Pre-Cal 40S

The Adventure Continues ...

2005-09-04T17:27:00.000-05:00

Our adventures in blogging continue....

Watch for 3 new blogs going live September 7, 2005 ...

Pre-Cal 20S (Grade 10)

Pre-Cal 30S (Grade 11)

AP Calculus AB (Grade 12)

So Long

2005-06-30T20:46:00.000-05:00

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 in the fall for pointers to new blogs for each of my classes. Some of the students from this class will be mentoring the students in the new classes. If anyone else (former students or other mathophile readers of this blog) is interested in being a mentor email me and let me know.

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

Class Survey Results

2005-06-16T12:17:00.000-05:00

The exam is over and we did a little survey in class. The results are below; 20 students participated. We also discussed the future use of blogs and wikis in this course. The consensus seems to be that the next class should have their own blog but there should be a link back to this one for the new students to see what the old ones did. We also talked about having students from this class volunteer to be mentors for students in next year's classes. I've got a few volunteers signed up already. If you'd like to mentor one or more of my classes (grade 10, 11 or 12) next year please email me or leave a comment below this post.

Without any further ado, here are the results of our class's survey. Please share your thoughts by commenting (anonymously if you wish) below .....

How prepared were you to write this exam? (Average score out of 100)
66.75%

How much effort did you put into preparing for this exam? (Average score out of 100)
67.75%

How good a job did your teacher do preparing you for this exam? (Average score out of 100)
89.55%

Did you have enough preparation using your calculator?
Yes 85% No 15%

Did you have enough preparation without using your calculator?
Yes 65% No 30% Middle 5%

Was I too hard or too easy on you??
Easy 5% Hard 0% Middle 95%

What was the best learning experience you had in this class?

group work (14)	review sites
math dictionary (8)	quizzes
online quizzes (3)	humour
lectures (3)	clearly detailed lessons
Go For Gold assignment	showing how math affects our daily lives and history
pre-tests	using stories to help us understand
this blog (6)

What was the worst learning experience you had in this class?

quizzes	too long getting back tests
online quiz (3)	none (6)
class time too short	sun shining on the white board
learning too fast	group work
this blog (5)	web assignments
not always going over homework	tests
homework (2)	exercises that have answers but not solutions

What suggestions can you share for next year?

no quiz for marks on blog	project work (3)	give make-up tests
fewer jokes and stories	more online quizzes	make blogging optional
more group work (4)	tell more jokes	give take home tests
an extra class every 2^nd day	homework should count for marks	don't use the same exercise books
keep blogging (7)	students should do more work at the board	more class participation
more time on binomial theorem	give tests back ASAP	keep using the same teaching strategies
go over selected homework exercises in class	have a mentor for this class

It's interesting to compare the items that were considered both the worst and best learning experiences. Also, take a look at the list of worst learning experiences compared to suggestions for next year. Help me do a better job next year by commenting on what you see here ....

Gearing Up For The Exam!!

2005-06-10T16:17:00.000-05:00

A whole lot of reviewing going on!!

Here is where you can login to the online quiz site to try your hand at the review quiz we made as a class.

There's lots more you can do to get ready for Tuesday!

Take this quiz on Probabilities of Compound Events.

Take this quiz on Conditional Probability.

Take this quiz on The Binomial Theorem and Probability.

Take this test on Combinatorics and Probability.

Take Harry Potter's quiz on Combinatorics. Try not to run into any walls. ;-)

Try this Probability quiz.

And finally, take your own customized quiz on a variety of topics we've studied. You can create customized review quizzes by choosing up to 15 questions from: Algebra, Trigonometry, Exponents and Logarithms, Geometry, Problem Solving and Graphs (Transformations). Create as many quizzes as you like and practice, Practice, PRACTICE!!! When you start each quiz a timer counts down from 50 minutes -- that's how you prepare for a timed test -- you take LOTS of timed tests! You can probably skip the Geometry questions and not all of the Problem Solving and Algebra applies to our course, but the kind of thinking you need to do for these questions WILL DEFINITELY help you gear up for the exam!

Remember, luck has nothing to do with it! It's all about doing your best! How well you do is a direct function of the effort you put into preparing!!!

Some Counting Review

2005-05-31T23:55:00.000-05:00

Here are some additional exercises on combinatorics. The interactive "tests" here will also give you explanations of why the correct answer is correct. Enjoy!

If you click on the [Back To {topic}] button at the bottom of each quiz you'll be able to find pages that give helpful lessons on each topic.

More Fun

2005-05-30T23:19:00.000-05:00

Well, you folks liked the last test so much, try this one on for size (6 questions):

1. What do you put in a toaster? ... Think carefully and scroll down.

AND THE ANSWER IS: The answer is bread. If you said "toast," then give up now and go do something else. Try not to hurt yourself. If you said, "bread," go to question 2.
2. Say "silk" five times. Now spell "silk." What do cows drink? ... Think carefully and scroll down.

AND THE ANSWER IS: Cows drink water. If you said "milk" please do not attempt the next question. Your brain is obviously overstressed and may even overheat. It may be that you need to content yourself with reading something more appropriate such as "Children's World." If you said, "water" then proceed to question three.
3. If a red house is made from red bricks and a blue house is made from blue bricks and a pink house is made from pink bricks and a black house is made from black bricks, what is a greenhouse made from? ... Think carefully and scroll down.

AND THE ANSWER IS: Greenhouses are made of glass. If you said "green bricks," what the heck are you still doing here reading these questions????? ... if you said "glass," then go on to question four.
4. It's twenty years ago, a plane is flying at 20,000 feet over Germany. If you will recall, Germany at the time was politically divided into West Germany and East Germany. Anyway, during the flight, TWO of the engines fail. The pilot, realizing that the last remaining engine is also failing, decides on a crash landing procedure. Unfortunately the engine fails before he has time and the plane crashes smack in the middle of "no man's land" between East Germany and West Germany. Where would you bury the survivors - East Germany or West Germany or in "no man's land"? ... Think carefully and scroll down.

AND THE ANSWER IS: You don't, of course, bury survivors. If you said anything else, you must never try to rescue anyone from a plane crash. Your efforts would not be appreciated. ...... If you said, "Don't bury the survivors" then proceed to the next question.
5. If the hour hand on a clock moves 1/60th of a degree every minute then how many degrees will the hour hand move in one hour? ... Think carefully and scroll down.

AND THE ANSWER IS: One degree. If you said "360 degrees" or anything other than "one degree," you are to be congratulated on getting this far, but you are obviously out of your league. Turn your pencil in and exit the room. Everyone else proceed to the final question.
6. Without using a calculator - You are driving a bus from Downtown Brooklyn (let's say starting at Court Street) to Brighton Beach in guess where (Brooklyn). At Atlantic Avenue, 17 people get on the bus. At Prospect Park, six people get off the bus and nine people get on. At Eastern Parkway, two people get off and four get on. At Newkirk Avenue, 11 people get off and 16 people get on. At Kings Highway, three people get off and five people get on. And then in Sheepshead Bay, six people get off and three get on. And now you arrive at Brighton Beach ... Scroll down for the question.

What was the name of the bus driver? ... Think carefully and scroll down.

AND THE ANSWER IS: Just look back at the question, look at the first line; it was YOU ... "You are driving a bus from..."
Humbling isn't it? And just think, you are among the most intelligent in the population. ;-)

Just For Fun

2005-05-29T09:25:00.000-05:00

I found this "test" over at Teaching and Developing Online. Try it out .... just for fun. ;-)

Below are four (4) questions and a bonus question. You have to answer them instantly. You can't take your time, answer all of them immediately.
OK?
Let's find out just how clever you really are. No looking at the answers in advance.
Ready? GO!!! (scroll down)
First Question:
You are participating in a race. You overtake the second person.
What position are you in?

Answer:If you answered that you are first, then you are absolutely wrong!
If you overtake the second person and you take his place, you are second!
Try not to screw up in the next question.
To answer the second question, don't take as much time as you took for the first question.
Second Question:
If you overtake the last person, then you are...?

Answer:If you answered that you are second to last, then you are wrong again. Tell me, how can you overtake the LAST Person?
You're not very good at this! Are you?
Third Question:
Very tricky math! Note: This must be done in your head only.
Do NOT use paper and pencil or a calculator. Try it.
Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000 Now add 10.
What is the total?
Scroll down for answer.

Did you get 5000?
The correct answer is actually 4100.
Don't believe it? Check with your calculator!
Today is definitely not your day.
Maybe you will get the last question right?
Fourth Question:
Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini, 4. Nono. What is the name of the fifth daughter?
Answer:Nunu?
NO! Of course not.
Her name is Mary!
Read the question again.
Okay, now the bonus round:
There is a mute person who wants to buy a toothbrush. By imitating the action of brushing one's teeth he successfully expresses himself to the shopkeeper and the purchase is done.
Now if there is a blind man who wishes to buy a pair of sunglasses, how should he express himself?

He just has to open his mouth and ask, so simple.

So simple it is...

Fundamental Principle of Counting

2005-05-24T22:35:00.000-05:00

This is a good review of the the material we covered in class today. It has step-by-step explanations and solved examples. There are even a few sample questions for you to try!

Here is another good review site from Saskatchewan. You can choose to review the lesson, get extra help and examples or try some practice questions & quizzes. Ignore the Assignment link; it's broken.

My 2nd Time Blogging

2005-05-19T09:32:00.000-05:00

Well its been awhile that i havent blog and i realized that i lost a lot of marks already and i know that it is bad. So Even though its a last minute blogging I still want to get this blogging mark. I really enjoy this unit because I understand it and i'm having fun while I'm answering this kind of questions. I like solving parabolas,circles, ellipse, and Hyperbolas, I think their cool. Just the name "Directrix" makes me think that this unit is interesting. I think I understand this unit very well and the only problem i have in this unit is answering the word problems and that's about it. I admit that I visit the blog once in a while and i know its bad, because it was made for us and we should benefit it. It's that sometimes I'm busy at work and when i got home I'm tired already to go to the computer and blog. Anywayz, i hope that i got my blogging mark this time and I also hope that my blog would make our blog participation a 100%, because I think I'm the only one who's not blogging.

ahh last minute

2005-05-19T00:57:00.000-05:00

well i was laying in bed juuust falling asleep and BAM i remembered i TOOOTALLY forgot to blog. so here i am in my pajamas half asleep blogging. lol. this unit i have to admit is pretty tough, its all about the formulas and the graphs. mr.k made a good point today, DONT try to figure out the problem before you draw your diagram. when you draw it out you can visualize what your looking for and then you can also see things you may not see without the picture. im trying my best to understand what each part of the formula does - and i suggest you all do the same because the first step of answering a problem is knowing what your looking for. so i wish you all good luck on the test. and if your up reading this .. GO TO BED!! ... lol night

another test, another blog

2005-05-18T21:45:00.000-05:00

so tomorrow is the start of our four day long weekend. but before that even commences we must not forget that we also have a test. we shouldn't get too ahead of ourselves. the conics test, in my opinion, a "thinking" unit. you got to pay attention to the formulas because the ellipse and the hyperbola have similar characterists but we shouldn't get them mixed up and lose marks on stupid mistakes. i too get confused, but with the help of the exerices as well as the worksheets you will learn to know the difference =) this unit was difficult but i guess that means that i need more practice right? well i have another test to study for, so i'm going to just end it here. good luck tomorrow.

Pre-Cal 40S

2005-05-18T21:18:00.000-05:00

here we go again.. blogs. Some people say that conics are pretty hard and some say its a piece of cake...... well not really. i just said that,lol. Personally I think conics are easier than exponents and logs but it still has its confusing times. I feel that its not as complicated and it doesnt have too much steps unlike logs.. well some people may disagree to this but hey we all have diffirent views and perspective in things. Conics isnt really that complicated if you remember what formula is suitable for the right conic. there's also the part where you have to determine wheter the conic is vertical or horizontal and finding the focus or foci well pretty much i bet you guys all know what i'm talking about so let me tell you something that most of you probably dont even know.. DID YOU KNOW THAT..... - The conics have been discovered by Menaechmus (a Greek, c.375-325 BC), tutor to Alexander the Great. - Appollonius (c. 262-190 BC) (known as The Great Geometer) consolidated and extended previous results of conics into a monograph Conic Sections, consisting of eight books with 487 propositions. - Appollonius was the first to base the theory of all three conics on sections of one circular cone, right or oblique. He is also the one to give the - name ellipse, parabola, and hyperbola. I bet my marbles you didnt know that! Well guys have good night and happy blogging. I wish us all luck for tomorrow's test!

conics

2005-05-18T19:49:00.000-05:00

Another test is here! let's see. the moment of clarity was.... well there are a few, except some stand out more than others. i was confused about how you get 'p' for the parabolas and now i get it! i'm pretty sure i get it. and hyperbolas i feel that i really get. but i don't think we have spent much time on circles and that is just something that i have to review over again. the general form is also something i have to look at but i'm sure that that is all in the math dictionary and that's fine because i can always look over it! so it's all good! and so yeah. i feel that this one of the units that i have had most trouble with when i first took this course. and now, i understand it waaaaaay better than i did last year! so it does kind of pay off to actually go over it twice. and just as long as you learn from it then it's worth it right? of course i'm right! well, now that i'm sure that i know more than i knew last year about this topic all i have to do is just study using the companion site and just review, review, and REVIEW! so yes. i must start reviewing now. bye!

hmmm...Another Hard Unit..well SOMEHOW...

2005-05-18T18:47:00.000-05:00

Okay. Here i am again explaining how i am doin' in this unit. First of all, conics is a unit where u need to memorize tons of formulas because of hyperbolas, parabolas, ellipses, and circles. However, conics was the first unit introduced to me last semester, as the first unit of the first term. Somehow, it's easier for me the second time around, but i'm still having trouble with the word problems, like usual. I've also learned some things that i've never knew before, like when to graph the hyperbola and which way it's suppose to be pointing at. Well, I guess this is it. 'Til the next blog or test.

Let's Make It 100% This Time!

2005-05-18T15:24:00.000-05:00

Test day tomorrow. Get your Blogging mark here!

If you haven't finished the Conics Review on our Companion Review site you should do it now.

I've collected a number of great links to help you learn and study. When you click on each link below you will be able to select:

A review lesson on the topic.
A selection of problems to review that have been solved step-by-step.
An online quiz with immediate feedback.
An "assignment" with some more solved practice problems

So here are the things you need to know about for the test with links to the resources described above:

If you like, you can also try this humourous conics quiz. Try it out; you'll learn something!

By the way, what do you think our chances are of hitting 100% blogging participation this time around? ;-) Let's go for it and translate that effort into 100% scores on this test!

Hyperbola Help

2005-05-16T16:35:00.000-05:00

Get help with your hyperbola homework if you need it. The site I've linked to has some exercises you can do tied to a java applet. It will show you what changing the values of "a" and "b" in the standard form of the hyperbola's equation will do to the graph. Play with it for a while .... it'll help you get a feel for the geometry behind the algebra. ;-)

Puddle of Mud

2005-05-15T14:49:00.000-05:00

This unit seems pretty hard. I think it’s because I didn’t do really well in analytic geometry in grade 11. A lot of the questions are on this kind of stuff. It feels like this unit is going really fast too. I thought it was just yesterday that we started learning about parabolas, when really we did ellipses. And now hyperbolas? Just when I was starting to get ellipses, Mr. K throws another one of those “folding lessons” on hyperbolas. I just hope that there aren’t any more sections in conics… at least for a little while. On the bright side, I hope I can catch up on these sections over the weekend.

The Muddiest Point

2005-05-12T14:29:00.000-05:00

Most of you seem to have a good grasp of the ellipse! Fantastic! If you need any help with your ellipse homework you can find it here.

By far the muddiest point in our class seems to be the parabola. Here you can play with the parabola as it's defined from the locus definition (which is what we're studying). Play with the java applets, there are two of them, to get a sense of the role "p" plays in the geometry of the parabola.

IMPORTANT: "p" is half the distance between the focus and the directrix when they are perfectly aligned vertically. By dragging the point "B" along the directrix you will sketch out a parabola. Look for when the point "P" is on top of the point "A".

The second applet will show you what happens when you move the focus around. We will discuss these things in class tomorrow, so even if this doesn't entirely make sense to you right now play with the applets so that you will understand what we're talking about in class. ;-)

There were a couple of other questions that came up in our Muddiest Point exercise:

about circles
arithmetic series
changing from general to standard form and back again

We'll be talking lots more about that last point. Please speak to me one-on-one about the first two -- there were only about 3 of you that were feeling muddy about them. ;-)

Parabolic Dishes and The Ellipse Game

2005-05-09T16:01:00.000-05:00

Today we discussed parabolas as conic sections in depth. In particular I emphasized how important it is to keep in mind the geometry of the parabola as you work with its equation.

Watch this! Tomorrow I'm going to ask you why parabolas are important in connection with satelite dishes, television and radio signals. ;-)

Tomorrow we will also review circles and begin our discussion of ellipses. Find out more about what an ellipse is and then you'll be ready to play The Ellipse Game:

Your mission, should you choose to accept it, is to find a focus. You will be given an ellipse of random dimensions and you will have to try to click on one of the foci. Should you fail in this mission at first, you will be given some clues. We will deny any responsibility for holes or other damage caused should you decide stick pins into a drawing board or any other item of household equipment.

Ready? Let's play!

test today =)

2005-05-06T08:14:00.000-05:00

so the test is today and just like everyone here mentioned, this was a very difficult unit. there are a lot of formulas that we have to know, and although it seems like a lot, just doing the questions and looking at all the info given, you'll eventually know which one to use. and of course attempting to do the questions is key. what i found difficult were actually the word problems, there is some critical thinking involved and i admit that i lack that. i know that i need more practice with them. having the review class yesterday i found was really helpful because you can work with the peers around you and makes studying less stressful when you're working together. my last thoughts are i guess, read questions carefully because knowing what is asked can help you to answer the question. good luck on the test today everyone =)

The Uncommon Ratio

2005-05-06T01:44:00.000-05:00

When we first started sequences and bases, I thought that it was going to be easy. It turns out I was wrong. For a long period of time I couldn’t answer most of the word problems in the unit. Eventually, I found out that it was because I was using the “common ratio” right out of the problem. Now, I know that you should write out at least the first two terms in the sequence and divide them to find the common ratio. There still are some small things that I have to remember, like adding the initial values when needed. I almost always forget to do this. I also, have to review some problems like the bouncing ball question. I’m pretty sure that there will be a question similar to this on the test.

Sequences and Series Blog

2005-05-06T00:16:00.000-05:00

First of all, I dont see that 100% participation in blogging happening. But at least there is a constant blog by the few individuals who actually visit this site from our class. Anyways, the only difficulty i have in this unit is the long answer problem solving (bouncing ball, army marching, etc.). I have trouble finding which equations to use from the information given, but everything else after that seems easier for me to do. Also remembering all the equations is a somewhat difficult task. I can remember the geometric formulas, but the arithmetic formulas are a little bit of a challenge. But the more i work with these formulas, the easier it will be to remember, so i guess i'll just keep doing more questions.

Confusing??????

2005-05-05T19:00:00.000-05:00

Well, here's my blog for my 1 mark on the test. Let me just say that I was confused in doing this unit. I must admit,that this was a very EASY unit for me. BUT, as the formulas were introduced to me, I got a little confused by the variables being used, such as m and a. The letter m is the number of "Means" required and a is the first term in an arithmetic sequence. I got confused by these letters because I was taught that the variable for the first term is T1, instead of a, but it doesn't really matter that much. It's just that it's easy for me to remember. Also, the letter m is a variable that is new to me and I just hope I can remember what it is. Also, doing word problems are my weakest points, especially those bouncing ball questions. And NO we ain't getting a formula SHEET. HAHA. I guess that's enough. 'Til the next test.

just a blog for just a mark

2005-05-05T16:17:00.000-05:00

hmmmm, once again it's another blog, because you know what's coming up! THAT'S RIGHT! ANOTHER TEST! well it's all good. i better make this count and do this fast cuz the show "Friends" is coming up =p so anyways. yes. sequences and series. when we first started this unit, I did not remember that i ever did this unit the last time that i took pre cal! and it still hasn't come back to me if i ever did. but anyways, what i found that was giving the me the most trouble was the problems with the ball. the bouncing one to be exact. and well, what exactly is a bounce? so earlier in class we're just preparing for the test tomorrow and well, it seems as if like i get everything else except for the ball one. i find it very likely there is going to be a ball question. or something very similar to it on the test! this unit isn't one of the hardest ones? but it is one of the shortest ones. and there are many formulas to remember, i hope we get a FORMULA SHEET! tomorrow! and yeah. well, i guess that just in case we don't, i'll try to memorize the formulas or learn how to build them. honestly though, i think i would remember them better if i knew how to build them, but the thing is, i can't remember how they are built. so i am just going to stick to the whole memorizing thing. yes, grammar in this case was very bad, but we're not in english so it's all good =)

Sequences/series

2005-05-05T14:56:00.000-05:00

Another test means another blog. Sequences and series seems to be an easy unit with the given information and formulas. But, the most difficult i had was problem solving. Problem solving was always very difficult for me, maybe it's just because it gets you thinking a bit more. The more i understand the more i know what im doing. With the arithmetic and geometric sequences and series, i find easy. Some questions from the review i find harder such as the bouncing ball. I understand every piece of information, but the only part i don't understand is the total distance it will travel before it comes to rest. Hopefully the notes and worksheets from last semester will help me on tomorrow's test.

2005-05-04T23:38:00.000-05:00

alright well ive managed to reactivate my account and i was about to go to bed but i figured, hey, lets NOT wait until the very last day as usual even though i enjoy being a rebel, and i decided to make my post now. this unit i have to admit it really confusing, this stuff is all new to me and im having trouble memorizing the formulas, actually, reading alexis's post helped me understand common rations and differences - so thanks for that. ive been working on memorizing the different equations but its still tough, but i guess the more i practice the better i will get at it ... and i recommend the same for all of you. dont wait until tomorrow to start studying for this because believe me, this is some tough stuff. i admit ive never really used the blogger reviews because i find them difficult to comprehend, but the ones mr. k just posted helped A LOT! so i suggest you all use them. and with that said ... im going to bed. good luck on the test =)

Moment of Clarity

2005-05-04T16:20:00.000-05:00

I found this unit a bit easier then the last unit, the only problem is that I can't remember all of the formulas. I would always have to look back and forth to my dictionary, so without my dictionary I would have been lost. I also find that I sometimes get confused with the word problems. The bouncing ball question really confused me, but it helped a lot when Mr. K explained it on the board. There was a moment of clarity there, now I feel that I can get a really good mark on the test.

Geometric Review

2005-05-03T23:17:00.000-05:00

As promised, here is a list of reviews for you ....

Geometric Sequences and Series - 5 Questions
Infinite Sequences and Series - 5 Questions
Convergent and Divergent Series - 5 Questions
Sigma Notation and the n^th Term - 5 Questions

You can also find a fairly detailed review here with step-by-step solved examples and 8 practice questions with answers.

Don't forget to bring your ruler with you to class tomorrow. You'll need it to play .... ;-)

blog, blog and blog.

2005-05-03T15:53:00.000-05:00

Wooo,,.. The test gonna be tomorrow,I need to post something to get my one mark. well, actually, I didn't know what can I post in this unit. formula, difference and ratio are the basic law in this unit. I think the better way to learn this unit is just need to remember those formula about geometric sequences, and arithmetic sequences. If there is a common difference ,then use the formula of arithmetic sequence, and If there is a commom ratio, then use the formula of geometric sequence. It is not hard to memorize these formula. But when you do your exercise, sometime I feel hard to working on thise question, but after you did those question and then do the next exercise, you will fell better and better. I think the more you practise, the more you get familiar with those formula and understand those questions well. Here, I just want to say that those formula is not hard to memorize it, but it was not hard to understand and familiar to use those formula.

G's and A's

2005-05-02T22:57:00.000-05:00

let me share a secret to you guys, one thing I keep on mind while doing this unit is that arithmetic sequences are based on slopes also known as the "COMMON DIFFERENCE" (d). The operations used for arithmetic sequences are addition and subtraction. ex: 3,8,13,18.... d=5 *use addition from left to right* *use subtraction from right to left* for geometric sequences just remember that we use COMMON RATIOS and its all about multiplying and dividing. ex: 12, 6, 3, 3/2.... r=1/2 *to be honest the only thing I really do to check if its geometric is that I divide it from right to left, I feel more comfortable doing that.* for sigmanotations and infinite sums(converging and diverging).. That's just something I have to work on to be honest.. And I know 2 days may not be enough but I'll give it my all on wednesday.. I hope my tips helped even a little bit. oh and hey if you already know how to do it and you just find my explanation more disturbing and confusing just stay with what you know and if I have any mistakes please don't be afraid to correct me. =) HAPPY BLOGGING!

Geometric Prompting

2005-05-02T20:03:00.000-05:00

The unit test is on Wednesday and the deadline is getting close to get your blogging done. In an effort to make your lives easier ;-) by giving you things to blog about consider this problem:

A student strained her knee in an intramural volleyball game, and her doctor prescribed an anti-inflammatory drug to reduce the swelling. She is to take two 220-milligram tablets every 8 hours for 10 days. Her kidneys eliminate 60% of this drug from her body every 8 hours.

Blogging Prompt

How much of the drug will remain in her body after 10 days, just after she takes her last dose of medicine? If she continued to take the drug for a year, how much of it would be in her system just after she took her last dose?
If the initial dose is halved, what will happen to the stabilization level of the medicine in the body?
If the recurring dose is halved, what will happen to the stabilization level of the medicine?
If the elimination rate is halved, what will happen to the stabilization level of the medicine?

A successful response to this blogging prompt will answer #1 above and at least one of #2 - #4. It will also show all work done to get the answers. If you want to check your work you can use this interactive applet. Instructions on how to use the interactive applet are here.

Have Fun and Happy Blogging!!

Bouncing Around

2005-04-29T15:14:00.000-05:00

The bouncing ball question from tonight's homework might be a little difficult to visualize. Watch this animation which shows the height of the ball bouncing and simultaneously draws the graph of it's height over time -- it'll help. We'll be talking about it in class on Monday.

Whew! Today was a tough class for me. Actually, the last few have been that way. I feel like I'm up there bouncing around the class, asking questions, trying to get everyone involved, and more often than not, it seems like the room is empty. You're all there in body but there seems to be a lack of spirit. What's up folks? Should I shower more often? ;-) Feel free to comment anonymously to this post if you like. It just seems to me that we've got a bit of a "disconnect" going on and I'd like to get past that.

BTW, can you tell if that ball is bouncing up? or down? Does it make any difference if you tilt your head 90 degrees to the left? ;-)

Fun With Sequences

2005-04-27T15:50:00.000-05:00

Can you tell arithmetic and geomteric sequences apart? Find out here.

Play with the Sequencer tonight! Starting number is the first term in the sequence. For an arithmentic sequence make the Multiplier one and change the Add-on; for a geometric sequence make the Add-on zero and try different values of the Multiplier. Once you've made your choices click on the [Calculate Sequence!] button. It might also be fun to see what happens when both are not zero. Try it! See what happens ....

Now you're ready for your blogging promts -- 3 tonight!

Blogging Prompt 1 of 3
What effect does a negative starting number have on the sequence? What effect does a large negative starting number have on the sequence? What effect does a positive starting number have on the sequence? What effect does a large positive starting number have on the sequence?

Blogging Prompt 2 of 3
What effect does a decimal multiplier have on the sequence? What effect does a negative multiplier have on the sequence? What effect does a large multiplier have on the sequence?

Blogging Prompt 3 of 3
What effect does a negative add-on have on the sequence? What effect does a large negative add-on have on the sequence? What effect does a positive add-on have on the sequence? What effect does a large positive add-on have on the sequence?

this is rachel

2005-04-24T22:02:00.000-05:00

alright well i pulled a blonde and forgot not only my user name but ALSO my password. i know ... its a talent really. lol but yes, i have to make my post under allisons name but its NOT allison. its RACHEL! so no she cannot share my blogging mark because its all mine. muhahah. im just evil like that. i remember this was the unit where i started to freak out and realize that holy crap im not going to pass precal, so i started doing my homework, studying, reading my math dictionary and i ended up acing the test and understanding logarithms and exponents, and its actually helped a lot this semester. i remember a lot of the formulas and how to solve the problems. its all been like one giant review, however there are those moments where i blank so i result in asking allie what to do because usually when i blank, she excels. were just cool like that. haha, but yes, it helps having someone else there for a second opinion, kinda like a second mind. this unit is a really tough one though i have to admit, so many different ways to solve the problems .. it makes it a little more difficult to understand what to do. luckily mr. k is doing more than enough to help us by supplying us with examples, questions to do at home, worksheets, quizzes. i actually really wish we would have had an online quiz this unit, i think it would have helped a lot of us but thats alright. i think the toughest part of all this is the graphing and remembering what the graph looks like. its kinda hard actually, but i pretty much understand the logarithms and that sort of stuff, so hopefully by tomorrow everything will click into place .. maybe i'll even remember my password OR my username ... still cant believe i forgot. oh well, remember people ... a logarith is an exponent ... good luck with tomorrow.. thanks allie for letting me post on your name. - rachel

word problems

2005-04-24T17:52:00.000-05:00

Mr. k do you have some websites about word problems like those half-life that have solutions already. I need a site too about graphing logarithms, because at the companion review site, these are the problems where I stock. I probably need to focus my study on this part of unit.

Mr K, I have a question....(^_^)

2005-04-24T14:31:00.000-05:00

I'm just wondering about logarithm problems like 2^x = 3^(2x+5), (long answer 1.a on the pre-test) and the answer is x = (5ln3)/(ln2 - 2ln3). My question is, when should I use the "ln" instead of "log"? I mean, if I solved that problem using common log and got x = (5log3)/(log2- 2log3), am I wrong? I have no problem on dealing with exponents and logarithms (i hope so, for my sake), just the use of "ln" and "log" confuses me. Im thinking to ask this question tomorrow, but maybe you don't have time tomorrow to answer questions.

It gets harder.. It gets tougher but you become smarter

2005-04-24T11:45:00.000-05:00

logs and exponents.. at first I thought this unit was easy from the start.. coz C'mon 2^2 that's easy right.. But then.. When Mr. K took out the big problems ( something like log2+(log3-log4)^3, I know there are harder questions than that I just made that up.. hehe) I'm like .........asdafsasdfjkashdkjhaskjdh................ yeah man, it didn't make sense to me.. It made my mind boggle! Slowly, I actually learned how to deal with these things.. what I do... is I remember the steps on how to solve it.. so I don't go like this on a test ....................(uhhh... what am I suppose to do next?)........ knowing what to do and what not to do, makes everything a lot easier trust me.. something I also learned is that when you see those crazy big problems with lots of numbers and symbols that you used to know but you suddenly forgot b/c of the test, don't think that the question is too overwhelming to answer.. try and open up your mind and ask, "kay where should I start?" and then slowly make your way up.. and lastly to able to past this unit... You just have to know how to use exponents, powers, multiply, divide, factor, ln and e and that's basically the whole sheebang..

Logarithm Blog

2005-04-24T03:04:00.000-05:00

I gotta say this unit is the most challenging for me so far. Whenever i try and do the questions on the stencils as well as the booklet, there are some things that get me stuck and it does get frustrating. But when it's explained over again during class, it comes back to me again, and i wonder how i didnt think of it that way. I admit that i haven't been going on this site as much as i usually do, and because of it, i think my knowledge of this unit is on the rocks. There are many helpful links here that will helpo me get through this and i know if i just focus more i can do well in this class. Hopefully this is the hardest it gets in this class. But if not then i'm always up for a challenge....i hope!

Hard Unit

2005-04-23T17:52:00.000-05:00

Is it me or is this unit really hard? I mean I read my dictionary often but when it comes to homework, its like learning a whole new subject. And yes I'll confess, I TRY to finish a whole exercise but end up finishing the first ten questions of every exercise because that's where I spend most of my time doing. The stencils were okay except for those compound interest questions because we've just started learning that unit. Logarithms is still hard and so far I am studying as much as I can but I'm worried that I wont pass this test. Just as Seyla said, I WILL be relieved after this test is done!

relieved

2005-04-23T13:37:00.000-05:00

when we first started this unit it seemed pretty easy at first, but as the days went on it got harder and more confusing. it was hard for me to solve the problems on the board and when mr. K did solve the problems and explained the process i realized that i couldn't get the answer because i had forgetten that a LOGARITHM IS AN EXPONENT. now that i have studied my dictionary and have tried to remember that a logarithm is an exponent, the homework seemed so much easier to do and the review classes had really helped out a lot. everything seemed to make sense now. this unit really gave me a hard time so i'm relieved that it is over.

Review and Learn With the Wiki

2005-04-22T15:15:00.000-05:00

Lots of homework this weekend! Today was our last day to review before the test on Monday. Don't forget to earn your blog mark before then.

If you didn't make your way through all the questions on our Companion Review Site today you can still access it here or from the [Links] menu over there --> on the right.

Over the weekend you can also try these online reviews to help get ready for Monday:

Working With Exponents - 5 Questions.
Exponential Functions - 5 Questions.
The Number e - 5 Questions.
Logarithmic Functions - 5 Questions.
Common Logarithms - 5 Questions.
Natural Logarithms - 5 Questions.
Modeling Real-World Data - 5 Questions.
Mixed Practice - 14 Questions.

Also, as we discussed in class, take advantage of the tremendous learning and studying opportunities available to you over at our wiki. Start small, just write the first step. The next person can annotate what you did. Another person can do the next step; and so on. Work together on this folks!

Make sure you can draw transformations of the graphs of both the exponential and logarithmic functions without using your calculator. Using your calculator too much can make your vision blur. ;-)

Have a great weekend! And don't forget .... NUMB3RS is on tonight ....

it makes sense!

2005-04-20T23:31:00.000-05:00

let's see... class today was quite interesting. i managed to understand what was going on! it's just so wow! i actually understood it! haha. but then i guess it does get easier if you see it more than once =P i find it sort of easy i guess to do the problems if you knoe how to read the problem right. and if you don't then you're going to have a hard time. so READ THE PROBLEM! logs and exponential stuff are the things that are sort of bugging me right now, but i guess that means that i just have to practise it more don't it? a logarithm is an exponent MUST REMEMBER THAT! so then yes. other wise, i think that this unit should be alright for me just as long as i do homework? haha, i'm working at it. :O it just hit me! Almost everything grows exponentially! haha. well i know that i have been told that, but i just remembered it now too! and it's so true! just a scary thought that what if the planet does have lots of people on it because it is exponentially growing. and then there aren't enough resources =/ that's a scary thought. LET'S DO OUR SHARE PEOPLE! RECYCLE PAPER! but maybe it won't be that bad? but anyways, if there is anymore needed to get this blog mark, please let me know =)

Modeling Annotated Wikis

2005-04-20T16:03:00.000-05:00

Here are some more examples of how to solve exponential modeling problems. The problems are followed by detailed, annotated solutions. There are also a couple of exercises for you to try and, of course, the answers are provided.

Even if you don't need the practice spend some time looking over the material there. Look at how it's laid out on the page. Is it clear; easy to read and understand? If you were going to rewrite it how would you do it? Would you incorporate any pictures or diagrams? Would you have some kind of table of contents linked to the various parts of the page? Maybe you would split it up into several different pages?

Then head over to the Logarithms and Exponents page of our wiki. There are 3 (or 4; depends how you count) problems for you all to solve, as a class, collaboratively. Explain the steps you take to solve these problems. Some guidlines:

Show all calculations done. They should be annotated, so that another student who missed class the day the material was taught will be able to replicate your work.
Explain what the numbers mean? Interpret the results in light of the problem given.

Over the next week or two I will also add similar problems to the other sections of our wiki. Drop by often, work together, and have fun!

The dinosaur problem is there .... waiting to be solved ..... ;-)

Spiral Prompt

2005-04-18T01:41:00.000-05:00

Blogging Prompt
Isn't this a beautiful picture? It's a picture of a giant sea shell in the Phuket Seashell Museum in Thailand. Have you ever seen this type of spiral shape before? It pops up in many places in nature. It's called a "Logarithmic Spiral." A successful response to this Blogging Prompt (you will earn your blogging mark) will answer ALL of these questions:

What is a logarithmic spiral? Write it in your own words, don't copy and paste. ;-)
What does it have to do with logarithms? i.e. Why is it called a Logarithmic Spiral? (Hint: Find out how it is different from an "Archimedian Spiral." Knowing what exponential functions have to do with it will help too.)
Find a picture, not of a seashell, that illustrates a logarithmic spiral in nature. Post it with your reply.

Have fun with this one!

Solving Purple Logs

2005-04-14T23:17:00.000-05:00

We're learning how to solve logarithmic equations. You can find an excellent two page tutorial here. Just click on [Next] when you get to the bottom of the page. The site is called Purplemath. It's really well done. It may even be worth spending some time there exploring. If nothing else, this may be a good time in the semester to take their Study Skills Self-Survey: "Do I Have What It Takes?" This may also be a good time to recall The Curve of Forgetting.

BTW, can you see the math in this picture? .... Not yet? .... Well, wait until we study Pascal's Triangle. You'll never look at a flower the same way again! ;-)

Laws of Logarithms

2005-04-12T14:44:00.000-05:00

Here is a review of the material we discussed in class today: the three basic laws of logarithms. One of the better features of this site is that the explanation is followed by annotated examples. After that, you'll find some exercises for you to practice with; this part is excellently done! Here's why. The detailed solutions are also provided, but they're covered up. By moving your mouse over the pink boxes, each step of the solution is revealed. Don't just wave your mouse over the answers. Try working the question using paper and pencil. If you get stuck you can reveal just one line. You can even try revealing just one side of the equation in the next step of the solution. Use this site wisely to get a hint when you need it. By the time you're done you'll know your stuff really well.

Random Order "To Do List"

2005-04-08T16:03:00.000-05:00

Enjoy your long weekend folks! Also try to get these things done as well, in random order:

Here is your first logs assignment, as promised. ;-)
For the few that were mentioned in class, start your quiz before 11:30 tonight.
Share your WikiThoughts
I'd love to get more Quizzing Feedback
Don't forget to watch NUMB3RS tonight.
Commit random acts of kindness. ;-)

Cheers,
Mr. K.

Exponential Assistence and Quizzing Thoughts

2005-04-07T16:38:00.000-05:00

Here is a great place to get help with your homework if you had any trouble understanding what was happening in class today. Similar questions, complete step-by-step solutions, and a brief online quiz.

Speaking of online quizzes, don't forget that our first online quiz expires at midnight tonight. Get started no later than 11:30 pm.

So far the feedback from those of you that have completed the quiz is very positive. The message I've received is that you want to do more quizzes like this. Alright then, we will. I've been doing some more thinking about this as well. I've decided that each of you will make up one multiple choice question for each unit that we'll be studying. When they are handed in I will enter them into the online database. When exam time rolls around the entire set of questions will be released for you all to review. This means we'll have about 25 questions per unit of study which we can use to prepare for the exam. I will develop a set of guidelines for this assignment which I will share in class, post here or both. This would also be a good place for you to share your questions, comments, complaints, compliments, concerns, confusions, anxieties and other general inquiries about this project. Your thoughts ....

Exponential Functions and WikiThoughts

2005-04-06T14:50:00.000-05:00

This site has several interactive activities to help understand what we were talking about in class today: exponential functions and their transformations. Read the whole page before starting the java applet.

After you click the start button, you'll find it helpful (and instructive) to flip back and forth between the original page and the applet window. There are 4 "games" for you to play. ;-)

The Definition of the Exponential Function
Increase and Decrease of the Exponential Functions
Range and Horizontal Asymptote of the Exponential Functions
Shifting, Scaling and Reflection of the Exponential Functions

Follow the directions given for each one .... after that your homework will be a breeze!

For those of you who like variety, this is another applet you can play with to look at how you can change the parameters a and b in the general equation of an exponential function: f(x) = a(b^x).

Lastly, as we discussed in class today, this would be a good place to share your thoughts about the wiki:

What does someone have to contribute to earn a bonus mark?
We had a suggestion of one contribution, one edit. Does a spelling correktion count?
Maybe we should just forget about marks altogether. Those of you that want to take advantage of this opportunity go ahead! You'll only benefit from it. Non-contributors may benefit also, but they wont get nearly as much out of it.

Your WikiThoughts.....

Online Quiz Goes Live Tomorrow

2005-04-04T23:58:00.000-05:00

In today's class we were working with trig functions, their inverses and exact values. In order to test your understanding of that material you'll be writing a quiz.

The quiz will be written online here. It goes live at 4:00 pm tomorrow and will no longer be available as of midnight on Thursday. When you get to the site follow these instructions:

Click on the big yellow "Sign Up" arrow.
Use only your first name and last initial as indicated.
Pick a username that will allow me to easily identify you, i.e. first name and last initial.
Make up any password you like.
Click on [Register] then [Search] by teacher's name (kuropatwa) and you'll find me.
Click on the box next to Pre-Cal 40S and then [Register].
Follow the instructions on the screen.

Actually, if you read each page carefully, you'll see that the sign up process is very straight forward and self explanatory. If you hit any snags email me and we'll sort it out together.

This quiz is timed. You'll only have 25 minutes to complete it once you've begun. It consists of 10 multiple choice questions. DON'T PANIC. Take your time. I know you'll all do well. ;-)

Good Luck!

Of Wikis and Inverse Trig Functions

2005-04-04T16:30:00.000-05:00

Check out the post just before this one for more info on our wiki. Today we decided that contributions to the wiki would be voluntary and count as bonus marks, 1 or 2 per unit test. We still need to decide exactly what someone has to do to actually earn that mark. Rachel suggested that each person make at least one contribution and one edit. Think about it and bring your ideas with you to class tomorrow. We'll talk more about it then.

Here is an excellent animation showing the relationship between each of the basic trig functions and their inverses. Spend some time there trying to understand what's being illustrated. Clicking on the little red square and dragging it left and right will help. Also, make a point of looking at all six of the examples available. Don't forget to hit [Load Example] after selecting each one.

Our Wiki Textbook

2005-03-31T11:31:00.000-06:00

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.

The Coin of the Realm: Comments Please

2005-03-26T16:20:00.000-06:00

We're on spring break until April 4^th. 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?

Last Minute Blogging

2005-03-22T09:33:00.000-06:00

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?

2005-03-22T01:05:00.000-06:00

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.

2005-03-21T23:03:00.000-06:00

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!

2005-03-21T19:10:00.000-06:00

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

2005-03-21T18:35:00.001-06:00

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

2005-03-21T17:30:00.000-06:00

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

2005-03-21T16:34:00.000-06:00

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

2005-03-21T07:43:00.000-06:00

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!

HERE!! HERE!!

2005-03-20T22:21:00.000-06:00

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??

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.
It COMPLIMENTS you when you're RIGHT!! ( swweeeeeettt...^_^)
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...
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!

The Coin Has Been Found!

2005-03-17T15:21:00.002-06:00

At 12:20 pm Thursday, March 17, 2005 the coin was found by Ms. Kozoriz in a locker on the 2^nd 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.

Some Online Help

2005-03-16T22:13:00.000-06:00

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

2005-03-16T00:35:00.000-06:00

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!

Quad Erat Demonstrandum

2005-03-15T22:05:00.000-06:00

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.

π Day!

2005-03-13T14:45:00.000-06:00

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 1^st 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....

An Identities Tool

2005-03-10T23:56:00.000-06:00

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!

My Progress In Class

2005-03-09T05:06:00.000-06:00

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.

Why Study Trigonometry?

2005-03-08T23:01:00.000-06:00

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

The Real Reflections

2005-03-08T21:17:00.000-06:00

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 .. =|

2005-03-08T19:59:00.000-06:00

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

2005-03-08T17:05:00.000-06:00

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

2005-03-08T17:00:00.000-06:00

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.

For the Test on Wednesday

2005-03-07T22:39:00.000-06:00

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!

Audioblogging: Pros and Cons

2005-03-06T21:48:00.000-06:00

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

Looking Ahead....NUMB3RS

2005-03-04T16:51:00.000-06:00

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!

Where Have We Heard This Before?

2005-03-03T23:31:00.000-06:00

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

2005-03-03T22:27:00.000-06:00

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....

symmetry_yrtemmys

2005-03-02T19:33:00.000-06:00

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.

Inverse Update

2005-03-01T22:41:00.000-06:00

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

2005-03-01T17:25:00.000-06:00

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...

Inverse

2005-02-28T22:25:00.000-06:00

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

2005-02-28T18:01:00.000-06:00

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. 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?

2005-02-28T08:05:00.000-06:00

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!

Reflections

2005-02-27T22:50:00.000-06:00

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

and horizontal 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

2005-02-27T16:14:00.000-06:00

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.

The Expanding Classroom

2005-02-26T19:22:00.000-06:00

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!

I found Pi's

2005-02-25T19:30:00.000-06:00

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

2005-02-25T14:36:00.000-06:00

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!

π Day Is Coming!

2005-02-24T18:34:00.000-06:00

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. ;-)

Where did I put that graph?

2005-02-23T19:57:00.000-06:00

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

2005-02-23T02:43:00.000-06:00

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.

Test Mark

2005-02-22T23:38:00.000-06:00

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

2005-02-22T23:11:00.000-06:00

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 =)

2005-02-22T16:16:00.000-06:00

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?

2005-02-22T16:12:00.000-06:00

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!

Really This Time, The Test is on Wednesday

2005-02-21T20:34:00.000-06:00

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

2005-02-21T18:29:00.000-06:00

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.

Going for the mark =)

2005-02-20T22:30:00.000-06:00

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!