Wednesday, March 28, 2007

Developing Expert Voices - Invitation to the Blog

As promised, I built a unique blog for your Developing Expert Voices projects. Email me and I will send you an invitation to the new blog. When you publish your projects on the DEV blog tag them with the name of your class (Pre-Cal 40S) and the topics covered by the problems you created.

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

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

Saturday, March 24, 2007


Hey there! Sorry my scribe wasn't up yesterday, but I had to work :(. So here we go...
Morning Class
We started out the morning with conversing about Aichelle's awesome scribe post and why it should be inducted to the hall of fame! We discussed her insightful use of colour and change in font to grab our attention so we realize what was important. We then discussed the way she took apart the questions we had been having trouble with the previous day and how that was an excellent EXPERT quality. Mr. K also took note of the apparent misinterpretation of his explanation for how to solve 4 to the exponent x - 9 to the exponent x and has decided to run us through that explanation again once we get back from our Spring Break.
Next we went over the changes made to our Developing Expert Voices document to which became almost like a chat box the night before because of the sudden number of people editing at once. Some good work was accomplished though and we now have our final rubric, YAY! A good question was brought up by a Jennifer from another class about whether or not outsourcing your project was a good idea or not. Mr. K stated that outsourcing was an interesting idea but by no means meant that you do your part of the work and then leave your partner in New York to do the rest alone. It is a team effort so must be done together. You are still responsible for your project and making sure you use your time to your advantage, so that it gets in on time. A reminder to
all: Don't forget your due dates! They are all clearly marked in the Google Calender Mr. K graciously made up for us on our blog, no excuses!

Finally we started our math for the day. Mr. K asked us as a class what the definition of an inverse was. Craig said that is was the negetive equivalince of a number
. y=f(x) ~ x=f(y) Graeme added that it caused the X and Y values to be reversed or exchanged. Mark then said that it changes the inputs into outputs and referred to Mr. K's analogy of Baby play and parent clean up ----->here for review . Mr. K put it simply as one undoes what the other does.

Mr. K then put up tables of values and asked us to fill them in...unfortunately they were exactly the same tables only bigger so took us no time at all! Haha. He "quickly" drew in the tables he meant to have included there and told us to again fill them in.

Mr. K then showed us what an exponential function was. F(x) to the exponent 2x. For example, He then explained to us that :
Input is the Exponent Output is the Power
Input is the Exponent Output is the Power
Input is the Exponent Output is the Power
Input is the Exponent Output is the Power
Input is the Exponent Output is the Power
Input is the Exponent Output is the Power
Exponential Functions turn exponents into powers. This is considered to be one of the most confusing and difficult units for students, who hate it for the exact same reason teachers love it; there are so many ways to manipulate the questions.

Mr. K now told us the nature of the inverse of an exponential function a.k.a a Logarithm.

Again he explained:
Input is now the Power Output is now the Exponent
Input is now the Power Output is now the Exponent
Input is now the Power Output is now the Exponent
Input is now the Power Output is now the Exponent
Input is now the Power Output is now the Exponent
Input is now the Power Output is now the Exponent
Logarithms turn powers into exponents.

Mr. K then asked someone to graph the an inverse. Craig's hand shot up before he had the chance to actually think about what he was getting himself into and so walked to the board trying to figure it out along the way. He came up with:

There was some disagreement within the class with that answer so the green graph was drawn. It was further explained by Craig and drawn more accuretly in red.
The red line is called F(x)=log2(x). We were then shown that the line between the inversed points on each graph should be perpendicular to the line y=x and that the y axis is the asymptote for the logarithm and the x axis is the asymptote for the exponential function.
Mr. K then explained how to write out a logarithm.

It is read: Log base b of c is a or log of b c is a. We then went over a review of changing the graph. x+2 shifts the graph 2 units to the left, -(x) causes a vertical flip, and (-x) causes a horizontal flip. To end the morning class Mr. K pointed out that the point (0,1) will always be present on the exponential function graphs and that the point (1,0) will always be present on the logarithm graphs.

Afternoon Class
This class started out with the handing back of our transformation tests. This was received with groans of disappointment and sighs of relief. We then moved onto a series of different log questions shown on the slides for March 23. Mr. K then again elaborated that :
A logarithm is an exponent
A logarithm is an exponent
A logarithm is an exponent
A logarithm is an exponent
A logarithm is an exponent
A logarithm is an exponent

Don't forget also that a base of 1 is always equal to 0! He explained that the most common error with these questions was that students did not follow the order of operations (Bedmas~ Brackets exponents division multiplaction addition subtraction) and that we no longer divide we MULTIPLY!
Well that is my scribe post..I'm not sure if the pictures of the slides are going to show up and if not then if someone could explain why not in the comment box so I could fix it that would be awesome!
The next scribe is CRAIG!!!!

Friday, March 23, 2007

Developing Expert Voices Rubric out of beta v.1.0

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

Developing Expert Voices Rubric

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

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

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

Creativity (up to 5% bonus)

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

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

Today's Slides: March 23

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.

Thursday, March 22, 2007

Scribe Postage # 2!

Hello everyone! It is me your scribe for today. I am filling in for Craig due to the lack of his presence in class. The class started off with Mr. K. asking if the podcast was a useful tool to any of us. It is indeed a useful tool to all of us, whether we use it as a review or help with our scribe posts. We learned that on April 17th we are going to have a Skype call with Eddie’s class. After the break, we will be discussing what we can talk to them about.

Next, we talked about the rubric for our assignment. It is due tomorrow at 9:00 am! So, people get busy revising, editing and putting your thoughts on what we need! There have been some changes and additions from a few people already but we still need to finalize it for tonight. Mr. K. also talked about being an expert. He said that being an expert is like being in the centre of a circle and being on the edge and pulling more and more knowledge in. Experts are constantly on the edge bringing in more knowledge.

Next, Mr. K put up some questions on the smart board for us to do as a review. As he stepped out of the class, what had happened was we, Chris, Vincent and I had solved the problems on the board with Richard’s help. Then, Richard took the role of “teacher” and moved us onto the next slide and enlarged the equations for all of us to see. Then, unknowingly, Mr. K. popped his head into the class and said at anytime we could put our answers on the board. Simultaneously, the class burst out into laughter because we were one step ahead of him. After that we clued him in on what was going on and he explained to us that the questions on the board were a bit different from the previous ones.

Also, any number to the exponent zero equals one.
We experimented with flips of graphs on fooplot by changing the equations.
This is what we got as our results. That was pretty much our class and if I have failed to exclude something within this scribe post or if I have made a mistake please tell me and I will fix it as soon as possible. Thanks. Homework is number nineteen and the questions on 20 that we did not do [10, 11, 12].
Oh, and the next scribe is Kasia which means lucky Craig will be the scribe when we get back from the break.

Today's Slides: March 22

Here they are ...

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

Wednesday, March 21, 2007

International Day for the Elimination of Racial Discrimination

Here is the movie we were talking about in class today. It's the first in a five part series. I only found 4 of the 5 parts here.

Update (March 24)
Thanks to Aichelle (and PBS) you can see the entire show here.

X-ponent men 3: The last stand

Hey everybody! I'm MrSiwWy and I'll be your scribe today! I don't have much time to complete my scribe post for today, as I won't be home until much later and I still have to practice for the talent show on Friday! Well, not much time so I'll head onto it.

As we all know, yesterday was the day when we wrote the terrifying identities test, and I bet that test left everyone with anything but a smile on their face. As Mr. K said the previous day, it was obvious that there was some anxiety concerning the formidable identities test. But despite all worries and the incredible tension in the room when we were attacking the paper with our minds, I hope everyone managed to perform adequately on the test. Now on for some actual knowledge that was conveyed our way.

Wednesday Morning:
Now that the identities test was clearly out of our way, it was inevitable that the following day would bring forth a new unit to our growing intellect. This seemingly excruciating unit is of course exponents and logarithms. But I must add, I do applaud Mr. K's method to introduce this unit, which will be explained in the very next paragraph.

This method of course, all begin with Mr. K up at the Smartboard. He waited there until class had essentially began, then showed us the introductory slide. This slide of course, consisting of numbers to help us segway smoothly into the unit. The slide consisted of these numbers:

Then Mr. K told exactly what we were to do, write each of these numbers in different ways. We were told that we must write each of the above numbers in different forms, but each must consist of an exponent. He started the ball rolling by giving examples of such for the first number, 2. The examples he gave were 4 1/2 and (1/2)-1 . These examples fit as 4 to the exponent half equals 2 since if you have an exponent 1/2, the number is first calculated to the power of 1 then the square of that number. In this case, 4 to the exponent 1 is 4, then the square root of 4 is 2. For 1/2 to the exponent -1, negative exponents, as we have learned in the past, mean we must take the reciprocal of the base, which in the case of 1/2 is 2. After he gave us these examples, he gave us time to determine more for each of the number. He said to either come up with four different ways or as many as we can for each. Then he gave us a while to work on them (although it felt like more than a while =p).

Once Mr. K stopped us, we began to convey all of our thoughts onto the Smartboard. We collectively assembled many different methods for writing each of these, and through writing these we noticed some very obvious patterns. Here are the slides of which our answers are integrated upon:

Just some of the possibilities of writing 2 exponentially. From writing these possibilities, we began to uncover a pattern to determine how to write a number in different ways using exponents. This pattern can be seen through the 81/3 which is equivalent to (1/8)-1/3. Using such examples can show that when we write any number to an exponent x, we can also write the reciprocal of that number to the exponent negative x.

From writing these values we further elaborated upon the aforementioned pattern. Then we quickly continued writing all of the possibilities for the next number, 4/9.

At this point, Mr. K asked if there were any ways we could come up with numbers with exponents that do not include the number 1. For exponents which do not contain 1, such as the exponent 2/3, this simply means that we must square both the numerator and denominator (if the base is a fraction) then take the cube root of both. For the exponent -2/3, we simply take the reciprocal of the base then apply the exponent 2/3.

At last, we wrote down some possibilities for the number 1/4. Another pattern emerged, concerning the number 1/4, this pattern was shown by the expressions (1/8)2/3, (1/32)2/5. This pattern seems to always have 2 as a numerator in the exponent, but increases by odd intervals for the denominator. As for the denominator of the base, it increases by a certain exponent, then is divided by 2. This pattern along with the other can help us when trying to write two numbers with the same base, which will be described in a little bit.

After we were done with all of those, and now that we knew there are an infinite number of ways to write any number using exponents, we moved on. But all of this was a great preparation for our real lesson for today. Solving the following equations:

2x = 64
272x-1 = 3
3x = 1/27

He taught us that we must solve these by making the bases equal to each other. If you set them equal to each other, since the bases are equal, they must equal the same number in the end, meaning that the exponents must also be equal. So if you set the bases equal, you can determine an unknown exponent since they must be equivalent. This is what we must know for this unit, as this is how we will perform and carry out logarithmic expressions.
Such as for the equation 2x = 64, we can solve this numerous ways, but as Mr. K said, and as we have learned before, we must set the bases equal to each other. The two most obvious ways to do so are as follows:

The above also states what to do in each step, although there are bound to be more complex problems in the future, leading to more steps. But each of the above show the basic structure for solving these equations; rewrite the equation with equal bases then you can get rid of the bases and set the exponents equal to each other. But remember, such as in the second example, make sure you keep the x when you alter the exponent if the x is in that exponent. Such as in 64(1/6)x, when the 2x was changed to a power to the base of 64, the x must still remain. Don't just change it to 641/6.
As for the other equations, the same mechanism was used for each solution, so just remember that if the bases are the same, then the exponents must also equal each other.
The work for each equation can be seen here.

Check them out if you want some extra reference. And that was that for the morning class, as these equations concluded the class.

Wednesday Afternoon:
In the afternoon class, we didn't learn anything as the afternoon was marked by a workshop concerning racism. In class we just talked about certain events, and Mr. K read out a story of which he was given to conduct the workshop. We began talking about incidents, and certain stories which pertained to the subject, and most of what we talked about in class can probably be found on the podcast. And that's about all I can say for now, as I'm running out of time.

Well that's my scribe everybody! Sorry if it came up late, I've already went back and forth with practicing for talent show and now my parents are angry with me so I have to cut this short. I won't have much time to edit this and even entirely complete it, so I'll be adding more to this post maybe later tonight or tomorrow, sorry for the inconvenience. If there's any mistakes, complaints, or anything whatsoever, just tell me, I still have to edit much of this post. I hope my scribe is useful to anyone that didn't attend class and it's at least sufficient considering the high standards on our blog. See you all tomorrow! OH and one last thing... the scribe for tomorrow will be...


Have a good night everyone! Don't forget to do your homework!

Today's Slides and Homework: March 21

Homework: Exercise 20, omit questions #10, 11, 12

Here they are ...

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

Tuesday, March 20, 2007

Lessons from the geese?

The geese who inhabit the wildlife preserve where we walk each day are back; not many, but a few as the ice begins to melt. I wonder if you see them yet, returning for spring flying along in "V" formation? Do you know what science has discovered as to why they fly that way?

FACT 1 - As each Goose flaps its wings it creates uplift for the birds that follow. By flying in a V formation, the whole flock adds 71 per cent greater flying range than if each bird flew alone.

FACT 2 - When a Goose falls out of formation, it suddenly feels the drag and resistance of flying alone. It quickly moves back into formation to take advantage of the lifting power of the bird immediately in front of it.

FACT 3 - When the lead Goose tires, it rotates back into the formation and another Goose flies to the point position.

FACT 4 - The Geese flying in formation honk to encourage those up front to keep up their speed.

FACT 5 - When a Goose gets sick, wounded or shot down, two Geese drop out of formation and follow it down to help and protect it. They stay with it until it dies or is able to fly again. Then, they launch out with another formation or catch up with the flock.

Are there lessons we can learn from a gaggle of geese? What do you think?


Wow I totally forgot about this =S I hope Mr. K still accepts this as a BOB even though I'm doing it the morning of the test =S Well anyways here we go. This last unit wasn't too tough, more or less it was exactly quite easy. The only problem basically was doing the proofs for the identities. Without practice those things can take quite a long time to figure out. They're not necessarily challenging, more like a longer processes to figure out then most other problems and really the only way to get better at them is to practice, so I hope you guys pracstices! Other then that, I don't really see anything else in the unit that was too complicated. However we must remember to "algebraically massage" the problems. Another problem was, it seemed that people forgot about factoring, and that is a possibility when doing this problems so remember that too guys! Most of you won't even see this post so I apologize. Once again I hope Mr.K forgives me for this one time I forgot and considers this as my BOB

Monday, March 19, 2007


Wow, it's already the end of the unit, there's only 1 more week until spring break, and only about 2 and a half months of school left! I guess time does fly when you're having fun. This unit has been pretty smooth sailing for me, well at least that's what I think. I really find the proving problems difficult though but hopefully that is something I can get through. I enjoyed this unit and I'm looking forward to the next one, whatever it may be. Well it's getting later and I should probably go to bed now. Haha. I'm pretty sure everyone is asleep already so I guess that's my cue. Have a good night guys and sleep tight. =)


Ahhh.. I nearly forgot to BOB. Hahaha. So anyways.. This unit was really awsome. What really surprised me was the different concepts asserted at different times. I thought this unit was basically a review of what we had previously learned in the distant past. For instance.. The left side of an equation has to equal the right side of the equation. That was pretty easy. And then there was a whole lot of different concepts and a long proof.. Oh great... Not fun.. Hahaha. So anyway... This unit was not that hard. There are some trouble with the identities that I can suffice but they are easily submissable within a few different areas of time and allot of practice itself. The only trouble I would of had is the memorization of the identities, but that was solved with us getting an identity sheet. Well at least I wont have to dance again.. Hahaha.. But dancing is fun anyways.. hahaha. What am I saying.. Oh yeah.. Well as per always Everyone Study Hard. Cause I am. hahaha And Have a GREAT DAY TOMORROW.. AND Excellent Luck on the test. Hahaha. I always wanted to blog this... Hahahaha.


Trigonometric Identities, what a hard unit to grasp. At first I didn't understand a thing. That was because I was absent on the day we started working on it. I wasn't present in class because of an extra-curricular thing happening. I didn't do most of the homework excericeises, but I wanted to catch up so I started doing them on a weekend. Honestly, I'm not confident about anything. I just get by when doing problems such as proving one side to the other. The identities are hard to rememeber, so I'm really happy that we're getting a sheet that shows all the identities. Well, I hope that everyone studies hard tonight. Good Luck!


Talladega Nights: The Ballad of Ricky BOBby

Another unit done! Wow, classes fly by so fast it's not even funny. Anyway I think this unit is somewhat complex, in the sense that you really have to look at what you're doing. One lesson I didn't really like in this unit is the proving section. Sure, it could be easy sometimes, but the proof that we did in the pre-test was kinda difficult. Anyway I like the way Mr. K makes the proof seem easy, haha. I dunno, maybe I'm thinking too hard in the problems, maybe that's why I'm having difficulties in proofs and whatnot. Right now my confidence is way down after what happened during the last two tests, so I really need to get a high/good mark in this test to bring my confidence back up again. If I find the test difficult tomorrow, I guess I just have to do it in the best of my talents.

Good luck to you all.

Bob # 2

Hi once again! Well this unit was really interesting. I found it to be one of the best units so far. The hardest part was the pre-test today because of the double angle identities. I find these questions the most challenging. The rest of the unit was pretty easy in terms of understanding and was fun. Overall I enjoyed this unit and look forward to the next one. Good luck to everyone on tomorrow's test! Bye.

BOB !!!

Hello again, back for another BOB. It seems just like yesterday since I did my other BOB post. Well,trigonometric identities, what a unit. This unit was easy at first considering the first couple days of class was just simple identities like switching tan into Sin/Cos. Then came the harder identities and the identities Sec,Csc, and Cot came into play. Then the sine dance, with sum and difference identities, and then double angle identities. That is when it became hard especially for me, and as I was asking other people in the class, they had the same answer as me. All in all I found the unit to be very tedious, because you had to memorize some of the identities, and have to check over your work simultaneously. I would like to say good luck and study hard, and especially practise those identities. GOOD LUCK !

Dino Petrelli


Wowww , Was this unit an interesting one,
Not one of my favourites but it was ok. Hey Sam you never did show me the sine dance, so i don't know it yet, you'll have to show me later. The pre-test was hard today during 2nd class so tonight I'm locking myself in my room till I get these identities down pat. Im sure we've all missed a few classes due to illness but boy was these first days the wrong ones to be sick especially at the beginning of our new unit, Mr.K to be honest I was sooo lost when I came back to class I prayed you didn't ask to put my answer on the smartboard since you made your new rule, about different people having to go up to the board. Well I did the exercises and though some were tricky, I feel a better about the test tomorrow. The pre-test was challenging but it helped a lot, see all of you guys in class tomorrow and come prepared.. oh yea sorry my bob is up the night before the test, I've had problems with the net.

Tito BOB

Omaesan! Man I wish I remembered to do this in advance to the test. The unit Identities sure was easy at the beginning wasn't it? I mean changing tan in terms of sin and cos cmon that was easy. Then it grew and grew into equations where its all a mess. But you'd have to think outside the box or look at the identities sheet to know what steps to take. Then there was the dancing class. Boy was that ever fun. Overall what a great unit. I hope everyone including me does their best on the test. Arigato gozaimasu!

With the words of the Red Jumpsuits and their song Cat and Mouse "I said I'd never leave you'll never change I'm not satisfied with where I'm at in life" aim high in life guys. But don't aim so high that even you can't reach.

Jojo Rock's Scribe post v2

Hey, can I have another moment of your time guys? It's another scribe post by your friendly and always supportive classmate Jojo! Man I feel so awkward just typing that. Anyways once again, I'm going to break down today's classes. Thank you Bert for choosing me as scribe. Giving me such an easy day (NOOOOOT). Even I struggled today and this is supposed to be my unit! I felt so confident at the beginning and as the unit went on I was blew away. Thank Jebus we don't need to memorize all those identities. Wouldn't that be a pain in the behind eh? Anyways....

In today's morning class we did some review work. Really wasn't review to me, some reason I don't remember seeing half of those questions before.

1-sec^2x is identical to..

a) -tan^2x b)tan^2x c)cot^2x d)csc^2 e)cos^2x

What my good friend John did for this question was write down the basic identity cos^2x+sin^2x=1. From there he divided everything by cos^2x because it would give 1/cos^2x on the right side which is equal to sec^2x. But also you end up with

1 + tan x = sec^2x

Simplifying this you get -tan^x = 1-sec^2x and your final answer of a!

The slides posted up by Mr. K shows a lot of what happened next. Like when given cos x = -1/3 and sin x < 0, we can find the value of sin x by drawing out out unit circle and by using the Pythagorean theorem we can find the missing side therefore just by looking at it we can easily the value of sin x. Thank you Sam for the wonderful work done in this question.

Everything is straight forward after that. We were given more questions which you can see in the slide show. Sorry guys no funny anime pictures or displays today. Maybe another time. Anyways I forgot to BOB, and I need to study for the test tomorrow and for the test in my history class... Ohh yeah SCRIBE TOMORROW is err let me check the list.. Since its an easy scribe tomorrow my very good friend MrSiwWy is who I will choose. Peow.

Today's Slides and Homework: March 19

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.

BOB's your uncle...

It's that time again folks, time to sit down at your computer for a couple minutes to reflect on the previous and increase your anxiety for the upcoming test. The Identities unit is probably the toughest one yet, based on the class' struggles with it. I myself have had some problems with the questions involving different thinking (eg. basics learned in grade 9 or 10). The use of the SMARTBoard hs somewhat increased our learning of the concpet because everyone has a chance to solve it, however sometimes the rest of the class needs a little more time to solve it on their own. Otherwise the time spent in class has been great. The competitions add a sense of fun, and excitement, as well as some tension between the usual competitors. As usual, GOOD LUCK to everyone on the IDENTITIES test. PUSH THAT ROCK!!!

BOBby Burnquist

Hey there again. Time for another Bob, this time for the identities test. To be completely honest I am completely out of control freaking out for this test. I am having difficulty figuring out which identities I should use in what questions so it takes me a long time because it is a major trial and error thing. I also can always get to a certain point in a question and then freeze up because I can not see what the next step is. I'm hoping that if I take a few breaths of fresh air and calm down....I will be able to suck in all the smarts of the class! MUHAHHAHA! Seriously though, this is the first test this semestre that I really feel is a brick wall, not because I don't understand the concept, but because I have a problem applying it properly. So I wish everyone else good luck on this test (and pre-test) and think hard so I can catch some of those brainwaves. *winkwink knudgeknudge* c ya this afternoon.

Sunday, March 18, 2007

Blogging On BOBbing

Well, this thid unit about trigonometric identities wasn't that difficult for me. I think that doing my homework every night really helped me a lot in this unit. It helped me noticed some patterns that made me understand when to use different identities at different times. I begin to develop a feel for every identity now.I think thats all i need to say for this unit. Study hard and good luck everyone for our test and pretest.


this unit of identities was a little hard for me because due of thinkin of other possible that it can be in sine, cosine and tan etc. the other problem solving was some eazy due to our sine dance that Mr. K and all class did standing up and dance to it to understand more better and help us in those small areas in the solving process

Overall, the unit went faster than expected but i have do more practice and doing the homeworks all over again to better in some areas to improve but i have give my luck on the pre-test and the big test on tuesday, good luck to everyone on it and let the spring time come faster (needed badly hahaha!!!)


Hello all, this unit has been easy and deadly hard at times. I have found most identities in this unit fairly easy to solve... spare a few. One thing that seems to get me is when the identities are simplified as far as they can and they are still long. Just end up going around in algebraic circles to come to the same conclusion. So I am feelin' fairly confident for the upcoming pretest and test. Though I am not looking forward to the Flickr assignment. Seems brutally hard to find something around us that has so many mathematical concepts pertaining to what we just learned. But hey, we have no say in this rubric so we'll just have to take it as-is.

The BOBinator

Hey everybody! I hope Mr. K doesn't consider this a late bob, but this was kinda the only time I could do it, seeing as I've been pretty busy over the weekend. Thank god I remembered to blog or else I would've lost one whole mark!!! Well, enough about that...on with the bob...
So we're now done our third unit, the unit of
identities. I think this unit began quite quickly, and lots of information was just thrown at us (especially for me since I wasn't there for the first class of Identities). But as the unit progressed, I think we kind of moderated our learning pace and things began to become more clear and visible in my mind. Mr. K was right, and throughout my bob I'll probably stress it repeatedly, practice is the only way to get good at identities. Homework in this unit is especially beneficial to understanding how to manipulate identities and mathematically "massage" them accordingly. If you payed attention and continued with your homework regularly, I don't think this unit would be particularly difficult. Don't forget, practice is the only way!!! So, overall, this unit went by extremely quickly, but for the amount of material we learned I think we went at well-regulated pace. In essence this unit wasn't too difficult, particularly if you kept up with your homework. There isn't much more to say, so I'll end this bob with a list of the common identities you should know for the test. They are as follows:
  • sin2θ + cos2θ = 1
    (note: you can derive other equations by dividing every term by either sin2θ or by cos2θ, which will give:
    tan2θ + 1 = sec2θ and 1 + cot2θ = csc2θ)
  • tanθ = sinθ / cosθ
  • cscθ = 1/sinθ
    secθ = 1/cosθ
    cotθ = 1/tanθ or cosθ/sinθ
  • remember the sine dance :
    sin(α+β) = sinαcosβ + cosαsinβ (change sign for α-β)
    cos(α+β) = cosαcosβ - sinαsinβ (change sign for α-β)
  • don't forget to watch for a difference of squares!


The end of a unit has come again.
One of the significant things I need to point out in this unit was I really really needed to practice.
YOU CAN'T MEMORIZE THE SOLUTIONS, but just derive them. I think another downfall of mine is when you try to remember all the solutions in a short amount of time and then you mix them up when your put under pressure. Ha ha yes, I shall be a prime example of that.

The sine dance, I admit that the dance doesn't really help (sorry for all your effort Mr. K) but the rhythm has definitely stuck in my head.

Am I ready for this test? Well, just a little more practice and it might be all right.

Good luck to all of you....practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice practice
that makes it perfect....

Until the next BOB.


This unit on Identities was quite interesting. I find that I favour these types of problems over any other problems, especially word problems. I understand that there are no exact guidelines as to do what next in any given problem, but that doesn't stop me from solving it.

Not knowing what to do next is quite the mystery at times and I find that amusing. The more you struggle to find the answer, the greater you feel when you solve it.

Overall, this unit was quick and simple. I'm not sure if I have any problems or had any problems over this unit. I'm guessing I might run into some eventually, so the best I can do is try to study. I will admit that the Sine Dance helped me remember the Sum and Differences but when I'm trying to recall it, I don't imagine the dance, I retrace its rhythm.

Good luck to you all on the test and pretest!

BEE OH BEE three.

hello hello again mr. BOB! well this unit was quite fun and challenging. The sine dance...haha...due to the lack of my dancing skills I got confused hahaha...but anyways I think I could remember those equations better by looking at them than doing the sine dance. Identities...they are pretty clever. Yup. I found this unit okay. It wasn't that difficult. Although, it does get sort of confusing when proving an identity is true because there are different ways to solve them. That is probably the most challenging part. Hopefully we all do well on the test. To everyone good luck!

Saturday, March 17, 2007

Flickr Assignment Rubric v1.0

Flickr Assignment Rubric
It is paramount that the picture be in tune with the purpose of the assignment. It should show, first of all, the student's understanding of how the photo is related to mathematics. The hot spots are important too, because that's essentially your way of teaching other people. Creativity is a factor, because keeping one's interest in the photo contributes to the learning process. Finally, the picture quality should be kept in mind too. If we can't see the picture, it's going to be hard achieving all the other requirements.


The picture must be tagged properly with the course tag and assignment tag. If tags are misspelled or no tags are present the photo cannot be graded and will receive a grade of ZERO. Not tagging your photo properly and accurately is analogous to not handing in your work or not putting your name on it.

Mathematical Content (50%) Hot Spots (35%) Photograph (15%)
Level 4
Packed with mathematical concepts/facts. (Minimum 7 concepts/facts.) All hot spots accessible; i.e. "smaller" hot spots are "on top" of larger ones, they do not obscure each other. All hot spots are actually labels and relate to parts of the photo (not on blank space with filled in notes). One or more hot spots include a link to a relevant supporting resource on the internet. Minimum 7 hot spots. In focus or appropriately focused for effect. The subject of the picture occurs "naturally," it is not a contrived shot. Really makes the viewer "see" math in a place they hadn't realized it existed. (Example: trigonometry)
Level 3
Significant number of concepts/facts included. (Minimum 5 concepts/facts.) All hot spots accessible. Most hot spots are actually labels and relate to parts of the photo. Not more than one hot spot on blank space. One or more hot spots may include a link to a relevant supporting resource on the internet. Minimum 5 hot spots. In focus or appropriately focused for effect. The subject of the photo has been "set up" or contrived yet still illustrates math found in "the real world." (Example: derivative)
Level 2
Some effort to include content evident. (Minimum 3 concepts/facts.) Most hot spots accessible. Most hot spots are actually labels and relate to parts of the photo. More than one hot spot is on "blank" space. May or may not include links to relevant supporting resource on the internet. Minimum 3 hot spots. In focus or appropriately focused for effect. Although it is a "real world" picture, objects have been used to "draw" the math. An obviously contrived shot. (Example: trigonometry)
Level 1
Very scarce content related to assignment. Less than three hot spots are visible or have information related to the theme of the assignment. It is evident that little effort went into finding and shooting a picture that reflects the theme of the assignment.
Level 0
Content unrelated to theme of assignment. No hot spots or mostly unrelated to the theme of the assignment. Out of focus and/or otherwise difficult to look at.

Creativity (up to 5% bonus)

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

  • unique and creative way of looking at the world, not something you'd usually think of;
  • original and expressive;
  • imaginative;
  • fresh and unusual;
  • a truly original approach.


I almost forgot to blog. Time is passing by so fast. It's crazy. This unit I would say is really difficult. I need more practice. I didn't even get to do the quiz. Hopefully I can do it on Monday. The thing that makes it very difficult is that there is really no right answer, well I mean there are different kinds of ways to get the answer and that's what makes it hard. Your not sure if you are doing the right thing and you wouldn't really know if you've got the right answer. OH OH OH ... I really enjoyed the SINE DANCE. Yea, like Mr. K said practice practice practice is all you need to get use to identities. Well then, I should keep going at it then ... have a good weekend!



Time is flying and here I am posting another BOB for another test. This unit I've had difficulty with. I found myself struggling a lot during the unit. At first it was hard for me to recognize what equals what. Things like how sin2θ + cos2θ = 1. Now I've managed to recognize them a lot easier. Proving is something I really suck at, too. However, practice makes perfect and the exercises are helping with the things we do in class but I still struggle now and then with things. But hopefully by this weekend and by Monday evening I'll have it down packed and be ready for the test on Tuesday. Yay! Good luck everyone, hopefully we all pass with flying colours. (:

Friday, March 16, 2007


Hi everyone! Our unit on Trigonometric Identities has come to an end. I really enjoyed this unit. We learned the different identities of trigonometry, especially the wicked awesome cool Sine Dance! XD

We also learned that we don't have to memorize all those Trig ID's. Mr. K said that we just need to memorize a few, such as sin^2(θ) + cos^2(θ) = 1. We can derive the other identities from them.

Mr. K said, "The only way to get good as this, is to do more of this..." For me, its a very good thing if you keep on practicing these problems. For some reason, the ID's get stuck in your head if you keep practicing and practicing.

I hope everyone will do well on the next test. NO PROCRASTINATING! XD


It's a bird, it's a plane, no it's Superman! No.... it's Bertman. Hey folks, I have the honours of being your scribe again for today. Today's class was quite short due to the quiz we had. It took up a little more than half the class so we still had enough time to correct the quizzes. None of you probably noticed but I was doing the sine dance in my head when I was stumped on a question. Too bad I can't talk much about the quiz because a couple of students missed it and Mr. Kuropatwa didn't post any of the slides.
Well anyways, Mr. Kuropatwa also mentioned that there would be a new math curriculum. There would be a Trades Mathematics, which is required for carpentry, plumbing, etc, Mathematics for the Sciences, which is similar to Pre-Cal, and Fundamentals of Mathematics, all coming in the near future.
Soon after, Mr. K showed us his very own webpage that he made for a couple of semesters now. It gives you a review of the all the units of the course. He said he will link to it on our blog and I think it'll be very useful for studying.
This has almost brought us to the end of the class but before that, we got into groups and had a little competition to see who could solve multiple choice identity questions. Right when the answers were put up the bell rang and class was over.

A reminder that the pre-test is on Monday I believe and for the students who missed today's quiz must make it up Monday at lunch. The test is on Tuesday and Wednesday is the beginning of a new unit. DON'T FORGET TO DO YOUR BOBS. HAVE A GOOD WEEKEND GUYS!

P.S. The next scribe will be Jojo stones! <-------- it was picked out of a hat

Today's Slides: March 16

Today's slides will not be published until Monday when the folks that missed the quiz have made it up. People that missed the quiz will make it up at lunch hour on Monday.

Until then, for those of you looking for slides, here's something to think about ...

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.

Sponge BOB

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sin(α - β) = (sin α )( cos β ) - ( cos α )( sin β )

cos(α + β) = (cos α )( cos β ) - ( sin α )( sin β )
sin(α + β) = (sin α )( cos β ) + ( cos α )( sin β )

cos(α -β) = (cos α )( cos β ) + ( sin α )( sin β )

SIN and TAN functions are ODD and COS functions are even.

sin(-θ) = - sin (θ)
cos(-θ) = cosθ
tan(-θ) = - tan (θ)

Proving the Identities will be one of the challenges for me. It is confusing because of the long and crazy solutions for.

Hopefully, the paper is long enough to put the identity proving part of the test... Hahaha...

Image Hosting by
The early bird catches the worm... So I decided to do my BOB while I am still unable to sleep... So this unit will be a challenge for me, partly because I wasn't in class for 3 1/2 lessons. But I kinda understand
most of the things in it. There was Eddie and his very inspiring message to us from Georgia. The SINE dance is one of the main highlights of this unit. Well, there's Pi Day, where we ate at least 12 different kinds of pie. I have had enough pie for the whole year! Here are something's I learned:

Thursday, March 15, 2007

BOB-ing 3

Honestly, I find this unit very difficult. I don't know how I will pass the next test considering, I might have failed the last two! Seriously, I get the concept and the overall jist of it but when it comes to like problems and proving, I can't seem to put everything together. It is so east as we discuss it in class but my mind seems to let go a lot of things after. I just hope I'll be able to learn from my mistakes. I know there's another test on tuesday and I can't seem to relax for it nor at least, be prepared for it. Questions are unexpected. So I'm going to have to expect that! I'm not doing good in this course, at least not as good as I want to. This unit has been easy in the beginning and the part where we simplify a complicated question is where i seem to struggle. I don't know why but I guess I panick too much. This is my early BOB because I want to get this out of the way with all the projects, homework, and work that I will have during the weekend. Good luck on the test guys!

New Cycle... Done Unit... Proof???

Hello Everyone. I'm the scribe tonight. (Sorry It's So late...)

Well today was a very interesting day.

The Morning Class =)
AKA. The Land of Proofs.

At first we talked about the Developing Expert Voices Rubric. The rubric in fact is a representation of our goals and beliefs on what should be done in the project. This proving that if we work the rubric correctly… We could easily get a higher degree of a mark. Well that’s what I think anyways… Hahaha

Afterwards we were asked to solve the question;
Hahaha.. Graeme, stepped up to the plate and solved it. Afterwards we all asked for an explanation.. hahaha… It’s so cool and funny when we do that…

Well anyways… Afterwards Mr. K directly showed us the AWESOME proof of the sin and cosine identities. Wow… It’s SO INTERESTING!!!!!!(very sarcastic…)

The most interesting part about it is how it incorporates the sine and cosine function with the unit circle. The most interesting thing about it (well for me at least) is how it uses functions that we have learned in past grades like the distance formula (Grade 10) to utilise the proof to the best extent.

You know.. I think that these are most likely going into our dictionary…

AKA. In The End...

Well we spent the afternoon... With some shocking events… Unfolded with a truthful and insane amount of work related activities…

To start off Mr. K gives us another Question to solve…

To explain this in thoroughly… the problem required is more of an inverse of what we learned. Instead of utilizing the concept of solving the more complex equation, we inverse and solve the simpler equation. Thus attributing the goals and responsibilities to the sine and cosine difference identities. After creating another attribute to simply the equation. We multiply the equation with the attribute simply and prove that one side of the equation is equivalent to the other side of the equation.

Afterwards Mr. K gave us the question
To solve this we had to realise that the question was actually equivilant to this (Well Danny realized it)

Afterwards (well before actually) we solved the equation and came up with this answer.
Afterwards we did this with cosine which lead to a multitude of answers. This stating that we can use cos(2θ) to solve a multitude of questions.

Note: Mr. K is picking who’s going to the smart board to write answers now… So be prepared and warned…

Afterwards we did this question which was a review of the previous question at the beginning of the afternoon class.

Surprisingly enough… With this we finished the unit on Identities… We then did some practice questions and…

Quiz Tomorrow..
Pre-Test Monday...
New Unit Wednesday…
Flickr Assignment #1 due after Spring Break..

Homework is Exercise the NEXT
Be sure to get your BOBS up… Again..

And… The Next Scirbe is… BERTMAN!!!

Today's Slides: March 15

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.

Wednesday, March 14, 2007

Pi it's history, it's present, it's the future, it's in my belly!

Pie was the yearning in our stomachs as we all walked into class pondering what kind of pie the others have brought.

For my blog I will give a couple of facts about pi. I was going to discribe the assignment, but thankfully Mr. K was 3.14 steps ahead of me. (ha ha)
->This is my graph about about how good all the pies were this morning. As you can see by the data they were all CRAZY GOOD PIEs (x-axis) and as a result TASTE BUDS WERE OUT OF THIS WORLD (y-axis). In other words I'm just trying to say that today was great. Even though I didn't taste all the pies, I could tell by all the groaning that everyone was satisfied! The red is a power curve and as it's value goes up, the size of my belly also goes up!!! hehe

First of all I would like to say HAPPY BIRTHDAY TO ALBERT EINSTEIN!!

Pi Day and Pi Approximation Day are two unofficial holidays. They are held to celebrate Pi (π) a mathematical constant. Pi day is celebrated on March 14 (3.14) (Sometimes it is celebrated on March 14 at 1:59:26 p.m. actually known as the pi minute because pi is rounded out to seven decimal places.) Pi Approximation Day may be observed on any of several dates, most often July 22 (22/7). I actually tried to read about the result that the rational number 22⁄7 is greater than π, but I sort have a few holes I need to fill. (Hey Mr. K, if your reading this could you explain that?)

As everyone was chomping on pie, Mr. K was explaining our assignments.

From what I understand is that for the photo assignment we need to take a picture of something that occurs NATURALLY in nature. (Not something we made up.) This picture needs to be about trigonometry.

Developing expert voices, I believe is an assignment that we have to be true to ourselves to accomplish. We need to realize our strengths and set the bar up higher and jump higher to get over that bar; we need to challenge ourselves. We need to push ourselves out of our comfort zones so we can really learn and discover what math is means to us. (I guess)

Other dates for us math people to celebrate!

March 14: A common approximation for Pi (3.14)
February 27: The Earth is estimated to have traveled 1 radian of its orbit since the New Year
July 22: 22/7 in the majority of date formats, an ancient approximation of pi
November 10: The 314th day of the year (in leap years, November 9)
December 21, 1:13 p.m.: The 355th day of the year (in leap years, December 20), celebrated at 1:13 for the Chinese approximation 355/113

That is the end of my first SCRIBE ever!!! I hope I was up to our class standards.

Developing Expert Voices

The Assignment
Think back on all the things you have learned so far this semester and create (not copy) four problems that are representative of what you have learned. Provide annotated solutions to the problems; they should be annotated well enough for an interested learner to understand and learn from you. Your problems should demonstrate the upper limit of your understanding of the concepts. (I expect more complex problems from a student with a sophisticated understanding than from a student with just a basic grasp of concepts.) You must also include a brief summary reflection (250 words max) on this process and also a comment on what you have learned so far.

You will choose your own due date based on your personal schedule and working habits. The absolute final deadline is May 31, 2007. You shouldn't really choose this date. On the sidebar of the blog is our class Google Calendar. You will choose your deadline and we will add it to the calendar in class. Once the deadline is chosen it is final. You may make it earlier but not later.

Your work must be published as an online presentation. You may do so in any format that you wish using any digital tool(s) that you wish. It may be as simple as an extended scribe post, it may be a video uploaded to YouTube or Google Video, it may be a SlideShare or BubbleShare presentation or even a podcast. The sky is the limit with this. You can find a list of free online tools you can use here (a wiki put together by Mr. Harbeck and myself specifically for this purpose). Feel free to mix and match the tools to create something original if you like.

So, when you are done your presentation should contain:
(a) 4 problems you created. Concepts included should span the content of at least one full unit. The idea is for this to be a mathematical sampler of your expertise in mathematics.

(b) Each problem must include a solution with a detailed annotation. The annotation should be written so that an interested learner can learn from you. This is where you take on the role of teacher.

(c) At the end write a brief reflection that includes comments on:

• Why did you choose the concepts you did to create your problem set?
• How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
• Did you learn anything from this assignment? Was it educationally valuable to you? (Be honest with this. If you got nothing out of this assignment then say that, but be specific about what you didn't like and offer a suggestion to improve it in the future.)

Experts always look back at where they have been to improve in the future.

(d) Your presentation must be published online in any format of your choosing on the Developing Expert Voices blog. url: tba.
Experts are recognized not just for what they know but for how they demonstrate their expertise in a public forum.

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

Novice: A person who is new to the circumstances, work, etc., in which he or she is placed.

Apprentice: To work for an expert to learn a skill or trade.

Journeyperson: Any experienced, competent but routine worker or performer.

Expert: Possessing special skill or knowledge; trained by practice; skillful and skilled.