Saturday, March 24, 2007

Scribelicious...

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 http://pc40sw07.blogspot.com/2007/02/lost-in-translationand-stretching.html . 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!!!!


















3 comments:

aichelle s. said...

excellent scribe post Kasia! I like the detail you put into the scribe post...everything was explained well and I believe you did a great job drilling what a logarithm was =) I had a hard time viewing the pictures...some of them had x's on them I'm wondering...if it was only me or if others had the same problem...and maybe the problem is you just need to upload them again ? I don't know...haha but good post!

Mr. Kuropatwa said...

Great Scribe Post Kasia! Reading it was like being there. ;-)

The reason the pics of the slides aren't coming through is this:

You used the link to the webpage where the slides can be viewed. I think what you wanted to do was display individual slides. To do that you have view the slide show and then do a "screen capture" on your computer and get the image into Paint (or some other program like that). Then you can upload it to Blogger from your desktop.

If that doesn't make sense ask one of the previous scribes how they've done it. On my mac I just hit a certain key combination and can copy any part of the screen I like. ;-)

Cheers!

RolandOD said...

Kasia, I am not in the classroom this year, but I remember teaching this to my students, and I greatly appreciate your transparent repetition of:
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.

I can hear Mr. K saying it over and over and over... and I haven’t even heard the podcast. I remember repeating myself just like that and then doing the same thing with the log function. Did his repetition work? Do you really understand that A logarithm is an exponent…? It’s so important, and more importantly it will make me feel better about repeating myself in class over and over again for the last fifteen years. So, Kaisa, I await your (or some other student’s) response to my question, and please remember that most math teachers need some positive reinforcement from time to time!