Thursday, February 17, 2005

Test Anxiety

I think I've got it -- test anxiety that is.

It was very disheartening for me today to see almost no one is reviewing their math dictionaries or doing their homework regularly. We're only a couple of weeks into the first semester and the first unit test is days away. I know no one wants to check in here just to get chided for not doing their homework but it seems to me you're all suffering from cognitive dissonance. Here is what I know from what you've told me:

  • You all want to get marks between 80% and 100%.
  • You don't do your homework.
  • You thought the information about the forgetting curve was helpful.
  • You don't read your math dictionaries regularly.
Hmmm....something here doesn't add up. All the material I've read says the best way to overcome test anxiety is to be prepared. I spend huge amounts of time preparing for each and every class we have and I think I have test anxiety....do you?

Tuesday, February 15, 2005

The philosophy of pi

Pi a neverending number with no apparent pattern in its list of numbers into the trillions. Can this be considered a obleque pattern of its own ? Does this number have more of a significance to life then just circles.? life as we know it has been random and never reapeating . Everything created has never been duplicated exactly. well at least not to the trillionth of a decimal. So if there is an end to pi would it in some way define everything as to how it is made or randomly generated? If a picture is created with each pixel graded in a 0-9 shade of black, based on the numbers we already know of pi it would never repeat. This to a certain point prooving that pi has some connection to lifes exsistance. Or maybe we have not found enough decimal places of pi to find that it has a pattern. As there may be an end to pi, yet to be discovered.

Test Postponed to Monday

Both my kids are sick. :( I'll be home taking care of them on Tuesday. Here is the review sheet I emailed in for you guys to work on. While it is not comprehensive it is nonetheless a good preparation for the test on Monday.

You can find another good online review for Monday's test here and online quizzes (look for topics #30 through #34) here. The [email results to instructor] link wont work for our class. Just use it as a personal study aid. We'll cover the material on graphing during the rest of this week (see my earlier post to preview the material).

Cheers,
Mr. K.

Monday, February 14, 2005

Unit Circle

Ok so here's deal is it just me or does everybody get the unit circle description thing but me? You know that thing Mr.K does with his arms when trying to find coordinates on the unit circle. I understand what he's doing but I don't see the Unit Circle when he does the hand/arm motions. Anyone care to explain the points and what not when doing the those arm motions so maybe i'll actually see the unit circle because i'm sure not seeing it. =(

Study Help

Hey Guys! I was thinking with the test coming up soon, we could all use every chance possible to review over everything we have learned - which is a lot. I decided to create a little study/quiz review for you. Just a few simple questions that will make your mind think, its mostly the formulas and some simple questions about the unit circle. (note: I'm horrible at making links so im just going to paste the website here so you can click it. Ha Ha sorry! Maybe someone could teach me how to make links at a later date).

CrossWord Puzzle Website: http://www.variety-games.com/CW/Puzzles/1221027110-puzzle.htm

I also have a few tips for you all to help prepare you for the test.

#1: Do NOT wait till the night before the test to study

#2: Learn your unit circle like that back of your hand. If your still uncertain KEEP TRYING. Believe me, it will help in the long run.

#3: Do or at least ATTEMPT all of your homework because it will give you practice with questions other than the ones Mr. K creates for us

#4: Don’t be afraid to ask questions if you don’t understand something. Chances are we are all confused about the same thing.

#5: Have fun with math. Don’t let it stress you out.

In case you were wondering what the correct answers for the crossword puzzle was, here they are.

CrossWord Puzzle Answers: http://www.variety-games.com/CW/Puzzles/1221027110-solution.htm

If anyone needs some help with something, they can just ask me and I can try my best to help you out. Just don’t ask me what 1 divided by 0 is because according to me, it’s 1. Ha-ha. Good Luck and Have Fun!

Graphs Tomorrow

I found a really neat site that illustrates the geometric interpretation of sine, cosine, tangent and cotangent that we we're talking about in class last Friday. Check it out! You can change the lengths of the lines in the figure by clicking on the point on the circle where the "sin x" and "cos x" lengths intersect.

Tomorrow we're going to talk about how to graph the sine, cosine and tangent functions. You can do a little preview here.

If you missed class today; you should know there was a quiz and there will be a unit test as early as Thursday.

Friday, February 11, 2005

Countdown to π Day!

π Day is Coming! The clock has started counting down! You can't tell from the picture, but the arms on this clock are moving in the mathematically correct direction: counterclockwise.

Pictures like this always get me wondering.....

  • What π time is it?
  • How much longer do we have to wait (in hours and radians) until it's π (pie?) time?

Blogging Prompt

Look carefully at the picture. Make up an interesting question about it. Blog your question and follow up with your solution tomorrow. Let's see how many people in the class can answer your question! ;-)

Happy Blogging!

Thursday, February 10, 2005

Around the Benz

Take a look at this photo I found at Flickr. It got me thinking: "Wow! Look; there's the unit circle!". Then I started wondering.....
  • How big are each of the angles, in degrees and radians, in the picture?
  • What standard position angles are being pointed to in the image?
  • What negative standard position angles are being pointed to?
  • What are the coordinates of those points in the unit circle?
There's math all around us folks! ;-)

Wednesday, February 09, 2005

Howlers!

Another benefit to late night blogging -- you just may get a laugh out of it. ;-)

"Howlers" are mathematical flubs, errors or evidence of innumeracy in the the popular media; "mismaths" if you will. The following two quotes were taken from actual newspapers, magazines or other public media from around the world. Sometimes it takes a minute or two to think about what's wrong with their math, but if you think about it you'll figure it out and maybe even get a good laugh out of it.

Here's Howler number 1:

Flight 427 had banked sharply to the left, rolled more than 180 degrees - past the point at which it's wings were perpendicular to the ground - and dropped 6000 feet in 23 seconds.

Imagine that plane's flight. What would it look like falling?

Here's another Howler tangentially related to what we're studying:

You may remember that pi is something to do with calculating dimensions of a circle and derives from dividing 22 by 7, a sum that can be continued indefinitely. Most folks are happy to leave the solution at 3.14 but last week Yasumasa Kanada, a professor at Tokyo University, announced he had calculated it to a billion decimal places on a supercomputer.

There are a couple of things wrong with that one. Think about it...and enjoy a good chuckle. ;-)

If you find a really good Howler in the press Blog it. If we get a good laugh out of it you can count it as your "one mark blog".

Blogging on Blogging

I didn't get to cover as much ground in class as I would have liked today but WOW! I thought it was a great class!

Today was the first day I really felt as though people were talking to me. There was a chorus of people answering questions and students "taking risks" by offering answers even when they weren't sure they were right. I have a lot of respect for people who take risks; try new things and generally experiment with the boundaries of their comfort zone. To all of you who took a risk today, as they say in french, chapeau. ;-)

We were talking about exactly what sort of post you're supposed to make to get that mark on your test and I tried to give you an answer in class. 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 two paragraphs 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 how to measure angles using both radians and degrees. Blog a brief paragraph identifing ways in which these two types of measurement 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 two large overlapping circles. List the similarities in the overlapping section and the differences in the appropriate 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!

Post Script or Bonus Info For Late Night Bloggers!
I had meant to hand out this assignment in class today but I forgot. I'll hand it out in tomorrow's class. You late night bloggers can get a jump on it if you wish by downloading it now.

G'night!

Tuesday, February 08, 2005

Circles and Triangles

What's the connection between circles and triangles? That's what we'll be talking about in class tomorrow.

Trigonometry has something to do with it. I found an excellent site that allows you to play and learn all about it. Start with Stick and Shadows Part I and play through to Going in Circles.

If you review this material before our class tomorrow you'll find class really easy to follow.

Monday, February 07, 2005

Why are there 360 degrees in a circle?

Hmm....why are there 360° in a circle? Is there something special about the number 360?

Well, as you heard in class today I've got some ideas about why this is so. I think it harks back (I love that turn of phrase -- it's so colloquial) ;-) to the ancient Summerians. Dr. Math seems to share my point of view and he gives an excellent explanation of what we were discussing in class today. It seems that the radian really is the most "natural" way to measure angles in a circle. Then again, if that were so, how many fingers would we have?

Friday, February 04, 2005

Day 1

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:

  1. Write the address and name of the site you most liked.
  2. Rate the site out of 100; i.e. give it a grade!
  3. Write a brief description (no more than 4 or 5 sentences) of the site.
  4. 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!