Pre-Cal 40S (Winter '07)

So Long ...

2007-06-29T09:37:00.000-05:00

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

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

Just to have a laugh or learn some math,

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

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

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

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

The places you'll go--

2007-06-19T10:13:00.000-05:00

You have brains in your head.
You have feet in your shoes.
You can steer yourself
Any direction you choose. --Dr. Suess, Places You'll Go

Seniors, it's almost graduation--what direction are you choosing? Juniors, where are your feet taking you this summer? Wherever you go, be safe!

My very best wishes,
Lani

Exam time!

2007-06-10T08:49:00.000-05:00

Your provincial exam is this week. I was thinking on your taking the test and remembering a day some 5 years ago when I was to write an extremely important exam.

I was mindful to get some sleep just prior to the exam and hoping that you will too for this reason:

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

from Do Teens Get Enough Sleep?

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

At the risk of sounding "mom-ish", have you taken this into consideration in your preparation to be your very best for your test??

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

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

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

Scribe

2007-06-09T22:11:00.000-05:00

Hello everyone! Sorry again for the late scribe. I just really needed some more time to study before the exam today. Hopefully everyone did a super good job on it! =D

Well, on Friday, if I remember correctly was review for the exam on Logarithms and Exponents, Probability and Trigonometric Identities. The reviews are done the exact same way we do our pretests! All the questions and answers are on the slides. Click here.

The exam is pretty much over so it's kind of a relief for all of us. There's still classes tomorrow!! Scribe for tomorrow shall be.....

I think the it's a new cycle, so I chooose.. Vincent!

- Sandy <3

Today's Slides: June 8

2007-06-08T16:24:00.000-05:00

PRECAL40S: LAST SCRIBE ... for me at least.

2007-06-07T18:59:00.000-05:00

HEY GUYS! sorry my scribe was a day late. I had work yesterday and came home very late so anyways I will be the scribe for yesterday and today ... here goes

JUNE 6, 2007: MORNING CLASS

We had an exam rehearsal for Circular Funtions

The answers are pretty straight forward ...

JUNE 6, 2007: AFTERNOON CLASS

We had another exam rehearsal for Combinatories

and again the answers are pretty straight forward ...

JUNE 7, 2007: MORNING CLASS

Yet, Again we had another exam rehearsal for Logarithm. We had a substitute for Mr. K. She didn't really gave us numbers to be in groups so instead we chose our own groups. Everyone worked on it but in the end we found out that we didn't have to hand it in. The answers are not up yet but I'm pretty sure Mr. K will put it up sometime later tonight. Well that's all for now and the scribe for tomorrow's class is .... SANDY!

Today's Slides: June 6

2007-06-06T15:45:00.000-05:00

NUMBER 11

2007-06-05T13:48:00.000-05:00

Editor's Note: This post is reprinted from an email that has been circulating around the internet. Some of the things stated as fact are false. It is a hoax. Please read the comments.

Mr. Kuropatwa

THE SECRET BEHIND NUMBER 11

I figured this has something to do with Math. HAHA! I think this is interesting as well. I don't know if all of these are true though. Maybe some of you have already read this...

TODAY'S DATE: JUNE 5, 2007

06/05/07

6+5 = 11

Pretty Chilling - read to the bottom. Try it out.
If you are a sceptical person - still read on as it's actually very interesting!!
This is actually really freaky!! (Mainly the end part, but read it all first)
1) New York City has 11 letters2) Afghanistan has 11 letters.3) Ramsin Yuseb has 11 letters. (The terrorist who threatened to destroy the Twin Towers in 1993) 4) George W Bush has 11 letters.

This could be a mere coincidence, but this gets interesting: 1) New York is the 11th state.2) The first plane crashing against the Twin Towers was flight number 11. 3) Flight 11 was carrying 92 passengers. 9 + 2 = 114) Flight 77 which also hit Twin Towers, was carrying 65 passengers. 6 + 5 = 115) The tragedy was on September 11, or 9/11 as it is now known. 9 + 1+ 1 =116) The date is equal to the US emergency services telephone number 911.
Sheer coincidence..?
Read on and make up your own mind:
1) The total number of victims inside all the hi-jacked planes was 254.
2 + 5 + 4 = 11
2) September 11 is day number 254 of the calendar year.
3) The Madrid bombing took place on 3/11/2004. 3 + 1 + 1 + 2 + 4 = 11. 4) The tragedy of Madrid happened 911 days after the Twin Towers incident.
Now this is where things get totally eerie:

The most recognized symbol for the US, after the Stars & Stripes, is the Eagle. The following verse is taken from the Koran, the Islamic holy book:
"For it is written that a son of Arabia would awaken a fearsome Eagle. The wrath of the Eagle would be felt throughout the lands of Allah while some of the people trembled in despair still more rejoiced: for the wrath of the Eagle cleansed the lands of Allah and there was peace."
That verse is number 9.11 of the Koran.
Unconvinced about all of this still ..?

Try this and see how you feel afterwards, it made my hair stand on end:
Open Microsoft Word and do the following:
1. Type in upper case Q33 NY. This is the flight number of the first plane to hit one of the Twin Towers.2. Highlight the Q33 NY.3. Change the font size to 48.4. Change the actual font to the WINGDINGS……………………
What do you think now????

Last Bob of the School Year!!!

2007-06-04T22:07:00.000-05:00

Hmmm... what does Craig have to say about the past unit??? Let's see, well it has been quite an easy one, which has helped out a lot, considering I have had so much else on the go! I'm not sure what else there is to say... I would post each of the formulas, but Graeme has already covered that, and we get a formula sheet anyway. Just as a reminder, watch the wording of the questions! Especially when they deal with the bouncing of golf balls and such (i.e. the final question on the pretest). Otherwise, this course has been a great one and I believe the unit was a good one to finish it off. Good luck to all on the test and the upcoming exam!!!

For the final time =D

BOB

2007-06-04T22:06:00.000-05:00

Well since this is the last one I guess I'll talk about how my year went in this class. First of all, I have to learn to stop being so lazy, do my homework, and study for tests. Can you believe this is only my 4th BOB?! I know what my potential is, and I guess it was my stupid choice not to work to the fullest. To be honest, I've only done the first 2 exercises out of the whole year. I'm going to struggle on this test as I did on every other and there's no one to blame but myself. So I ask myself, am I going to study tonight? We'll find out..

Have a good night boys and girls

BIP: bob in peace...

2007-06-04T21:43:00.000-05:00

My last bob.... Some what happy but sad too, ill have nothing to complain about anymore. This last unit on sequences was pretty fast. I'm not sure this was the easiest one, it was just interesting. Not much i can really say about it. it's just about figuring out the formula and substituting everything in the right place, BUT I'M NOT SAYING IT'S EASY! Anyhow, i feel i got the main concept of this unit. Hopefully i can make this my best test so far but, good luck to everyone on this last test AND ON THE EXAM IN 7 DAYS hope everyone passes the course.

PC40SW07.BLOGGINGONBLOGGING.FINAL

2007-06-04T21:24:00.000-05:00

WoW! (Acronyms for World of Warcraft FTW) I can't believe this is my last bob of pc40s!

Sequences! What a unit that was; the unit really displayed math (Patterns was a large header: Math is the science of patterns!). At first, I found the unit quite easy. Then, it became a tiny bit more complicated (but not really) and was still without a doubt easy.

In my whole opinion, I think that this unit was just about remembering the equations (that are given to us anyway?). Arithmetic sequences, Geometric sequences, Series, Series, Series, Sequences and more Sequences! Also don't forgot about infinite series, the Sigma notation (I think that's what it's called) and Converging/Diverging.

Yes yes. This unit includes it's own puzzles but overall was less difficult than the other units.

Good luck to everyone on the Test Tomorrow morning! Sleep early and drink lots of water =)

PS: I almost forgot to blog 3 times today and 2 over the weekend (I would not remember at all, then I suddenly have it in my head. The next moment, the idea was gone again) Good thing I finally did it before I forgot AGAIN!

LOTD(Lesson of the Day): DO YOUR BLOGS WHEN YOU REMEMBER (**The first time)

Bye bye, no more blogs fr: ME <---

BOB

2007-06-04T20:53:00.000-05:00

Last unit of the course, probably the fastest too. This basically means the course is over and all that's left is......DUN DUN DAA THE FINAL EXAM!! But you guys don't have to worry, you're all so very bright and smart. I predict that you all will do well on the exam. As for this unit, fairly easy and simple to comprehend. Main idea is to remember the formulas, terms and concepts. If you got all that, the rest is common sense and knowing how to interpret the problems. However do not under estimate the fact that nothing comes easy, so don't expect an easy test to end off what has been an awesome class to be apart of. Good luck to everyone.

BOB - The Final Frontier

2007-06-04T19:04:00.000-05:00

I hate Star Trek :\

This is the final BOB guys, but certainly not the last. I think.. Well sequences is basically read the problem, figure which equation to use, figure out any unknown variables if needed and simplify. I hope I can find it easy to do this. This unit was as short as me yet we crammed a lot of information into that short period of time. Hey remember when I broke Miles' toy snake? Boy was that depressing.. Anyways I have a load of studying to do and that movie won't make itself. Good luck on tomorrow's test and in the near future's exam. This is Jojo Rocks logging off for now. In the words of Derek Zoolander, I bid you all a farewell.

"What is this? A centre for ants? How can we be expected to teach children to learn how to read... if they can't even fit inside the building?"

SCRIBE

2007-06-04T18:48:00.000-05:00

Another scribe post in the words of Jojo Rocks.

Was surprised finding out I was scribe of all days. Yet today was pretty interesting. In the morning we had our pre-test, a very interesting pre-test mind you and it seemed everyone had a fine idea how this unit worked. Good thing the equations were on the board. I have enough trouble remembering every other equation... Anyways we were put into groups and the room lit up with conversations. My group was interesting, 2 great minds working while 1 great mind in progress (me) layed back with a question mark on his head nodding to everything they agreed too. Just kidding.. Time ran out quickly so we had to wait to see how some answers turned out the way they did.

So yeah, the afternoon class came right away. My mind was sorta somewhere else since I have a short film wit ha script to create by Thursday I think. But yeah we went through the 5Th question on the pre-test since it had some issues for some people. although a lot of people had different rounded numbers we all were pretty close. Funny how a funny worded problem had so many solutions to it. The podcast recording stopped working again. Twice. Blamed it on Richard, the usual stuff. After that was all over and done with we did some homework based questions as review which are on the slides.

There was an interesting talk about the Koch snowflake and how there are 10 different dimensions. Mr. K explained how a square won't see a sphere and how we'd see ourselves as worms if we saw in the 4th dimension. Very hard to comprehend but sounds very easy to say. Don't you love that? Scribe tomorrow is... SAM!

Just kidding Sam, Sorry Jeng your it!

PRECAL40S: LAST BOB

2007-06-04T18:15:00.000-05:00

WOW! This is our last unit and its about SEQUENCES. Also this is our last blog for this semester. What can I say? I've learned so much about sequences. At times it can be very confusing because you wouldn't really know which formula to use but with the workshop we do in class helped me a lot. That's all there is to it. Practice ... practice.

Aw, I'll miss this class. Thee best class ever.
Well, GOOD LUCK TO EVERYONE ON THE TEST TOMORROW.
Its our last one, lets ACE IT! haha! :)

FInal BOB

2007-06-04T18:02:00.000-05:00

Well, this unit about sequences is relatively easy. There is nothing to say about this unit because all this unit is about is just knowing when and how to use certain formulas on a given time. Just remember that if you don't know the answer just put the number 6 as it will most likely be the right answer.....XD. I hope everyone will do well on our last test...

BOB IIIIIIII

2007-06-04T17:38:00.000-05:00

Hello, back for my last Bob of the year and what a unit to end off the year. This unit was one of the better units we have had all year in my opinion. Other then the memorizing of the equations and when to use them, it is simply all fitting an equation into the problems and plugging in the value. I found this unit to have been difficult at first especially when doing the homework, although after the memorization of the equations and when I had to use them, the questions were a lot easier. All though the unit seems easier then the others, I believe the questions can become very hard and the difficulty of the test may become a challenge. All in All I believe this unit was one of the easier ones and as long as I study once again tonight, I think I am going to be ready for the test. Study hard and good luck guys and gals for the sequences test and the long awaited Provincial Exam next week.

-B,O,B

2007-06-04T17:31:00.000-05:00

This is our final BOB for this course... Our last unit, Sequences, has concluded. We are now going to prepare for our last test.

I found this unit very cool because I learned a lot about sequences... We learned the formula for finding the "nth" term of the given arithmetic sequence to be...

tn = t1 + (n-1)d

And for the geometric sequence...

tn = t1 (r)^n-1

We also learned how to calculate the sum of a given arithmetic sequence. Instead of adding all the terms, we could simply use this formula...

Sn = (n/2) (2t1 + (n - 1)d)

For a geometric series...

Sn = t1 (1 - r^n)/(1 - r)

I hope everyone will do their very best... Remember, its our LAST chance to improve our term mark...

PreCalculus: The Last Bob.

2007-06-04T17:29:00.000-05:00

This unit comes to an end and so does the year. As of today there is exactly one week left before our final exam. Is anyone as excited as i am? I'm kidding, of course! Well, this unit has been okay... sort of. I'm not too sure I'm that great at it yet. However, tonight should help a bit! Lots of studying. Fortunately I have nothing else to worry about except pre cal now. So gives me a great opportunity to practice more. Since practice makes perfect. Back to sequences, though. I'm not too sure if this unit test is going to be as good to me as the others. Hopefully I'm able to do just as well as the other times. Good luck to everyone! Hopefully you guys do very good as well. (:

BO8

2007-06-04T17:07:00.000-05:00

Once again another unit is finished and out of the way. Sequences was a pretty easy unit and I really enjoyed it. Once the formulas were out of the way the work got a bit easier. Now that the test is tomorrow, I wish everyone the best of luck and hope that everyone finished off on a good note ready to go into the exam. Well once again another BOB and the last chance to reflect on a unit. Good luck tomorrow guys and girls!

Today's Slides: June 4

2007-06-04T15:54:00.000-05:00

2B + O --> BOB

2007-06-03T19:16:00.000-05:00

Well this last unit was a good one to leave off on. I actually had and am still having a little bit of trouble with the homework because I keep mixing up which formula's are used for what and what goes where within them. But with the blog open in front of me it's not that bad. I'll have it pegged by tomorrow. But just to clarify...

To find a term in an arithmetic sequence:
tn = t1 + (n -1) * common difference
(I used t1 because that "a" confused me for a good long while, had no meaning for me)

To find a term in a geometric sequence:
tn = t1(common ratio)^(n-1)

To find the sum of the terms in an arithmetic series:
Sn = (n/2)(2t1+(n -1) * common difference)
or
Sn= n(t1 + tn)/2

To find the sum of the terms in a geometric series:
Sn = (t1(1-r^n))/(1-r)

To find the sum of the terms in an infinite geometric series:
Si = t1/(1-r)

So I'm going to finish up my homework now.
byebye

bee oh bee number eight!

2007-06-03T17:34:00.000-05:00

Well I guess this is the last bob I will do for this school year. Sequences and series are quite interesting to me. It's interesting how you can form series out of sequences...and sequences out of series! Yes...This unit has been quite fun, fast and a little easier to understand. It wasn't as hard as I thought...but problem solving might slow me down if I don't know what Im supposed to do! As well as formulas...I can't remember those haha...but I will. So good luck to everyone on the test. Hope we all do well.
I guess I'll reflect on the whole semester as well. The semester has been great. At the beginning of the semester I did okay and second term came and I didn't do as well. Combinatorics and probability were quite challenging for me. I did like the transformations unit though. Every moment in our class was great...like pi day...where we all got sick of pie and didn't want it anymore...when we carried on with the rest of the questions while Mr. K. stepped out and we laughed when he came in to tell us to do the questions...when we had that conversation with Eddie's class...everything was fun!.. from the smartboard to the old traditional white board...which personally I like better. I miss the math dictionary...haha...it would have been cool because if we still did it on the white board we could have written: END OF COURSE. haha which would have been exciting!!!!! but to everyone...good luck on the test, exam and future studies whether you choose to go to college, university, take a year off, come back or are continuing here at DMCI. BYE everyone for now!

The Last BOB

2007-06-03T16:08:00.000-05:00

Hmm, I'm still worried about this sequences test. I understand pretty much everything and I think this unit is quite simple, but I just have this nagging feeling that Mr. K is going to be up to something and make those questions hard on the test, haha. Anyway, wow, this class, course, whatever you call it, was fun. I'll never forget the conversation we had with Eddie and his class from Georgia, the day when the SmartBoard was hooked up (It was pretty funny when Mr. K was trying to learn how to use it. :D sorry Mr. K), and how we implemented it in our class. I wish everyone luck for tomorrow's pre-test, Tuesday's test, and the final exam.

I'll see you in 3 months Bob.

2007-06-03T12:34:00.000-05:00

Is it just me, or does anyone else see the countdown on our blog state that the exam is in 220 days?! OH man, wish we had that much time, but it's just my computer's clock playing tricks on me, haha. Well anyways, on to my final bob for the course.
I can't even begin to comprehend how fast our year passed by, but all I can really remember is all of the times that we shared in this class. I really believe that this was a momentous semester for me, and never before have I resided in such a healthily and welcome classroom. There were so many occasions that I simply cannot forget, such as Eddie and the event of conversing with his class in Georgia, or how we intuitively utilized the smartboard for everyday class. Well, enough about that, I believe there's still an overall course review BOB or something similar at the end of the year. So on to talking about our final unit; sequences.
When we first started sequences, I couldn't believe how simple it was. The questions themselves were relatively straightforward, and even the thought-provoking questions just require the implementation of given formulas. All we really have to do is stop and analyze what is being asked, the sixth term, the distance the ball travelled, what is S100, etc. I believe that this test shouldn't prove too difficult for anyone in the class, and hopefully everyone will perform incredibly on our final test.
GOOD LUCK TO EVERYONE ON THE PRE-TEST, TEST AND NEXT WEEK'S FINAL EXAM!!!

BOB-ing 8

2007-06-03T12:13:00.000-05:00

WOW, I can't believe that this is the last time I'll BOB. Such a tremendous experience and a really interesting journey I had in this course. I've been struggling, really... This unit is easy though. It's pretty straightforward. There's nothing much to say about this short unit. With its low level of difficulty, we are able to catch up on our schedule and still retain those 3 days of review. I hope everyone does well on the test. I know Mr K. will find a way to complicate this simple unit but I think we'll be prepared by then. Just remember the formulas.

Also, remember:

n - the rank

d - common difference in an arithmetic sequence

r - common ratio in a geometric sequence

t₁ - first term in a sequence

a - also indicates the first term in a sequence

t_n - n^th term

S_n - the sum of the terms until n^th term

GOOD LUCK ON THE UPCOMING TEST and THE MOST AWAITED PROVINCIAL EXAM!

2007-06-03T11:47:00.000-05:00

Hello!it's albert M. and I'm the scribe for the last friday. Since we're done in all of our units, we are just preparing for the last test which is the "Sequence" and also for our upcoming provincial exam this coming June 11. We just go over with some problems like these: the first one was just a warm up so it was easy. You are just going to use the formula to find tn and that's it.
First thing that we did was, we divided 8748 by 36 and got a quotient of 243 then we took the 5th root of it and got 3 as the common ratio. Then, we used the formula, plug-in the numbers and solve for the missing term.

(n-1)
using this formula tn = t1r we apply what we had learned in logarithms to find the value of n.

First one:

k = 1 tells you that k will starts at 1 and will end at 4.

Therefore plug in 1-4 for the k in to the 3k.

Chris showed the long method or the sum formula to get it done.

Second one:

k = 0 tells you that k will starts at 0 and will end at 3.

Therefore plug in 0-3 for the k to the 2^k.

Chris used the long method again to show it is the same.

Mr. K asked us to come up with two more different sigma notation for the same value and here's some of our answers. You can write the sigma notation of the same value in infinity ways.
We can use what we have learned to Mr. Green in his video clips that you can find in youtube, as we get the common ratio for the numbers in geometric sequence or you can divide the first two numbers, if you get r<1 then it converges and when r>1 therefore the answer diverges which you can see above.
We got the perimeter of the first triangle = 42

the perimeter of the second triangle = 21

the perimeter of the third triangle = 10.5

You can notice the pattern already didn't you?

try to get its common ratio by dividing the second number to the first number or the third number to the second one.

Lastly, use the formula for infinity then you'll get 84 as an answer.

This is so pretty straight forward so i won't explain it.

We are working on the last question which is the last clip but the bell rang already so we're just going to continue it on Monday which will be later discussed by Jojo who rocks!

Research Assistant

2007-06-01T19:05:00.000-05:00

Here I am again with another research assistant! For our final unit in the entire course, Sequences, I have compiled a list of links to help anyone review or practice for the upcoming test. I found these sites earlier today, hopefully they can help anyone who needs help trying to understand or anyone in search of extra practice for this unit's test.

REVIEWS/TUTORIALS

http://home.alltel.net/okrebs/page131.html

http://www.sparknotes.com/testprep/books/sat2/math2c/chapter12section2.rhtml

(The following four are from the same site, just broken into separate portions.)

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54a_seq.htm

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54b_series.htm

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54c_arith.htm

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54d_geom.htm

PRACTICE QUIZZES/TESTS

http://rutherglen.ics.mq.edu.au/math106S206/exercises.html
(scroll all the way down, select the second choice then click "get the quiz")

questions: http://www.math.umn.edu/~stanton/3113/exam1.html

solutions: http://www.math.umn.edu/~stanton/3113/pracexam1soln.html

I hope that these links can be utilized to help anyone review for the upcoming test, of which I wish everyone good luck! Have a great weekend everyone!

Today's Slides: June 1

2007-06-01T15:44:00.000-05:00

Scribe

2007-05-31T17:33:00.000-05:00

Hey it's Bertman and it looks like I'm todays scribe.

We started the morning gonig to the gym for the M.A.D.D multimedia presentation. Driving under the influence is a serious offense that dangers yourself and everyone around. Driving high goes the same way, so don't do it!

Anyways we started the afternoon class by watching a youtube video created a by Mr. Greene. The video shows him teach and show everything and anything about our unit, sequences in a matter of 3-4 minutes. Amazing isn't it?

Heres the link : http://youtube.com/watch?v=WjLSz-nNLBc

Following thw questions from the slide, the sum of the intergers 1-5000 can be found by using Gauss' formula. Where "n" = 5000, "t1" = 1 and "d" = 1. Simplifying we get a huge number, 12 502 500.

To find the sum of the numbers from 1-5000 that are multiples of 7, you start by dividing 5000 by 7 to get a value. Which is 714 different numbers. Using Gauss' formula again, "n" is now 714, "t1" = 7 and "d" = 7. Simplifying we get an answer of 1 786 785.

To find the sum of the intergers between 1-5000 excluding the numbers that aren't multiples of 7 can be found by just subtracting the 2 answers previously solved. Mr. K also told us we would be normally given this question and not the first 2.

Now we get to the super-bouncy ball questions!

There are 2 distances the ball creates. Distances bouncing up, and dropping down.
The distance of the ball when it's going down decreases by 1/4.
The distance of the ball when it's going up decreases by 1/4

By using the geometric formula, when it's going down, "t1" = 200, "r" = 3/4 and "n" = 4 since we want to find the distances after it hits the ground for the 4th time. When it's going up, "t1" = 150, "r" = 3/4 amd "n" = 3. By adding both numbers we get a total of 893.75.

There is another way to solve this type of question. When using 150 as "t1" the total distance from that first initial bounce to the second is 300. Therefore "t1" can be 300. The other values are the same and you get 693.75 as an answer. Don't forget the add the distances you left out depending on where you started. By adding 200 we get the answer again of 893.75.

Everything else are on the slides, from the sum of inifinity formula and the relationship from the value "r" to the words convergence and divergence. I don't know if we're supposed to pick scribes now that all the units are over but I choose Albert M.

Today's Slides: May 31

2007-05-31T16:26:00.000-05:00

Yesterday's Slides: May 30

2007-05-31T08:43:00.000-05:00

The internet was down at the end of the day yesterday. Here are the slides ...

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

Sequence Sequel v.02

2007-05-30T15:51:00.000-05:00

Hey guys! This is Jann, and I'll be your scribe for today! =D

We started of our lecture with some "quickies"...

1. Find the value(s) of "r" in 5r^4 = 80

Solution:

In order to solve this question, we just use algebraic methods...
2. In the geometric sequence, if t1 = 3 and r = 2, find t3.

Solution:

If we can recall the rule for geometric sequences from last class...3. If the first term of a geometric progression is 1/3 and the common ratio is -3, find the next 3 terms.

Solution:

In order to solve this, we can simply use the geometric sequence rule to find t2, t3, and t4...

4. Determine the common ratio for the geometric sequence; 1/(x^1/2), 1, (x^1/2).

Solution:

In order to solve this problem, first we pick either the first, second, or third term. We can concentrate on that term to find the common ratio, "r". There is one catch, if we let n = 1, our common ratio will be 1 since "n-1" is the exponent of the ratio. If we use n = 1, then the exponent will be 0, meaning, r will equal 1 (anything to the power of 0 is 1)...

I'll pick the 2nd term...Then, Mr. K told us the story of the great Johann Carl Friedrich Gauss

So, I'll try to tell the story.. XD

One day, Gauss' teacher asked his students to "find the sum of the numbers from 1 to 100". During his time, there were no papers to write on, just slates. His classmates started to add up all the numbers, starting 1. (Man... this is gonna take forever...) Gauss didn't touch his slate and thought about it for approximately 1.5 to 2 mins. He wrote the number 5050 on his slate and handed it in to his teacher. (Even the teacher doesn't know the answer to this one...)

The big question was... "How in the world did he do that?!"

This is how he did it...

1 + 2 + 3 + 4 .... 97 + 98 + 99 + 100
100 + 99 + 98 + 97.... 4 + 3 + 2 + 1

101 101 101 101 .... 101 101 101 101

If we add 2 copies of the sequence, in which one is written in reverse order, we could see a pattern...

Then, Gauss simply put together these numbers...It means that the number 101 has been obtained 100 times in his method. He figured that this answer has been added twice. Therefore, he multiplied the answer by 1/2.

In other words...

t	+	(t + d)	+	(t + 2d)	+ ... +	(t + nd)
(t + (n-1)d)	+	(t + (n-2)d)	+	(t + (n-3)d)	+ ... +	t

(2x + (n-1)d)

+ ... +

(2x + (n-1)d)

Since 2t + nd = t + (t + nd) = t₀ + t_n,

For any arithmetic sequence, the series could be found by using the Arithmetic Summation...

x+ (x + d) + (x + 2d) + ... + (x + nd) = (n + 1)(a₀ + a_n)/2
or

Where:

"Sn" is the sum of all the numbers up to the "nth" term
" n " is the rank of the nth term
" t1" is the first term in the sequence
" d " is the common difference

A series is the sum of numbers in a sequence to a particular term in a sequence.

For a geometric sequence...

Sn = t1 ( 1 - r^n)/(1 - r)

Where:

"t1" is the first term
"r" is the common ratio
"n" is the rank of the term

Finally, we talked about the "Sigma Notation". It's a short-hand way of writing a series.
The "funky" looking "E" is a Greek letter for "sum". The number above the "E" means "to find the value of n, until we have obtained the nth term of the sequence. "n-1" means that this is the initial value of the sequence; meaning, you have to start evaluating at n-1. "2n - 1" is the "rule" of the given sequence.

That's what we did for this class. (Finally, I have edited my scribe post! Yay!)

Oh well, good night everyone! I'm tired...

Next scribe will be... once again... "BERTMAN" XD.

Scribe - Introduction to Sequences

2007-05-29T18:57:00.000-05:00

Hello to everyone once again. Today I am scribing on both the morning class and the afternoon class. In the morning class we had a test on probability so there isn’t much I can talk about there. That’s it for the morning class. For the afternoon class, we started a new unit called sequences. Before we jumped into the work, Mr. K talked to us about fractal and showed us a video on it from www.youtube.com. If you would like to take a look at it, you can look to Mr. K’s post. After that we started off by taking a look at some problems:

Find the next 3 numbers in each sequence of numbers.

4, 7, 10, 13, , , … Answer: 4, 7, 10, 13, 16, 19, 22…

3, 6, 12, 24, , , … Answer: 3, 6, 12, 24, 48, 96, 192…

32, 16, 8, 4, , , … Answer: 32, 16, 8, 4, 2, 1, 0.5…

1, 1, 2, 3, 5, 8, 13, , , … Answer: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

From each of these sequences, we can find out if they are geometric, arithmetic, or neither. Also if it is geometric, then we can find the common ratio and if it is arithmetic, then we can find the common difference. Here are some definitions to help you out:

Sequence: An ordered list of numbers that follow a certain pattern (or rule).

Arithmetic Sequence :(i) Recursive Definition: An ordered list of numbers generated by continuously adding a value (the common difference) to a given first term.
(ii) Implicit Definition: An ordered list of numbers where each number in the list is generated by a linear equation.

Common Difference (d):(i) The number that is repeatedly added to successive terms in an arithmetic sequence. (ii) From the implicit definition, d is the slope of the linear equation.

Geometic Sequence: (i) Recursive Definition: An ordered list of numbers generated by continuously multiplying a value (the common ratio) with a given first term.
(ii) Implicit Definition: An ordered list of numbers where each number in the list is generated by an exponential equation.

Common Ratio (r): (i) The number that is repeatedly multiplied to successive terms in a geometic sequence. (ii) From the implicit definition, r is the base of the exponential function.

Well that’s it for today and that just about covers everything that we went over today in class. Hopefully this helps you guys out a little bit more.

The next scribe is…Bertman!

Homework is exercise 45!

Today's Slides: May 29

2007-05-29T15:46:00.000-05:00

Here they are ...

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

We lost today's audio. There was a problem with the mic at the start of class. I thought it had been fixed. It wasn't.

Here is the movie we watched and another like it illustrating some of the things I was telling you about:

proBOBly should have done this sooner....

2007-05-29T08:04:00.000-05:00

Haha morning of the the test! Not the best time to bob... Well this unit I'm feeling fairly confident in considering the amount of effort I have put into the homework in the exercises and on the blog. A couple of the questions are still worded trickely so I'm fairly certain that a 100% won't happen as I seem to go too fast and miss simple things in the questions on tests. So my goal for this test would be to take it slow and meticulously..... and still finish on time.

BOB IIIIIII

2007-05-28T22:51:00.000-05:00

Hello once again, back for my seventh BOB. Well what can I say this unit was a little hard towards the end of the unit, because of the permutations and counting sections which were mixed together. Although I am a little uneasy about those types of questions i believe this test should not be that bad after all. Probability was simply just a concept you had to learn and once you had the hang of it you can challenge any problem you liked. This is why I believe the test should not be difficult, unless there are many counting questions, which I bet there are. So all in all i found this unit to be quite straight forward and not very difficult once the concept is learnt. Good luck to all and make sure to study hard, Probability Test tomorrow morning.

ProBOBility

2007-05-28T22:49:00.000-05:00

Hello. It's me again with my bob. So I think that this unit is a pretty straightforward unit. The situations and concepts are easy to understand and the content in the exercises is pretty straight forward. The only problem that I have is that the tricky questions that Mr. K gives us that throws us off. Hahaha. Very Tricky. But at least I get the unit. Haha. So Hope for the best, and everyone do good on the test. Good luck, so long, have fun studying. Cause I am. Haha.

SECOND LAST BLOG?!

2007-05-28T22:40:00.000-05:00

Sorry I just posted now. I had work and i just got off. Anyways....Probability what can I say? Its true its the easiest unit but its hard to write down on the paper because there's so many ways you can do it and its hard to decide which one is right. I didn't really like probability ever since junior high well ever since I knew what it was. But whenever we work on problems in class I start to like it more and actually get it. Hmm ... well this is long enough. I'll leave it as it is and study!

GOODLUCK EVERYONE ON THE TEST TOMORROW!

Blogging on Blobbing

2007-05-28T22:15:00.000-05:00

Well, this unit about probability started off as relatively easy....then it became a lot harder. The quizzes were sort of a wake up call to me that i need to study more and finish this year strong. I really need to study more on this unit because ever since junior high i struggle on probability. I wish all the best to everyone. Good luck on the test and hopefully we all do well!

Probability Pre-Test

2007-05-28T22:04:00.000-05:00

Hello, i am the class scribe for this evening. We started today's class with a pre-test, because tomorrow is our long awaited test on probability. Basically the Pre-test had lasted almost the full class, because many of the students had questions about the questions on the pre-test. So to not get carried away here are the questions and the solutions to the pre-test questions.

question #1: Twelve people including you are members of the choir. The choir director is going to choose three members to attend a workshop. The probability you and two other members will be chosen is:
a. 1/4 b. 3/10 c. 1/12 d. 1/10

The answer is 1/4, because you are going so it is 1 * 11c2, because there are 11 members left and the director needs to pick two of them. It is all over 12c3, because it is over all the possibilities. So once that is calculated it is 1/4.

question #2: Rex is playing a guessing game. The probability he will guess each question correct is 0.3. What is the probability he will guess exactly 5 out of 10 questions correctly?
a. 0.15 b. 0.10 c. 0.29 d. 0.80

The answer is 0.10, because he must get 5 out of 10 questions correct so it is RRRRRWWWWW.
So it is 10!/5!*5!, because there are 5w's and 5r's. Then the 10!/5!*5! is multiplied by (0.3)^5*(0.7)^5 which is the binomial theorem. So once it is all worked out you achieve the answer of 0.10.

question#3: You choose 4 digits from the numbers (0-9), with no repeated digits. To win a prize only two numbers need to match the four selected by the computer.The probability, correct to the nearest one hundredth that you will win a prize.

The answer is 54.76%, because you must take the amount of numbers you are able to match with the computer to win a prize in this case 4c2, 4c3, or 4c4 numbers and divide them over all the possibilities which is 10c4, and add them all up. Once added and reduced it should give you a fraction:23/42, which is 54.76%.

question#4: The serial number of a $10 bill contains 8 digits. If your $10 bill contains the digit 7 at least once, you win a prize. What is the probability that your $10 bill will win?

The answer is you must find the probability of when there are no 7's and then you take the complement. So no 7's is basically 9 out of the possible 10 numbers to the exponent (^) of 8, because there is 8 digits. It gives you an answer of 0.4305, so to get the probability that there is a 7 you must take the complement, so 1 - 0.4305 = 56.95%. which is the answer.

question#5: Jeff takes a lunch to school on two days, and on the other three days he buys it. If he takes lunch he is late for his fourth period class 15% of the time, but if he buys it, he is late 35% of the time.

A) what is the probability that Jeff arrives on time?

The answer is that we take percentages of the two times he arrives and add them together to form the answer. So P(o) = P(to) + P(bo) = (0.4)(0.85) + (0.6)(0.65) = 73% which is the answer.

B) If Jeff was late, what is the probability that he took his lunch to school?

The answer is that you must take the probability he was late and took his lunch to school divided by the time he was late and brought his lunch plus the time he was late and bought his lunch. (0.4)(0.15)/(0.4)(0.15) + (0.6)(0.35) = 2/9 or 22.22% which is the answer.

So he is all of what we had done in class to day, when viewing this scribe post make sure to check the slides if you are confused, because it may help you find the way I had shown the answer. Make sure to study because tommorow is our Probability Test.

Tommorow's scribe is Robert P.

Ohh my BOB

2007-05-28T21:41:00.000-05:00

Chello everyone. Another unit has come to a close, like most of you have already said, and I think probability can be the easiest thing to comprehend yet the hardest thing to write on paper. Don;t you hate that, knowing exactly how to solve problems in your head, but don't know how to write it? Or maybe that's just me... Anyways, I'll wrap this up since I should study. Funny how remembering to do this also remembered me to study. Ohh my lanta.

BOB

2007-05-28T21:32:00.000-05:00

Another unit done and I'm starting to see a trend. As we start the unit, the concepts and questions seem to be quite easy to grasp for everyone, especially with this Probability unit. However, once the pre-test approaches most of us (from the classes reaction, correct me if I'm wrong) seem to be surprised at the complexity of some of the questions. Whatever it may be, the only way we can possibly improve upon that is study, study and study. Exams are coming very soon and we only have one unit left. Let's finish this year off strong. Good luck on the test tomorrow everyone.

BOB # 7

2007-05-28T21:06:00.000-05:00

Hello to everyone yet again. Wow probability has come and gone and the test is tomorrow. This unit started off pretty easy and then it just got harder. On today's pre-test I found question 3 really difficult. To get through this though I will study tonight and try to do well on the test tomorrow. I wish the best of luck to everyone! See yah tomorrow!

bee oh bee number seven.

2007-05-28T19:23:00.000-05:00

hello. the end of the unit has come once again and here I am bobbing...probability...I never really liked this unit at all due to the fact that it is challenging...haha I found it challenging ever since junior high. I was able to understand the things we did in class, well most of it. Quiz number one was quite surprising because it showed me what I knew or didn't. Then quiz number two I did a little better, which is good. This unit was difficult for me because I don't realize what is right in front of my face. Hopefully though, on the test I will be able to figure out what is in front of me. Good luck to everyone and hopefully we all do well.

BoB

2007-05-28T19:02:00.001-05:00

Well to start off this unit was simple...It seemed like a piece of cake, but right now that point of view that I have just changed... This unit is really difficult, it requires a lot more thinking than I thought it would. The way the questions are worded and the solutions that seem to be the exact opposite of what you do... It's either you over think or under think how to answer the question...

Well the test is tomorrow and I am NOT looking forward to it. I don't feel that I'm ready for it. But there's nothing I can do about it... :P... Oh well I'll just say good luck to everyone... :P

BOB

2007-05-28T16:02:00.000-05:00

Hello everyone! Once again, we have finished another unit of our course. Probability has been a very interesting unit because it practices your thinking skills. For me, figuring out chances on how a certain thing will occur is pretty cool. I found the "Tree Diagram" very interesting because it shows you the sample spaces of a certain event.

I hope everyone will do well on this test. This is our 2nd last chance to improve our test marks... -_-

Good luck y'all!! XD

Today's Slides: May 28

2007-05-28T13:29:00.001-05:00

Probability

2007-05-27T23:12:00.000-05:00

Friday is grueling days ever because of 2 unexpected quizzes from Mr.K

First we started-off with this. The very first thing to do is to make a tree diagram and fill out the probability for each cases .The probability that Tony will move to Winnipeg is 2/9, and the probability he will marry Angelina if he moves to Winnipeg is 9/20, all you need to do is to multiply to the probability that Tony will move to Winnipeg and marry Angelina.To get this, all you need to do is to multiply the probability that he is moving to Winnipeg which is 2/9 and the probability that he is not marrying Angelina 11/20.
To get this multiply the probability that he is staying which is 7/9 and the probability that he is not marrying Angelina which is 19/20.This is the probability of drawing four aces in a standard deck of fifty-two cards.
This is the probability of drawing diamond cards.
This is the probability of drawing an ace and a diamond.
All you need to do is to add the probability of drawing four aces and diamond cards, then subtract the probability of drawing an ace and a diamond.To answer this question, you need to make a Venn Diagram. Then from that diagram you will see that ten out of twenty-five students doesn't like either Dr.Pepper or Diet Dr.Pepper.

This is the probability of choosing two green dresses out of six.
This is the probability of choosing four dresses out of nine.
This is the probability of choosing six dresses out of fifteen.
All you need to do is just by dividing the favourable cases over the possible outcomes.

First thing is to make a tree diagram and fill out the probability for each cases. Next is to get the probability of an SUV that has air conditioning and divide it by the probability of having a passenger car that has air conditioning plus the probability of an SUV that has air conditioning.

To get this, just add the probability of drawing a defective blade first and then a good blade and the probability of drawing a good blade first and then a defective blade.
For the 1st question, you can't use the number 0 as the first digit, so you nine choices left.
The 2nd digit, you can't pick the same number that you use before so you have nine choices left. The 3rd digit , you can't pick the same number that you use for the 1st and 2nd digit, so you have 8 choices left. The 4th digit, you can't pick the same number that you use from the previous three, so you have 7 choices left.

For the 2nd question, just divide the possibility of having an odd number by the total number of possible digits.

For the 3rd question, break the question into 2 steps,one is that ending in zero and the other is ending in 5, then add both . Then divide the answer by the total number of the possible digits.

To get this, get the probability of getting exactly four hits out of 6 throws. Then, raise the probability of hitting to the fourth power and then the probability of missing to the second power.

That's it folks.By the way we have a pre-test tomorrow,sorry for the late scribe .The next scribe is DINO.

BOB-ing 7

2007-05-27T21:28:00.000-05:00

I'll go straight to the point. The Probability Unit evokes chaos in my mind. In short, probability is one of those units in Math that makes me go, "WHAAAT?!" It may not seem like it because I don't do it in class. But seriously, in my head, I do it a lot. I grasped the concept easily. However, the application of that concept is the real puzzle to deal with. Maybe, the struggle originates from lack of practice and absence of confidence with myself. Like in the last quiz, I doubted myself so much that I erased the solutions for two questions that transpired to be correct. That was really... KJ (kill joy). Another frustration dawned upon me as the week concluded and the weekend commenced. I promised that I would be practicing during the weekend, but I failed to such a thing. Some problems throw me off because of too many disturbances. I really hope that I do well in this test, but not without a lot of practices. Maybe I should start after this BOB! Anyway, this year is about to end and I couldn't ask for more with a fun class already at hand. But, it's so fun that sometimes my attention linger over other topics. My BOB ends here and I hope you all had a great weekend and good luck on the upcoming pretest and test! See you guys tomorrow!

I hope that all my practices will pay off. Good luck guys! I know I need that too! HAHA!

BOB 7

2007-05-27T21:13:00.001-05:00

Well, I thought that this probability unit was kinda easy. When we had the quizzes, I was surprised! It was hard, and that led me to think that I needed more practice for this unit. I'm just hoping that the test won't be as quite difficult as the quizzes. Those quizzes really got me surprised. Anyway, I wish everyone luck in the test, we're going to need it.

B O B

2007-05-27T20:24:00.001-05:00

Hrm, yet again it's time to blog. This unit went by quite fast. During the beginning of this unit, the problems were without a doubt easy and included no difficulties for me. However, as we progressed, I found that there were questions (such as those on the quiz) that surprised me.

On the otherhand, I should've been more responsible for completing more of my exercises than I have. I found that since I did not practice as much, I struggled at times and found that I was stuck; not knowing what to do next on certain questions.

Truthwise, I will "try" to do more practice questions tonight and we'll see how I fair on the pre-test and test.

Good luck everyone on the pre-test and test this coming week!

BBOOOOO for BOB

2007-05-27T19:46:00.000-05:00

So apparently we have a test on Monday ... wasn't in class on Friday unfortunately for the quiz. This unit that people call "probability".. is the story of school life. This is the unit i dread every year. This unit Probability was so difficult, hands down this has to be the hardest unit . I honestly wish we had like an extra week so i can actually take the time to understand this unit a bit more, i know for sure this is going to be my worse unit yet.
But, for everyone else Good Luck because i know you'll all need it just as much as i will.

Boron-Oxygen-Boron

2007-05-27T18:30:00.000-05:00

I almost forgot to bob for the upcoming probability test until I checked the blog and saw Sandy's. And to iterate Sandy's statement, the provincial exam is only 2 weeks away! I can't believe that we've blown through the year in almost no time at all (well at least it felt like that) and what a blast it's been. Though I'm feeling really down because of all the cruddy marks I've been getting recently, but I've really enjoyed this course so far. This was the first class which presented a functional lesson solely integrated upon the smartboard. But enough about reflecting over the entire year, this bob's supposed to be about just this unit xD. This unit of course was probability. This unit wasn't terribly difficult and didn't present a lot of tribulations, especially seeing as the final portion of probability incorporated one of our previous lessons: combinatorics. Just remembering that a probability can be found by dividing the amount of favorable outcomes by total amount of outcomes is how you arrive at the wanted probability. Well this unit was very relaxed and somewhat straight forward, but as Mr. K left us (made me sad )= ) we were responsible for our own learning, and showing by my quiz marks, I wasn't exactly a very reliable worker. But as for the rest of the unit, there wasn't really anthing new that was unique to other units except for the exciting colloquy we had with Eddie's class in Georgia! It was quite a surreal experience, seeing as it's quite intriguing to converse with people from other regions of the world. I think we were all excited to chat with the class over in Georgia, and when the day came, we really enjoyed it. I think it was quite an extravagant episode in our bevy of pre-calculus memories. But with that said, I can't wait for further conversations from the class over in Georgia. This was my bob, good night everyone. As for the test:

I WISH EVERYONE GOOD LUCK ON THE PRE-TEST AND TEST!!!

99.9 BOB FM! (8)

2007-05-27T17:31:00.000-05:00

Every single time I arrive on our blog I think about how close the provincial exam is. 2 weeks from tomorrow! It's really time to start studying. As for this unit, I didn't do great on my quiz, but the mistakes were really dumb. -_-" As soon as I seen the correct answer I realized I had made a stupid mistake. Regardless of the quizzes, I think this unit is pretty straight forward and not that difficult at all. I hope to do as good on this test as my logs one. (: Hopefully everyone else does really good as well. Good luck to everyone with the up coming test! <3

Today's Slides: May 25

2007-05-25T15:55:00.000-05:00

The Winnipeg Georgia Connection

2007-05-25T00:38:00.000-05:00

I thought you might be interested in this follow up to our gizmo conversation with Mrs. Davis' grade 5 class in Gerogia. I've mirrored the post in it's entirety from her blog. Listen to the various mini-podcasts at the end:

Canada/Georgia Connection on Gizmo
May 22nd, 2007 9:02 am

The blogicians and the students in Darren Kuropatwa’s Pre-Cal 40S class participated in a Gizmo call last week. The blogicians had prepared some questions that they wished to ask the high school students. Gizmo has a neat feature that lets you record the conversation as you are talking. It did pretty well but does have an echo effect from time to time. As I listened to these podcasts I really marvel at the learning that occurs. I kept thinking how much was going on and how much can be fostered with these types of connections. I think you have to have a plan of action as if you just connect and talk you may lose some focus. It was a thirty minute call that was filled with some many unexpected turns that were so worthwhile.

What a good space to give kids practice with public speaking. Both ages were nervous but the experiences they got speaking will serve them so well. I think both sides learned so much from each other. The older students were unaware of some of the constraints involved while teaching elementary students (listen to the chat box podcast), the ability to look for dramatic and outstanding pictures for presentations (listen to the Flickr podcast).

On a scribe post after the Gizmo talk, Grey-M one of the high school students said the following:

I must say that trying to answer something on the spot is brutally hard (These weren’t easy questions either) so people, including me, were a little hesitant at times to respond. So that was a fun deviation from our usual routine.

The younger students are in awe of the older students but in these kind of connections they learn to step back and decide if they agree or not. They learn that that is OK.

Johnny from the blogicians posted the following after the talk:

We just did a gizmo chat and it was quite delightful with a pre call math class and it was nicely spoken by me and my classmates. Mr. K was the teacher of the class I asked about chat box and how they use it and Danny replied “We use it to learn all over the web and it sort of saves time instead of commenting”. I sort of agree with him what do you thing do you agree or do you disagree? If you don’t know what it is try looking it up and using it.

You get to discuss so much and the best part is you are having authentic conversations with the students and encourgaging their honest input. It builds great learning communities. This can only make things better in our classrooms. This is great practice for them and us. The teachers get to do a lot of learning too. We’re learning how to best orchestrate these experiences. We’re learning how to help these kids on their path to becoming global citizens. The more experience we can give the kids with this type of learning the more they will be able to help us shape its’ most effective use. These are the types of literacies we need to be developing in all our schools.
I’m still thinking about all this….. the possibilities, how to involve others, and on and on….

It was a day to remember - a day of connections and learning between some very inspiring students in Canada and Georgia.

Links to podcasts:

Podcast 1: Introduction and special bond

Podcast 2: Eddie Chris Online Safety

Podcast 3: Eddie Vincent Being responsible while blogging

Podcast 4: Emmy Danny Flickr

Podcast 5: MV Chris Craig B.O.B (Blogging on blogging) and convincing middle school teachers to let students blog

Podcast 6: Tina Vincent Grey-M The best and the worst of blogging

Podcast 7: Johnny Richard Danny Chat Boxes

Podcast 8: Eddie Aichelle How does blogging advance your learning as a fifth grade student?

So, when you were writing your scribes and BOBs on Circular Functions did you ever imagine a grade 5 student from Georgia would drop by, read what you wrote, be interested in it? That he would blog about it which would lead to all these ripples in the blogosphere? That all this would eventually connect you all, on a very personal level, with a class of grade 5 students half a continent away?

When you publish your learning online, even if it's tough stuff like math, you have an audience that spans the globe, grades and geography.

Did you ever imagine something like this would happen? ;-)

Probability Practice Produces Perfection ... Probably

2007-05-23T22:21:00.000-05:00

As promised here is a little extra probability practice for you ...

And some links for learning ...
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.

Photo source: Harry Potter's Platform 9 3/4!!!

Exactly why are doctors so cagey?!

2007-05-22T16:49:00.000-05:00

Hey it's MrSiwWy here to present to you the scribe post for today! I'm the scribe for today's rather intriguing but yet solemn class. I say solemn as I think that the main question our class was focused around pertained to very serious matter. But anyways, onto the scribe post for
Tuesday, May 22, 2007.

Our class began with Mr. K outright stating to the class that we're on the verge of the end of probability, and the beginning of our final unit: sequences. He then told us that he won't be present the two following days, but that we only have two things left to learn in probability, one of which incorporates one of our earlier units: counting and combinatorics. He presented us with an example of such a question. This question was regarding the arrangement of students, like we have been presented with in the past.
If students are to be seated in 7 desks, what is the probability that Mark and Robert are sitting together?
Basically, we take amount of favorable outcomes, which would be the amount of ways Robert and Mark can be seated together, then divide that by the total amount of seating possibilities.

We quickly moved onto the class for today, and very soon, we transitioned into the question that Mr. K left us off with on Thursday; "Why do doctors have do so many tests? Why are they so cagey?" Once Mr. K put up the question we were to dissect, he set us up in small groups of four. This smoothly yet appropriately forwarded the momentum of our class into the actual lesson. This question can be seen on the following slide:

If we think about each of the four possibilities, we have to realize that the test is to check for cancer, so if it tests positive when the person really does have cancer, then the test succeeded, meaning that it has a probability of 98%, or 0.98. This means the remaining probability (that the test failed by showing negative, when they really have cancer) is 2%, or 0.02.
But as for people who do not have cancer, if the test shows positive, this means that the test failed, and this probability is in fact 2%, or 0.02, and the remaining probability (to test negative for those who do not have cancer) is 98%, or 0.98.
And as I stated at the end of the slide, a tree diagram can really help. So here is a tree diagram that was used to calculate the probabilities of each of the questions on the following slide.

Mr. K later asked us to construct this tree diagram to help us understand the question's calculations, but really, to create one beforehand is more of a help.

Here we see that Mr. K coded certain important aspects for various reasons. These reasons are very vital when contemplating a method to approach each question.
The blue underlined portions indicate that we're dealing with people who have cancer.
The green underlined portions indicate that we're dealing with people who do not have cancer.
The small circular flower symbols indicate total amounts of people that have cancer.
The small stars indicate total amounts of people that have been tested positive for cancer.
The last two are particularly important because the main question that we were originally asked was what the probability of a patient that has cancer is also tested positive for cancer. In order to arrive at this, we must dignify how many total people have cancer, and divide that by the amount of people that were tested positive. We've already learned that in order to find the probability of an event, we take the amount of favorable outcomes and divide that by the total amount of outcomes. So in this case, we take the amount of subjects who have cancer, and divide that by the total amount of times that the test would show a positive result. That is why Mr. K signified each of the above portions. This was taken care of in part 4 of the above questions, but before that, I'd like to outline how to achieve each of the answers in the entire slide.
In order to determine each of the answers shown on this slide, we used the tree diagram above in conjunction with the sample group of 1,000,000 people.

This part was simple. Since we know that there are 1,000,000 people, and 0.5% of these people have cancer, that means that 5000 people have cancer, and the rest don't. The rest can be found by subtracting how many that have cancer from the total of people, this gives us 995000.
In this part we use the tree diagram to determine what percent of people that have cancer will test positive. To do this we multiplied the amount of people that have cancer, then multiplied that by the probability of testing positive, which is 0.98. This gave us 4900, the answer presented in the slide. For b, since we know 4900 tested positive, the rest of the people who have cancer must have tested negative, and that number is 100.
Here we repeated the same process used in part 2, exact that we used different values since we're looking at only the people who do not have cancer. We know that there are 995000 people that do not have cancer, and as I outlined earlier, since the test would fail if it said positive, we would have to find 2% of 995000. This, as shown, is 19900, and to find how many tested negative, we just subtract this from the total. 995000-19900 gives us an answer of 975100.
The final part was compounding what we determined in the previous steps, and in essence, determining the answer to our original question. First we take how many people altogether tested positive, we get this simply by adding those that have cancer that tested positive together with those that don't have cancer but tested positive. For b, we know that of the people that tested positive, 4900 of them actually had cancer. So to find the original question at hand, this was the work shown. I already described how this was found, here is the work:

As he showed us that vertical line separation between the C and the P, the class began wondering what that represented. This introduced the class to conditional probability. The way Mr. K described such a probability was "when we have inside information" beforehand. Usually when we have dealt with probability we knew that either one thing or another can happen, then another event can happen in one way or another. But in conditional probability, we know that one of these events is going to happen in such a way. In this question, we knew that our answer only concerns when we know that the test is going to be positive. He gave another example of conditional probability using three jars containing marbles. He says that if jar one has 3 blue and 3 red marbles, jar 2 has 2 blue and 3 red, jar 3 has 2 blue and 2 red, then he doesn't look at any of the jars and pulls out a blue marble out of one of them. In this case, we know that the marble that he pulled out is blue. Given the above information, what is the probability that it is from jar 2 of pulling a blue marble from jar 2? This isn't word for word, but I believe that was the basis of the example Mr. K conveyed to us. The basic idea is that we know that the marble is going to be blue, similar to how we knew that the test was to be positive in the first question today. So to sum up conditional probability:
Conditional probability is when we have some inside information on the events at hand, basically when we know some of the information before we even start to calculate.
When we are dealing with conditional probability we write P(P1P2), where P1 is the probability that we're looking for, the vertical line says "given that we already know", and P2 is the event that we already know.

Once we were finished with that question, we moved onto a very similar question, in which he just changed "cancer" to "industrial condition," 98 % to 99 % and 0.5% to 1%. Here is the question along with the work, of which I will of course explain.

Here we see both a tree diagram and the work to the solution for the question.

I represents those with industrial disease.

H represents those without industrial disease.

P represents those that tested positive for the disease.

N represents those that tested negative for the disease.

Here we see that we found the probability that someone has the disease and also tests positive for the disease by dividing the favourable outcome (probability of having the disease) by the total amount of testing positive. This is exactly the same case as finding the probability of having cancer and testing positive for cancer, just with different probabilities.

So in this class, we fully determined the answer to the question that Mr. K had left us with on Thursday afternoon.

Doctors aren't necessarily cagey, but run the tests more than once to make sure. If we look at the results that we achieved by both questions, we arrive at the fact that if someone really has the disease and tests positive, there's not a good chance that it's for sure. Thus, doctors run tests more than once not for fun or anything of the sort, but in both cases it's more likely or equally likely to be tested positive and not have the disease, so it's good to be sure before breaking such news to a person.

And that concluded our class for today, with the lesson of conditional probability that was presented to us today, as Mr. K said, we don't have a lot left in this unit. This was my scribe post, and I hope it was clear enough for anyone to understand. I still need to fix some content up, really don't like how my Computer is so resilient, especially seeing as I can't get to any pod casts. =/ But as soon as my computer begins to cooperate with me I'll get everything fixed up and tidy. Please just contact me if there are any concerns, questions, complaints, errors, etc. Have a good night everybody!
oh yes, thank you John for reminding me. The scribe for tomorrow will be: Jann!

Today's Slides: May 22

2007-05-22T13:25:00.000-05:00

LONG Weekend = LONG Scribe

2007-05-18T16:58:00.000-05:00

This class was the second one of the unit of PROBABILITY. That is, as Grey-M stated in the last scribe post, the easy unit of PROBABILITY, but anyway...

...The class started with the student elections. 3 of the 4 candidates for the executive council were in our class so it was a fairly bid deal. (To see the results, check the post prior to this one by Sandy.)

After that, we reflected upon the extraordinary video display by Richard in the previous day's candidates' speeches. We liked it so much in fact, that we searched YouTube for it. We didn't find it, so instead we watched a video that was completely irrelevant to math, or anyone in our class for that matter =D.

Then, we got down to some "ACTUAL MATH!"

The first slide shown was a little too easy I believe, but Mr. K. didn't find it as such (haha!)
Then, Mr. K presented us with on that was a little higher on the difficulty scale. We were to "TEST THE QUESTION FOR INDEPENDENCE".
We'll take a quick trip back and review exactly what an independent variable is:

Thank You Grey-M! =)

Now, to test a question such as:

30% of seniors get the flu every year. 50% of seniors get a flu shot each year. 10% of seniors get the flu even though they've had a flu shot. Are getting the flu and getting a flu shot independent events?

•The first step is to look at the set. (In this case it is the SENIORS)
•Next, identify the categories. (Whether they GOT THE FLU SHOT or NOT)
•Now, we identify what event can occur to each category. (they can GET THE FLU or NOT)
• The fourth step in the solving in this problem is to draw a tree diagram:
•Now we can write in the probabilities of each event.
•Then, find the favourbale outcome, or the outcome which we want.
•Now just calculate the probability of the favourable outcome and compare it to the given percentage:
Here we see that the probability of catching the flu and getting a shot is not 10%, it is 15%. This means that they are not independent events.

Next, we moved on to questions that dealt with events that were "MUTUALLY EXCLUSIVE". This means that it is a situation in which one(or more) of the outcomes of the event becomes impossible if the other(s) is(are) chosen.
EXAMPLE:
If Mr. K. were to pick from the class one boy, he will not be a girl. If he picks a girl, she cannot be a boy.
An event can be determined to be mutually exclusive (or "disjoint") if the probability of getting both outcomes is zero(Ø), also known as an empty step.

**both events would be written as "A", "(upside-down U)", "B".**

After that we did problems that asked for the probabilities of "AUB" (A or B). If it is mutually exclusive, then simply add the probability of "A" and the probability of "B".
However, if it is not Mutually Exclusive, we must also subtract the probability of "A and B", because it is not A OR B if both are chosen:

We continued the class by doing more questions dealing with "AND" and "OR" and finished off with a couple situations for which we had to decide whether it was either:
INDEPENDENT or DEPENDENT and MUTUALLY EXCLUSIVE or NOT MUTALLY EXCLUSIVE.
This can be found in the slides (2 posts previous to this one).

To finish off:
•CONGRATS RICHARD AND VINCENT!
•Hope everyone's Long Weekends were better than mine.
•TUESDAY'S SCRIBE IS MR. SIWWY!!!
•Enjoy your day off =D

Congratulations!!

2007-05-17T22:03:00.000-05:00

Well.. since our homeroom does contain 3 out of 4 candidates for the school elections this year... I think this blog deserves this post.

Congratulations to Richard who is next years wonderful President!
and... Congratulations to Vincent who is next years wonderful Vice-President!

You guys worked hard and you both deserve your positions on the executive council. I'm definitely looking forward to next year with you two. (:

So again, congratulations to the both of you. =)

Today's Slides: May 17

2007-05-17T10:33:00.000-05:00

TranSCRIBIN'

2007-05-16T21:01:00.000-05:00

Well today we had some different classes....

We started off with a Gizmo call to the Blogical Minds class in the US. Unfortunately I had completely forgot that this was going to happen in the hectic last couple of weeks so I did not have any questions prepared for them. But they had plenty for us :-). I must say that trying to answer something on the spot is brutally hard (These weren't easy questions either) so people, including me, were a little hesitant at times to respond. So that was a fun deviation from our usual routine.

But to the mathematics....

Easy mathematics :-)....

Well we all seemed to grok this probability thing. Today we learned to distinguish between dependent and independent events and how to calculate dependent event probabilities.

A dependent event is an event that the first event effects and and independent event is an event that does not depend on what happens in the first event. So we did a few questions to demonstrate this concept...

The only one event that effects the other event is the removal of the card without replacement because that changes the sample space.

Changes in sample is not the only way to cause dependency. If something within the sample space is changed it changes the odds of the events as shown in the next question.

When a marble is drawn it is replaced with a marble of the other color changing the odds and making this another dependent situation. We got the odds at the end of the probability tree by multiplying along the branches. Then to get a combined probability figure you add all the favorable outcomes.

As we saw with other questions this process generally works for calculating the odds of a singular/series of event(s) . We also found another way this relates to combinatorics in this class because Mr.K showed us that the questions can seem different but they will actually be the same like the flipping of the coin and the children. So this concept seems to be fairly simple but Mr. K will find a way to make this hard on the test. Which I hope will be soon so we can get a few days of review at the end of the year.

Auf Wiedersehen (See if answer tips can get that)

Today's Slides: May 16

2007-05-16T15:33:00.000-05:00

SCRIBE! ( ^.^) Introduction to Probability

2007-05-15T19:35:00.000-05:00

Hello fellow classmates and readers! I'm Tim-Math-Y your scribe for today! Today we looked at the beginning of our new unit: Probability. We talked about things such as favourable outcomes over total possible outcomes, certain events, impossible events, sample space and other interesting things.

We started off the class by looking at this interesting question:

There was no right or wrong answer in this exercise.
Mr. K was looking to see what we thought of probability and why we chose each numerator or denominator.

While going over each solution that the class came up with, we found that 1/(infinity) is pretty much equal to zero since it comes so close to zero.

Here we find that 4/9 (0.444 repeating) + 5/9 (0.555 repeating) = 9/9 (1)
It is quite interesting to see that these two repeating numbers added together gives us the value of 1.
What we were trying to get to here was the fact that if a number comes so close to another number, we can assume that it takes that form (Ex. 1/infinity = 0)

Next we took a look at the meanings of probability and it's characteristics, including sample space.

Notice that the "Compound Event" examples are involved in one of our last units, Counting. Specifically, the Fundamentals of Counting.

Next we observe carefully more characteristics of a probability.

The slides today are quite self explanatory.

Next we looked at some examples of probability.

Next we looked at examples that involved finding the sample spaces.

To find the sample space of the problem, we find the total possible outcomes either through a tree diagram or a chart/table.
We are usually only asked this when there aren't a large number of possibilities (will be too much work)

Now we look at more examples:

To find the probability, we divide the total number of favorable outcomes by the total number of possible outcomes.

Now we look at a really hard example:

This is one of the attempts of solving question 1a, by one of our fellow students, John

Running out of class time, Mr. K steps in to give us the solution:

Remember that making mistakes benefits the class in learning*
Mr. K makes a chart with the times the bus will arrive at the top and the times of the train will arrive on the left.
Doing this, we find the total number of ordered pairs: also known as the sample space :)

Well that was all for today guys. I know it isn't as flashy and isn't that long or awesomeness to the max but yeah, I was sidetracked a lot today haha.

Well, that wasn't too bad. Most of it was self explanatory.

Tomorrows scribe is... hmmmm...

Grey-M..

Sorry, didn't know who to pick, and it's almost SAMS BDAY HAHAH!

Today's Slides: May 15

2007-05-15T15:43:00.000-05:00

BOB

2007-05-14T12:12:00.000-05:00

Well this unit went by pretty fast huh? So fast that I almost forgot to do this....again =S It was a pretty simple and quick unit. Mainly involved with graphing and equations I found every concept pretty easy to grasp. On the quiz and pre-test I did fairly well. I think the test won't be too complicated but I could be wrong, so I'm going to look over a bit more of the unit until the test comes later in the day. Good luck to everyone on their test!

BOBING before the Election

2007-05-14T11:00:00.000-05:00

Wow... This week has been so hectic. Haha Well this unit was ok. I understand most of the unit in general. The only problems that I have with the conics unit is the problem solving questions. Maybe that's because I don't have a proper understanding of the unit becuase of everything that has been going on. I am un sure about the test but it's alright. I wonder if there is any repremend for today and this bob. Hah. So I'm off to study again.. Good luck on the test and have a great DAY.

BOB !!!!!!

2007-05-14T10:28:00.003-05:00

This unit on conics was somewhat difficult for me. Especially the part of the unit on the hyperbola, because I did not comprehend all of what the hyperbola was about. Other then the transverse and conjugate axis and the equations of an elipse and hyperbola to be the same. I found that the circle and parabola part of the unit was very easy for me because it was basically review from grade eleven. I found the elipse part of the unit to be also not as hard because it was straight forward and I understood it very well. All in all i found this unit to be alright, although sometimes difficult, it was alright.

BOB

2007-05-14T08:45:00.000-05:00

Well, this unit about conics is relatively easy because it was just all mechanical. The only thing about this unit is unit is I always mix up the terms like conjugate axis and transverse axis. I personally hate the paper folding stuff because it is so repetitive but we learned a lot from it. Anyways, thats it for my sixth BOB I need to go to school now.

Mother BOB

2007-05-14T07:44:00.000-05:00

First of all I would just like to say Happy Mothers Day to all the people who are like a mother to someone. The world needs to be nurtured by someone.

Anyway this is the END of the CONICS section.
It felt like the unit went by fast. I enjoyed the paper folding.

The unit consisted of parabolas, circles, hyperbolas and ellipses; which was pretty straight forward to understand.
The only thing is some of the problems towards the end were a little more difficult, other than that OK.

MR. Siwwy, good post.

GOOD luck you guys on our test later on.

BOBing (Can't think of anymore names right now i'm so tired)

2007-05-14T07:22:00.000-05:00

This unit was super fast (which could end up to be a good thing or a bad thing...i would say bad) it felt like we spent maybe 4 classes max.
Otherwise this unit was pretty good understood most stuff because it was somewhat similar to what we did in Grade 11. Love the fact that there's actually formulas to follow and memorize, not like counting. The only thing that I'm not liking about this unit it is the last part where Mr.K started applying it to real life things in those problem solving format, i found those pretty difficult, i either was over thinking it or not thinking at all.
I'm actually almost very tempted to say this unit was relatively ....easy! Almost seems to good to be true(it's a trick), but i know Mr.K is gonna shove those words down my throat eat them and choke on them when we get the test.

Food For Thought

2007-05-13T23:05:00.000-05:00

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

BOBbing On BOBbing

2007-05-13T23:01:00.000-05:00

Another unit come and gone. The pre-test and test loom over the class, as nervous students prepare for "the day of two tests". Myself, I'm continuing with my busy life and finally sitting down at my computer at 11:00 pm to write a quick BOB. This unit has been fairly tricky considering the introduction to quite a few new topics, while embellishing on older ones.
The hardest part for me so far is simply remembering which formula goes with which shape, and what the difference between the horizontal and vertical versions of each. However, it is a very correctable problem with lots of practice. I'm sure most of the class is comfortable with the material, or at least that's what I thought based on Friday's class. So , without further ado, "Good Luck!" I think I will eat a bowl of Lucky Charms for breakfast tomorrow, "They're Magically Delicious!" Although, I don't think I'll need it, and I hope no one else does.
Do I even have to say it???

Research Assistants

2007-05-13T22:09:00.000-05:00

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

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

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

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

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

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

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

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

The Research Assistants List

Conics
MrSiwWy

Sequences
MrSiwWy

Photo source: HoP Mad Science Fair: Jon and Natalie

BoBiNg

2007-05-13T21:51:00.000-05:00

Guten Tag,

Awesome test wooo! I am über-prepared for this puppy! Just going to do some of mista siwwy's links to make sure. Don't know why but I just completely grokked in fullness this unit. Though kinda disappointed that we lost our last review class for the exam. But that's why the blog exists and I'm sure that Mr.K will have all sorts of mathematical goodies posted for preparation for the exam. Well I wish everyone luck!

(P.S. Miles! Remember the VB.NET book!)

Happy Mother's Day, BOB.

2007-05-13T21:05:00.000-05:00

So here's my sixth bob so far this year. Conics, has actually been fun. (: Math is fun if you know what you're doing and understand it. Haha, it's weird but true. This unit has been pretty straight forward. I just have to remember to look at the question completely before drawing a graph. That's where i usually make my mistakes. -_-" But other than that i understand the concepts and everything. I think this test is going to be a good one. (: I don't have much else to say. Good luck everyone on the pre test and test tomorrow! =D

B.O.B.

2007-05-13T20:35:00.000-05:00

It seems this unit went by quite quickly. There isn't too much to say other than it was simply straightfoward; parabola, circles, hyperbolas and ellipses.

Though this unit is quite simple and easy to understand, I am uneased by the way this unit seems "too" easy. I know there's going to be something that I'll miss but that's only because that's been happening in the past.

Well, the only way not to become a victim of worrying is to practice!

By the way, nice review posted Mr. Siwwy! hehe

Goodluck to everyone tomorrow! On the pretest and test! =)

BOB

2007-05-13T20:09:00.000-05:00

Hey y'all! We have finished our unit on Conics. This has been a really short unit. We've learned about the standard formula of a parabola, circle, ellipse and, a hyperbola. We did a few paper-folding to help us find some patterns and relationships between the points and distances. This unit has been very easy to understand.

I hope everyone will do good on the test tomorrow! =D

Ohh my lanta!

2007-05-13T19:40:00.000-05:00

Ohh my lanta, I almost forgot to BOB.

Anyways, conix was pretty much a very short unit. I didn't even know what the unit was called until I read the other BOB's. It was such a smooth unit that I actually got everything we were being taught. Good luck on the test guys.

Bob 6

2007-05-13T19:27:00.000-05:00

Well one more unit is over and it's time to bob again. I personally found this unit pretty fun with all the paper folding. It was pretty easy and I hope that I do good on the pre-test and the test. That's all I have to say for now so I wish everyone the best of luck on both tests. Bye now and see you guys on Monday!!!

BOB

2007-05-13T17:24:00.000-05:00

Somewhat, I think this unit is one of the understanding units of all the course we have taken so far... with all the hyperbola, circles, ellipses and parabolas are like half, half to me and i think i will do good in the per-test and test on monday's class.

I wish that all of you a good monday and having a good mark with the tests and studying till you cant no more haha!!

BOBa Fett

2007-05-13T16:51:00.000-05:00

Hi all!

I'm really confident about this unit. I understand everything and whatnot, I feel like everything is going right, but, I get some more practice problems. The links provided by MrSiwWy are good and can help us do better on the test. Remember, perfect practice makes perfect.

Good luck to all!

Research Assistant

2007-05-13T14:28:00.000-05:00

I remember when Mr. K told us about this, I was ecstatic. I want to help =) This research assistant post will be concerning the Conics unit , and I hope I do it correctly. Well, I went on the net and found some resources to help anyone who doesn't fully understand the unit yet, and to help give people some extra review for the test tomorrow.

REVIEW/TUTORIALS
http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/emat6690/Insunit/conicsunit.html

http://www.scit.wlv.ac.uk/university/scit/maths/calculus/modules/topics/precalc/conics/learn.htm

PRACTICE TESTS/QUIZZES
http://www.absolutevaluepublications.com/studentworkbooks/principlesmath12/PM12%20Conics%20Lesson%207.pdf

http://mathforum.org/mathtools/cell/a2,12.15.4,ALL,ALL/

I hope I did this right, and even more so, I hope it helps whoever see's this and follows the links. I already used some of the practice quizzes to help me review, hope they help you as well. Good night!

Pre-BOBulus

2007-05-13T11:48:00.000-05:00

Wow, I hate my internet. Took me hours just to get this fully functional BOB up, it's a miracle I arrived at the "create post" successfully. Well here goes my BOB.

I think the unit of Conics was a breeze. Extremely easy, nothing truly difficult was presented to us, and the very little homework. But, I do have a rant regarding what Mr. K said concerning people going up to the board. Throughout the course, we've seen the utilization of the smartboard optimize and manifest itself as the base learning mechanic of the class. But we always seem to see the same people go up, while the rest of us just watch. I guess it's good to experience learning through visual means, but kinesthetic learning is a good change of pace to help us fully engulf ourselves in the information being presented. I don't think it's a big deal, however. Many of us are probably more visually-oriented learners now. Well, that was just a rant, all this free time due to this incredibly easy unit got me to thinking. I don't suggest anything though, I'm just sharing my view. Back to the unit, Conics brought back the well known parabola and circle back from last year's precalculus class, and also introduced some new funky sections for us, such as the ellipse and the hyperbola. As long as you know the properties and definitions of each conic section, you'll be fine. Reiterating my previous description, this unit was extremely easy. I hope (and am strongly believing) that everyone will do great on this test.

GOOD LUCK ON THE TEST TOMORROW EVERYONE!!!

BOB

2007-05-12T23:02:00.000-05:00

Personally, I think this is one of the easiest units of the course... The simplicity and ease of having a formula to follow is just great.

It was a very interesting and fun unit for me and I think that, as a class, we can all get good marks on it.. :P

BOBIN` NUMBA 6!

2007-05-12T20:44:00.000-05:00

I would say this unit was really fun. It was like half math and half art class. Putting a bunch of dots on the paper and folding them and not knowing that we made an ellipse and hyperbola! It was pretty amazing. Also Mr. K's "ALMIGHTY SWORD" haha. It was pretty funny. I've learned so much about ellipse and hyperbola, I also learned more things about parabolas and circles. They're all connected in some way or another. Well, goodluck on the pretest and the test everyone! :))

BOB-ing 6

2007-05-11T23:42:00.000-05:00

I really like this unit... That's all I have to say. I grasped the concept pretty much faster than I did with the other units. I'm more focused than ever on Math mainly because I know that I have to strive harder to accomplish my goal in this course. I like this unit too because it's a breath of fresh air. I mean that we've never encountered ellipses and hyperbolas. Now, I've learned something different and interesting. They're easy to manipulate too! The equations are pretty much the same and that's what's going to confuse the minority. Also, those applications seem difficult but not really... They're okay... I think I'm going to do well on the test. I hope! So, good luck to me and to everyone else!

bee oh bee number: Mr. K's favourite number...6

2007-05-11T20:56:00.000-05:00

This unit was quite interesting because we got to see Mr. K's almighty sword in action and see how circles, ellipses, parabolas, and hyperbolas are related to eachother. I found this unit easy in a sense but also a little challenging if I don't know what the information in front of me really is. All I have to do is look at it more carefully then I can determine what is being asked of me. The quiz which I knew about then forgot about that same day caught me by surprise haha...but I think I did well on it. Hopefully we all did. Hopefully I do well on the test because I really like this unit. It's interesting. So to everyone, good luck on the pretest and the test.

ess-see-are-eye-bee-ee

2007-05-11T19:52:00.000-05:00

Today’s class started out with us being divided into separate groups and one panel. We worked on questions that Mr. K. prepared for us on the smartboard because we were supposed to have bus ridership. Before that Mr. K. talked about the gizmo call we are going to have with Eddie’s class. Remember: comment on the gizmo blog post.

Question 1:
For this question we must plant a coordinate plane on the diagram. In this question we placed it in the middle. Since we placed the coordinate plane in the middle our vertex is zero. To find the maximum depth, first, we must find the equation of the parabola. The equation of the parabola is x² = 4p y. This equation is not complete because we do not know the value of p. To find the exact value of p we plugged in a point from our graph. Then once we found p our equation was complete. From that equation we found x when y was at 3m. We found x to be ±√50 or ±5√2. After that we found the measure of the distance from those two points, which was 2√50 or 10√2.

Question 2:
For this question we determined the equation of the parabola by drawing a sketch from what we were given.

Question 3: For this question we determined that the equation we were making was for an ellipse because the definition of an ellipse is - a locus of points that move in such a way that the sum of the distances from a given point, p to a and p to b is the same.

Question 4:
For this question we drew a sketch to helps us find the equation for the parabola and we also substituted values from one of the given points to help us determine p.

Question 5:
To determine the equation for this hyperbola we to into consideration what was given and we also the slope to determine a and b.

This concludes our class and my scribe post. If I have failed to leave any important key points or information please tell me so and I will fix it right away.
Also, our pre-test is Monday morning and our test is Monday Afternoon.
Tuesday, we will start probability.
Don't forget to bee oh bee!
oh my gosh I always forget...haha the next scribe is Timmy...

Today's Slides: May 11

2007-05-11T15:56:00.000-05:00

Don't forget to comment on this post regarding our upcoming gizmo call with Eddie's class."

Here they are ...

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

S-C-R-I-B-E

2007-05-10T20:26:00.000-05:00

Good evening to everyone. Sorry if this post is late, I passed out on the couch while watching the hockey playoffs (Buffalo vs. Ottawa) and just woke up, haha. Anyway, here is today's scribe post.

MORNING CLASS

We started off the morning with word problems.

1.

This problem was solved by yours truly (ahem haha). From the given question, we are given that the foci are (+6,0) and the focal radii is 4 units. Since we know what the focal radii is, we could determine the vertices of the hyperbola by subtracting the focal radii from the foci. Doing those, we should get (+2,0) as our vertices. Thinking about it, the x-value of the vertices are the same as the a value in an equation of a hyperbola. We then get that the a value is 2. We already know the c value of the ellipse equation, so that's enough information to solve for b by using the Pythagorean identity, c²=a²+b². Substituting are values, we then find out that the value of b is the square root of 32, or 4 rt.(2). Now that we have our respective values, we can now write our equation.

In this question, it doesn't matter what form you leave your equation on because it doesn't specify whether you leave your equation in standard equation (the equation above) or in general form (the equation below). Moving on...

2.

This problem should be pretty straightforward as it is like one of the problems we did yesterday/2 days ago.

3.

This problem is a bit different from the ones we did. In this problem we were given the directrix of the parabola (x-2=0 or x=2) and the vertex (-1, 3). From that we can determine that the parabola opens to the left. Also, from the data given, we can also determine the p value, which is 3. Now that we have enough data, we can determine the equation, which is on the image, in red colour.
Note: the equation underlined in blue is wrong because we forgot to consider the vertex.

4.

Now on to the "real" word problem. This problem requires some thought and some manipulation. From the graph given, we can see that we drew a Cartesian plane on the graph so it would make it a bit easier for us. We plotted out several points on the graph like (10,0), which is the distance from the origin/cliff, (0,40), which is the vertex of the graph/height of the cliff and (?,30) which is the point that we're trying to find. From the solution on the image, we can see that we used the point (10,0) to determine the value of p, which is -5/8. Now that we've found p, it's as easy as substituting the values and solving for x. We then find out that x = +5, but we reject -5 because if we throw -5 distance, we're throwing into the cliff. Also Mr. K pointed out that since it's a word problem, we ALWAYS have to put our answers in a sentence.

5.

This problem seems to be straightforward, but requires a bit of thinking, like any other else. We know that the center is at (0,0) as it is given, and a vertex which is (rt.(6), 0). Thinking back, we know that the x-value of the vertex is equal to the a value in the equation of an ellipse. Now that we know a, we can solve for b by putting in 9 for the x value and 5 for the y value. We then find out that b = rt.(2).

We end our morning class here.

AFTERNOON CLASS

We started our afternoon class with a quiz. I'm kinda hesitant on putting up the solutions here because some of us haven't written the quiz. But if you want to see it, check today's slides. After the quiz, we went to our groups and solved a couple of problems.

1.

This question got most of us wondering. But Grey-M figured it out and once he put up the solution, we were all like, "oooohhh I see I see". It seems pretty straightforward.

2.

We didn't really get to finish this problem because the bell rang, beckoning us to go home and have fun!! But we did the first part of the problem, which seemed pretty straightforward.

The next scribe will be Aichelle.

NOTE: THE PRE-TEST IS ON MONDAY MORNING, THE TEST IS ON MONDAY AFTERNOON. WE WERE SUPPOSED TO HAVE THE PRE-TEST TOMORROW BUT WE HAVE BUS RIDERSHIP TOMORROW SO MR. K MOVED IT ON MONDAY MORNING. TOMORROW'S CLASS WILL BE A WORKSHOP.

Gizmo Call to Eddie's Class

2007-05-10T16:32:00.000-05:00

We're planning a gizmo call to Eddie's class on Wednesday next week. In order to avoid any awkward silences let's see if we can make a list of some pre-planned questions the grade 5 students can answer ... just something to get them talking and feeling comfortable.

Why not take a look at their class blogs and see if there is anything you find interesting there about what they are learning. (I liked their comments maps.)

Post your ideas for converstaion starters in the comments to this post.

Photo source: Questions

Today's Slides: May 10

2007-05-10T16:30:00.000-05:00

One HYPER-bola morning...

2007-05-09T16:04:00.000-05:00

One HYPER-bola morning, still worn out from the exhausting activity of origami, we immediately began identifying the similarities and differences of the equations of horizontally-oriented hyperbola and the vertically-oriented hyperbola. We enumerated the similarities first then we moved on to the differences.

After each discussion about the similarities and differences of each equation. We talked about what if the equation is equal to - 1. Well, it's simple... YOU JSUT CAN'T HAVE NEGATIVE 1 ON THE RIGHT SIDE. Therefore...

THEN, we tried a couple of problems... PIECE OF CAKE!!!

The graph looks like this... and the asymptote is determined using:

SECOND PROBLEM...

This is the graph of the hyperbola described above.

This concludes our lesson for today. Gladly, I didn't have to make a scribe post for two classes, considering I have been busy lately... That was easy! Anyway.. the next scribe is JOHN!

Today's Slides and Homework: May 9

2007-05-09T10:24:00.000-05:00

Here they are ...

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

And here are your homework assignments ...

Parabolas, circles and ellipses:

and the answers ...

and the hyperbola exercises ...

and answers ...

Conics Scribe Post

2007-05-08T20:25:00.000-05:00

MORNING CLASS:

We did two questions on ellipses to start things off for the class, here they are:
Now the question didn't ask for a sketch but Mr.K told us to make one anyways. However without making the sketch this question would be real tough to answer anyways so the sketch helps =D. You'll find in a lot of these questions you'll need to make a sketch even though the question itself doesn't state that.

For this question the sketch allows us to find the values necessary to make an equation of the ellipse. Knowing the sum of the focal radii is 6 units we can find the value of a (semi-major axis) because a is half the value of the sum we get that a is 3 units. Now that we've found the value of a we now have to find the value of b (semi-minor axis) because that's apart of the equation of an ellipse. We first must find the value of c in order to apply the Pythagorean Property c² = a² - b² which will allow us to find the value of b. To find c we just turn to the foci provided by the question. The distance between them is 4 units, the value of c is half that which gives us 2 units. Now we apply the Property, 2² = 3² - b², and get b² = 5 so b = √5. Having those values we get the equation written on the slide.

I won't explain the solution to this question, it seems pretty straight forward already from the slide. However there were a few important things that sprung from this question that I will talk about. It was very interesting how we just dove into finding the radius and centre of this circle. But how do we know it's a circle? Why not an ellipse? So here's some important things to remember when doing questions that don't state what kind of Conic it is:

- equations of circles always have the same coefficient value on the terms x² and y²
- equations of ellipses have different coefficient values on the terms x² and y²
- equations of horizontal parabolas have a y² term and a x term
- equations of vertical parabolas have a x² term and a y term

(VERY IMPORTANT REMEMBER!!!)
For the next part of class Mr. K just went over in detail the Focal Radii Property and Pythagorean Property of the ellipse (check slides 3 and 4 for what is potentially going to be dictionary notes!)

Then we picked up our sheets with the big circle on it (got from the beginning of class) and drew a point just outside of the circumference preferable 2 cm. Then drew 25-30 points on the circumference having making the points closest to the outer point jumbled up together. Then just like the other day when we folded the paper to make an ellipse we did the same kind of folding method to make......A HYPERBOLA! =D Then DING DING! Class ends.

AFTERNOON CLASS:

Having done the folding in the morning class, we sketched out the hyperbola we just created by making the folds. Then we drew in the foci points and discovered a few things....- line PF1-line PF2 = line QF1-line QF2 = line RF1-line RF2, therefore, any point drawn on the hyperbola when connected to the two foci produces two lines with a constant distance between them
- labeled A1 and A2 on the slide are the vertices, the distance between the two, line A1A2 is known as the Transverse Axis
- folding the paper so that the foci are on top of each other we see that when we open it up we get a line that's directly perpendicular to the transverse axis, the end points for this line are labeled B1 and B2, this line is called the Conjugate Axis
- half the transverse axis is the semi-transverse axis and that's labeled a
- half the conjugate axis is the semi-conjugate axis and that's labeled b
- drawing a line from the centre of the hyperbola to F1 we find that the value of this line is the same as the value of a line connecting B1 to A1, therefore a² + b² = c²
- drawing dotted lines parallel to the conjugate axis going across A1 and A2, then drawing dotted lines parallel to the transverse axis going across B1 and B2 we see a dotted box
- using the dotted box we draw a dotted diagonal line from the top left corner to the bottom right corner anda dotted diagonal line from the top right corner to the bottom left corner
- these diagonal dotted lines represent the asymtotes of the hyperbola
- slides 5 and 6 show the equations of horizontal and vertical hyperbolas

This was the last thing we did in class, a question on hyperbolas. We never actually got to finish the question, Mr. K finished it off for us. It's pretty much self-explanitory. What's important however is, posibility of a PRE-TEST on FRIDAY and TEST on MONDAY!

oh and next scribe will be........VINCENT!

Today's Slides: May 8

2007-05-08T16:13:00.000-05:00