<body><script type="text/javascript"> function setAttributeOnload(object, attribute, val) { if(window.addEventListener) { window.addEventListener('load', function(){ object[attribute] = val; }, false); } else { window.attachEvent('onload', function(){ object[attribute] = val; }); } } </script> <div id="navbar-iframe-container"></div> <script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script> <script type="text/javascript"> gapi.load("gapi.iframes:gapi.iframes.style.bubble", function() { if (gapi.iframes && gapi.iframes.getContext) { gapi.iframes.getContext().openChild({ url: 'https://www.blogger.com/navbar.g?targetBlogID\07510132015\46blogName\75Pre-Cal+40S\46publishMode\75PUBLISH_MODE_BLOGSPOT\46navbarType\75BLUE\46layoutType\75CLASSIC\46searchRoot\75http://pc40s.blogspot.com/search\46blogLocale\75en_CA\46v\0752\46homepageUrl\75http://pc40s.blogspot.com/\46vt\0751918750566317688867', where: document.getElementById("navbar-iframe-container"), id: "navbar-iframe" }); } }); </script>

Thursday, March 31, 2005

Our Wiki Textbook

OK folks, here's another tool to help us ..... our very own Wiki Textbook!

You'll notice a new link to our Wiki Textbook in the [Links] list over there on the right. A wiki is basically a website that anyone can edit. In many wikis you have to be a registered user to participate. Some people worry that by allowing everyone on the internet to edit their content that spammers, roaches and miscreants will vandalize the site. That's possible. What's more likely is that an interested global community will work together to create something excellent! Also, the wiki records every version that has been or ever will be published so if someone comes to our house and makes a mess we can easily clean it up. ;-) Watch this to see what I mean.

Our wiki is open to everyone. The benefit to registering is that every time you contribute to the wiki your name is recorded as a contributor. If you want me to register you just email me and I will. Check out our wiki and let me know what you think.

Saturday, March 26, 2005

The Coin of the Realm: Comments Please

We're on spring break until April 4th. This week I decided to start another blog; one for my personal growth as a teacher. At first I thought I would avoid mentioning it here as I had hoped to participate in an extended discussion with other teachers in the edublogosphere. There's a whole side to education that students are unaware of: the planning, crafting, learning side of being a teacher. But the more I think about it the more I feel I could learn a lot by hearing from you, my students. So, if you're interested, you can find my new blog here.

Those of you that have created your own posts and have had others comment on them understand the title of this post. There's a viceral excitement that comes from having someone comment on something that you wrote. It's encouraging and motivating to keep blogging when someone else takes the time out to share their thoughts. Those of you that have blogged with Mr. Kaminsky over at the GCHS Math Blog know that it's even more encouraging when a person you don't know leaves you a comment.

We also know that our blog is getting fairly widely read. We've got regular visitors from British Columbia, Alberta, Georgia and Michigan to name just a few. I'm going to address this next bit to them:

You folks also probably understand the title of this post. I know that I would love to read your thoughts about this blog. I know my students would too. If you come across a post that any of us have made that stikes you in some way, please leave the poster a comment.

Take your time; think about it; no pressure.

I think that's the "next level" in our journey. To have the involvement of a larger, global community. My students and I can only benefit from your collective wisdom in myriad ways. I think we would all be encouraged to write more thoughtful posts, to make sure our spelling and grammar stay sharp, and most importantly, dialogue with other people. To the math teachers out there just think of the excitement you could generate in a young person but discussing math with them! Is there any greater joy?


The Coin of the Realm: Comments Please?

Tuesday, March 22, 2005

Last Minute Blogging

Now this is what you can call last minute blogging. Working through the online identities and the identities in the booklet made me forget to blog last night. So far in this course, this is unit that i'm not comfortable with. I've been trying out the online quizzes and at first I barely passed, but after going through it again, and not by remembering which one was the right answer, but by going over my notes and working it out in a step by step order, I was able to do the really well on the quizzes the second time. There was just some steps I missed that led me to the wrong answer. I've been practicing these identities and i think all that i've done will help me get a decent mark on this test....hopefully.

Quizzes or Questions?

I was just on my computer cramming and going trough the rest of the online quizzes, when it came across my mind that I didn't blog yet and the next test is tomorrow. So, what better topic to blog on then the online quizzes. For some odd reason, I have trouble doing my work from the exercise booklets. I find it harder to get off my lazy.....bum and get all of my books out to do the work. Maybe, it is just more convenient to do my math near the computer because I'm on everyday anyways. Or maybe it’s because I spend the whole day in school in front of the same books doing the same work, its just depressing being near them too long. Sure, its fine doing work in school for a while, but too much of anything is always bad. I'm not saying that I'm going to stop doing my exercises, but I will try to get a little variety out of my homework. Personally, I prefer some of the online quizzes rather than the exercises. Mainly, because some of the web sites show exactly what you did wrong in the question and the correct way to do it. If not, most of the quiz links on this site have other links near them that even teach you step by step how to do it from the beginning. It’s amazing what useful things you can find on the internet.

Monday, March 21, 2005

so allie you may have beaten me but its not about the speed, its about the quality. so let me just say bring it on gurlie. lol nothing wrong with a little bit of competition in math. as someone whos taken this course before and STRUGGLED in this unit im finding the blog is so much more helpful, it gives us extra examples that we can try at home and helps us communicate with the people in the class who are usually quiet. see im not one of those people, im usually the one talking during class because its how i am, or going "allie help me." i found that its best to work on some of the problems with two people, because even when your stuck and ready to give up you just ask the other person which step they used next and you include it in your equation and presto, you can find the answer quicker. also practicing these kinds of questions over and over again, until you eventually start doign a problem and a little light bulb goes off (well not actaully but ooo that would be so cool) and you realize you recognize this part of a problem from a DIFFERENT problem you did before. THATS when you know that youve had enough practice, even then it never hurts to keep trying. mr. k puts up all these websits for us to use so take advantage of them, hes not just wasting his time because he has nothing better to do, hes doing it because he WANTS to see us all pass and graduate. were entering into the last semester of high school of our LIVES. this is the end of the road, why give up now? ok im starting to get all sappy because im thinking about grad... i dont wanna graduate. something tells me the math just keeps getting harder. lol = scary! but yes, good luck on the test everyone!

Bonus For Bloggers!

As a bonus for those of you blogging tonight I just wanted to let you know that on the test tomorrow the last page is a list of all the identities we've learned similar to the one on our Companion Review Site. You'll be able to just rip it off the test and use it as a reference throughout. This means you should focus your studies tonight on PRACTICING APPLICATIONS of the identities; don't worry about memorizing anything. ;-)

More practice here (answers), here (click on [Calculus Book 1] --> [Functions and Geometry] --> [Trigonometry]) and here.

To get good a this sort of work you have to practice .... it's all just a question of identity .... ;-)

PROCRASTINAT....uhhh

procrastination - To put off doing something, especially out of habitual carelessness or laziness. although i hate to admit it but pulling things off to the last minute is my ultimate pet peeve. and because we all choose to wait until the last minute this can become very stressful. so i was looking at some great sites and i came across this one in particular dealing with stress and procrastinatin. Fourteen Tips to Help Special Educators Deal with Stress although it may seem like a lot of reading, it's actually very helpful. and i know most of you out there probably won't read it at all, just know that it's here for you. anyways today in class we went to the mac lab and did 10 review questions. i found it very helpful because it deals with the things that we are learning. also having those pop ups and helpful hints when you click on the wrong answer, comes in handy. to conclude this post, i would just like to say that if you do at least attempt to do the work and ask for help, chances are you will learn more than if you don't. learning is like catching a ball. the thrower (mr.k and helpful resources), throws the ball (which in the info that we're learning), and it's up to us (students) to not only catch the ball but also get better in catching all the different types of curve balls that come across our way. okay i gues that's it for now. haha rachel i beat you!

Blog

Well, here I am again. I just realized something before I started typing this. I forgot when the test is again =D . So, I am studying right now, and at the same time doing this one mark that I need. So far in this unit, I never knew how identities was really easy. I mean last sem with Ms. A, my identities test was 12/46. I did not know how to get the left side to equal the right side because I wasn't paying attention or I just didn't know how to do it even though I got mad help, but when Mr.K told me to just change everything into the state of Sin and Cos, then it got easier for me. Also, Mr.K should've given us more of those identity problems to work with so we can get better and better at it. I've also thought of identities to be one of the hardest subjects in math because some of my friends cannot handle it. In the sum and difference identity, how does tan(a-B) and tan(a+B) work? Well, I hope this is enough. 'Til the next test..........

my one mark

since i missed three days of classes, somewhere after identities i figured out i was lost. identities is not something you have to remember, but more of practicing how to solve identities. im not sure how well ill be doing on my test but hopefully last semesters work will help me out. i remember last year i had trouble with double angle identities and i may have trouble again. i know i have a lot of catching up to do so gotta get to work. and a lot of homework too. i dont think this is much progress for me for the last few days but its just to show where im standing in pre cal right now. there's always homework and practice. and the help of a teacher. i just hope im not too far behind. i haven't seen you (mr.k) in a while but next time i need all the help i can get =) i hope this is good enough for my one mark!

Another test... another blog

Let's see... well, the time where I can remember where there was englightenment for some people was when we were doing the trigonometric identities. actually it was that unit. i remember where alexis 'voiced' out her englightenment in a different way. that just shows that she learned something and that if she learned something, chances are there must be a few more other people who have learned something too. I was one of those people. I remember the last time that i took trigonometric identities, i had a hard time remembering all the identities and corrolories and such, but seeing them again for a second time helped me to remember them better. especially the sine and cosine dance! hahaha. i think that whatever we do in class i understand what we do, but once i get home and try to do my homework, it's kind of tough, but no worries, i shall settle down soon and try to do the homework again. hmmmmm, well, i think that pretty much wraps it up!

Sunday, March 20, 2005

HERE!! HERE!!

Lately, I still felt that I was a little behind the class and remember last time I said that I was going to do something about it and I found a SOLUTION! It was infront of my face all the time.. It was just there waiting to be used and to do its purpose.. "HERE" yess... the "HERE LINK"! Let me just say that Mr.K doesn't put these links to be stared at.. It was written to serve its purpose of helping us to learn and improve our studies. Personally I found out that its easier for me to learn from the online quizzes than from the assignments. WHY??
  1. Because if you're wrong, it gives you a clear and profound explanation afterwards which is fantabolous because you learn from it and you improve.
  2. It COMPLIMENTS you when you're RIGHT!! ( swweeeeeettt...^_^)
  3. You have an abundant resource of quizzes and tests and its waaaaayy better than being limited to the 20 questions in our assignments. And lastly...
  4. It's just fun to do!!

Although there is still a flaw on doing online quizzes.. Sometimes the explanations aren't written in english (I think its speaking some math dialect..) What I mean by this is that the explanations are too hard to understand because of the depth of the explanations so I just give it a, "HUH??!"

Well I just wanna say that let's make use of these "HERE LINKS"!! It's a very helpful tool and personally I don't think Mr. K would waste he's time putting these links and web sites for nothing right? In the end, I just hope I do good on the test and I hope you guys do pretty well too.. CIAO!

Thursday, March 17, 2005

The Coin Has Been Found!

At 12:20 pm Thursday, March 17, 2005 the coin was found by Ms. Kozoriz in a locker on the 2nd floor in the southwest corner of the building. Congratulations to the Science Team! (Kozoriz, Ottenbright and Wiste) The coin was an Israeli half-sheckel. The hunt lasted 3 days, 23 hours and 50 minutes. Over $100 was raised for young Leah's communication device. We had over 100 participants this year! Thanks to everyone who played we hope you had a great time!

Some interesting anecdotes from this year's coin hunt:

  • Mrs. Armstrong actually opened the locker 41 minutes earlier, but she had used "techniques not available to students."
  • Mr. Ottenbright, who spent every spare period looking for the coin, was heard to ask: "Are the periods getting shorter?"
  • Just before the clues were released on π Day, Mr. Beaumont was heard to say: "I'll have this solved in 30 minutes."
  • Mrs. Zaporzan and Mrs. Silva were found hunting through the ledges of the memorial alcove "looking for the coin!"
Share any other anecdotes you may have about the goings on during the coin hunt using the [comments] link below.

Wednesday, March 16, 2005

Some Online Help

Here is a short, 5 question, true or false quiz on identities taken from another ThinkQuest.

Some more online trig quizzes can be found here. It's an excellent review broken up into three sections: (1) Definitions of Trigonometric Functions; (2) Values of Functions in the First Quadrant and (3) Trigonometric Identities.

Here you'll find a preview of what we'll be studying on Friday, solving trigonometric equations, with a short 5 question quiz at the end. More of the same here.

PS Did you find it yet?
Someone will tomorrow ....
new hints on the walls and monitors .... ;-)

Thinking About Identities

Here is a great little ThinkQuest on how to solve trig identities. They have some excellent worked examples of quite challenging identites followed by some identities for you to prove. If you've been finding this unit difficult the students that built this site also did an excellent job of explaining what to look for in solving identities and how to go about it.

After looking at the trig identities ThinkQuest you might be interested in making one of your own. It's challenging and takes a lot ot time and energy. But, if you're interested talk to me about it. You might be interested in looking through the ThinkQuest Library for more inspiration or lots of good educational websites made by students for students.

Coin Hunt Update!
A number of hints have been posted around school and on the announcement monitors to help you solve the last few riddles and find the coin .... Remember, it's a race! The first person or team to find the coin wins the pizza party!

Happy Coin Hunting!

Tuesday, March 15, 2005

Quad Erat Demonstrandum

Were studying Trigonometric Identities and Sum and Differences Identities so I decided to make a post about Q.E.D and here's what I found:

  • Quod Erat Demonstrandum(KWAWD eh-RAHT dem-on-STRAHND-um) “That which was to have been proved.” Traditionally placed at the end of proofs, the QED is now usually indicated by a small square. A few students have clung to use of the traditional letters, in the hope they might be interpreted as “quite elegantly done
  • A great many Latin phrases are still in common everyday use in English such as quid pro quo ("something for something"), sine qua non ("without which not") and status quo ("state in which").
  • Besides from Q.E.D., Latin terms are commonly used in mathematics. Quod Erat Faciendum(KWAWD eh-RAHT FAH-kee-END-um) “That which was to have been shown.” Abbreviated QEF, it was traditionally used to mark the end of a solution or calculation. It is rarely used now. Lets impress our professor by putting it at the end of exam problems.

Sunday, March 13, 2005

π Day!

It's finally here! It's π Day tomorrow. Mmmmmm ..... that Pi(e) looks good .... and yet .... I can't help this feeling I have that something is not quite right about it ..... can you put your finger on it? ;-)

Tomorrow also begins the 1st Annual Mystery Coin Hunt! All players can pick up their clue packages in the MPR at 12:30 pm. Who will be the first to find it? How long will it take them? Will they share their pizza? ;-)

Boy, who ever imagined a Monday could be so exciting?!?

Somewhere on the property of DMCI a coin has been hidden. Hidden so carefully and cleverly that it cannot be discovered by chance or simply by looking for it. On March 14, π Day, the coin's location will be revealed buried in a series of riddles and puzzles. Until it is discovered the coin's location will remain a mystery....

Thursday, March 10, 2005

An Identities Tool

This web tool can help you solve some identities. If you're having trouble with any of your homework try typing one side of the identity you're working on into this tool. It's really kind of neat! It "talks" to you. Slowing explaining and illustrating each step of how it is thinking about the problem.

There are a few caveats you should know before you use it though:

  • It only has 25 identities in its database; there exist considerably more. Especially when you throw in all the corrolories we can derive.
  • It will only accept monomials as denominators in rational expressions.
  • Human beings are infinitely creative and prone to sparks of insight; gifts that computers will never have.
You can also find more help here.

Have Fun!

Wednesday, March 09, 2005

My Progress In Class

Well my progress in this class is exceptionally good compared to the other times I have taken this course. I kind of have it bad since I haven't really been in & stayed in a math class for a while, so this makes it hard for me because the knowledge from precal30s that is required from a student, was 3 years ago (for me that is...LOL). But even still there are techniques to do well in this course. I personally find, that doing all the questions in the exercises as instructed by Mr. K helps a lot. Some questions may get repetetive and tedious to do, but then again repetition is a good way for a person to learn, or so I've been told. The brain can withold information longer through repetition. But of course there are those hard questions that make you want to throw your book out of the window. Just relax, it's not the end of the world. Even though you may get stuck on certain questions you should attempt it at least once. And if you still don't get it you should ask a peer. Asking questions and having an inquisitive mind is a good way to get further in this class. Asking peers not only does the inquisitor a favor but your peer as well. This is because if you are able to teach someone a concept, that means you understand it as well. So, by asking other classmates questions, you get help in understanding a concept and the person teaching it to you further develops their understanding of the concept. If you don't understand something you shouldn't be shy to raise the issue up because, it's likely that someone else in class has the same question as you. Therefore you'd be doing them a favor as well. Not only that, but if you don't take the chance to ask questions then there might not be another chance. I've been told that, "The only person who can really help you, is yourself," and I strongly believe in that. So keep asking questions because they'll benefit you. I'm sure your buddies or Mr. K would be glad to help you out if you do have questions. I think that those things have brought me to success in this course, aside from the other obvious ones like: actually going to class and listening. Well I hope this is good for a mark since Mr. K was expecting one from me this time. Remember guys don't be shy to ask questions.

Tuesday, March 08, 2005

Why Study Trigonometry?



This is very cool! They won the Oscar for math! Trigonometry no less!!



The Real Reflections

It seems to me that I understand pre-cal this semester a lot more than ever! This even includes last semester when I was taking pre-cal 30S for the second time. I’ve noticed a while back that everything we’ve learned in pre-cal 40S is mainly reflective of pre-cal 30S. For example, the sine and cosine graphs we are using excessively were taught to me and most likely you last semester. Since I understood it last semester, it is not that difficult to relate it to many of the problems I’m facing in my work now. Sure, there are some new things to remember that are new, but in my point of view, I’ve already learned half of it from my previous math class. Another thing that has helped me out was being in Mr.K’s class for pre-cal 30S. Because of this, I’m used to his teaching methods and don’t really need to adapt to a new class or new study habits. This may have another advantage to those returning students like me. What I mean by this is that we can get or old math dictionary back from Mr.K. As I mentioned above, there is a great deal of our current math that is reflective of pre-cal 30S. Our old dictionaries would probably help us out a great deal right now.

dun dun dun .. =|

Alright well I figured I would wait until the day before the test to make my post, just because Im being a rebel. Lol, and because ive been stumped about what to write about. This unit was one of the hardest for me last semester, but it seems that this year, it just seems to click in a lot better. I remember panicking when I was writing this test, and not understanding what was going on, and thinking “oh I know the rules, its giong to be so easy” -- and not studying to hard. Turns out it was harder than I thought, and you actually need to know how to APPLY the rules to the problems. The only way your going to learn how to do that is through TRYING and ATTEMPTING every problem he gives you for homework. You will notice that lots of the questions involve steps you’ll need to take in answering other questions, so they all kind of tie together. When your writing your test, im not sure how everyone goes about it, but I know that what I do first is read through the whole test, so I know whats coming up later. If I come up to a question I don’t understand .. I skip it. BUUUUT! I come back to it later. NEVER leave a question blank, even by trying it you might get part marks, but by skipping it your leaving yourself no hope. Don’t panic during the test, stay calm and remember -- YOU CAN DO IT! (said in the voice of the guy from “the waterboy”) I love that movie, lol but yes. Back to studying. So good luck everyone, and as mr. k would say … CHEERS!

three types of transformations

What we just finished learning was transformations and graphing. It included symmetry, inverses and reflections. Since alli has a post on symmetry and brad has a post on inverses, and kevin had reflections. i did all three. just like graphs can be transformed, my example is not a graph but a picture. In the first column you can see the image as a symmetry about the x axis. In the second column you can see the image as an inverse and in the third column you can see a reflection also about the x axis. To view the picture just click here http://www.boomspeed.com/catherine_c/transformation.jpg Its still the same picture but transformed in three ways.

Another Day, Another Test

What I've learned in this transformations unit is that there are three types of transformation: symmetry, inverses and reflections. Also, when you're graphing reciprocal functions, the invariant points are -1 and 1. The hardest thing for me in this unit is the trigonometric modeling. It's really hard for me find an equation and graph the problem at the same time. Just like I said before, graphing is my weakness in math and it has always been my weakness before. All I want to do is try my best on this test Also, I try to do the problems on the internet, but I can't resist playing games at the same time as well.

Monday, March 07, 2005

For the Test on Wednesday

wow! that audioblogging thing is pretty cool! but the whole factor thing about having to pay the money just make the long distance call, but other than that i think that it is a good idea. hmmmm, i'm trying to think of more meaningful uses for using this audioblogging, but it's pretty tough. well, let's see. if for any reason you feel too lazy to type and stuff you can always call and just post the audioblog that you made up with just a few clicks and that might be a meaningful use? :O or you can have friends come over or whoever and you can ask them or take a survey on what they think about math and how it relates to the real world. you might also be able to call and then have a friend post your audioblog if you don't have internet access? but what else? hmmmm, i don't know. but i'll go onto the portion of where i'm trying to get my mark!

Let's see. well, i think it's the class where we started to learn how to draw the graphs of the reciprocals and where it dealt with the whole situation of having asymptotes and roots and invariant points, etc. I just always use to guess on how the reciprocal graphs should be drawn and i usually got them right. The thing is, i never really understood how the graphs behaved or shaped until the class on where Mr. K talked about how, as one co-ordinate is increasing the reciprocal is decreasing and vice versa or something like that. I think it was as the x-coordinates are increasing, the reciprocal is decreasing so it would be going in a downward direction and as the y-coordinates are decreasing the reciprocal is increasing so then it would be going in the upward directions. I think have them backwards or wrong, but overall it depends on the graph that is being drawn. While Mr. K was showing us the whole concept on how to graph them, when he go to the point of where he actually explained the part about the reciprocals, that's where the light bulb went off inside and i understood things clearly for that moment! and i understand it now and again but i think i have to review the notes again just to make sure.

As far as my progress in the course is going, i think i'm at a steady pace? I try to do as much of my homework as i can and i hope that i can do an exercise where i have attempted all the questions before giving up! I guess that's pretty much every exercise but I guess it's really more of the will power and discipline issue that i'm lacking. BUT no worries! i am working on that!

I wonder if this is enough for the mark?

oh yeah, i just read the previous posts and i read the one about the questions and being a spokesperson and stuff for the other students in class. the blog that is called 'where have we heard this before?' and that is also another thing that i am working on. for one thing, you can consider it to be something that you can just do for yourself. you don't have to think of what other people think about you, so you're just trying to help yourself out and get a better understanding so that you will become more successful in understanding the material and in the process you can be helping out other people in your class as well! so once again... that is something i am working on!

Sunday, March 06, 2005

Audioblogging: Pros and Cons

Listen to the audioblog below for a Blogging Prompt, but mainly because it's cool! ;-)

this is an audio post - click to play

Friday, March 04, 2005

Looking Ahead....NUMB3RS

Looking ahead to Monday, we'll be studying some practical applications of the sine and cosine functions.

This site has some good visual examples of what we'll be looking at. Scroll down past the guy on the bike and click on the little purple button; it'll show you a neat animation of what we'll be looking at.

Also, sin(c)e it's Friday don't forget to watch NUMB3RS. The show is becoming so popular, one fellow has even started a blog about it!

Thursday, March 03, 2005

Where Have We Heard This Before?

It's not my habit to make two posts in one night, but I just read this and couldn't pass up the opportunity. The site is called Common Errors in College Math and I was immediately attracted to the link Student Shyness, which reads like this:
a common error is that of not asking questions.

When your teacher says something that you don't understand, don't be shy about asking; that's why you're in class! If you've been listening but not understanding, then your question is not a "stupid question." Moreover, you probably aren't alone in your lack of understanding -- there are probably a dozen other students in your classroom who are confused about precisely the same point, and are even more shy and inarticulate than you. Think of yourself as their spokesperson; you'll be doing them all a favor if you ask your question. You'll also be doing your teacher a favor -- your teacher doesn't always know which points have been explained clearly enough and which points have not; your questions provide the feedback that your teacher needs.

If you think your teacher may have made a mistake on the chalkboard, you'd be doing the whole class a favor by asking about it. (To save face, just in case the error is your own, formulate it as a question rather than a statement. For instance, instead of saying "that 5 should be a 7", you can ask "should that 5 be a 7?")

And try to ask your question as soon as possible after it comes up. Don't wait until the very end of the example, or until the end of class. As a teacher, I hate it when class has ended and students are leaving the room and some student comes up to me and says "shouldn't that 5 have been a 7?" Then I say "Yes, you're right, but I wish you had asked about it out sooner. Now all your classmates have an error in the notes that they took in class, and they may have trouble deciphering their notes later."


Sound familiar? ;-)

Absolutely Rational....Hungry for π

Some sites to play with:

Try this to play around with rational functions, just like we did in class today. The applet will transform the graph of 1/x using a vertical stretch (A), horizontal shift (B) and vertical shift (C); 3 parameters. It'll show you the graph and then ask you to guess the values of A, B and C; graph your guess and if you're wrong ask you to guess again...very cool!

This GIZMO (Andrew shared one of these with us a little while back) will give you a chance to play around with different parabolas and then see what effects different applications of the absolute value function will have on the graph....also very cool!
Note: You can only use one GIZMO once per day for free. Don't log off the GIZMO site until you're really done playing with it. ;-)

This is here because I just can't stop thinking about π Day....getting hungry....



Wednesday, March 02, 2005

symmetry_yrtemmys

okay let me try this one again. being that i've taken this course last sem, i understand things more clearly. i personally couldn't really learn just be hearing information, instead, i learn more with doing things as well as seeing them. so actually having diagrams and working with them in class and in assignments, i've learned more and actually understand it. i guess because i've taken this course everything is easier but if you actually do your homework and pay attention to mr.K when he talks, it really helps in the long run. in class we are learning about symmetry/reflections. and it occured to me that it's everywhere. even in places that you'd least expect. anyways i was crusing along the internet and found some really cool pictures of symmetry; hense the title of this post =) these pictures are of a tiger. i found the first picture really cool because tigers really have a symmetrical face. i never knew that and it's quite interesting to see. using the magical wonders of paint i took the same picture of the tiger and cut in the center, copied the image, and aligned it so it would be symmetrical. which would be picture #2. the two images, as you can clearly see, are almost identical. ha =) pretty cool.

Tuesday, March 01, 2005

Inverse Update

Because we are learning about inverses, and i was the one to answer the blogging prompt about it, i though i'd show you the original of the "inversed" picture.
Inverse:Original:
I was able to find the original of the inversed picture by using Adobe Photoshop. I used the invert tool and it came up with this. Its pretty cool how all this ties in with what were learning. This just makes it easier to understand, and i think i have a good understanding of it so far. I gotta say i'm pretty hooked on this blogging stuff.

Symmetry

Check out this site. Try playing around with the choices of Graph Type and Function Type (even, odd, neither). See if you can figure out what the essential difference is in distinguishing which functions are Even, Odd, or Neither.

One idea to keep in mind here (and while recalling our work on reflections and inverses) is symmetry. There are many types of symmetry. Can you identify the kinds of symmetry that exist in the transformations we've been studying: reflections, inverses, even functions, odd functions?



Sometimes we come across symmetry by accident...





Somtimes by design...