So Long ...

We had our graduation exercises today. A gentle push into the world for all of you. I hope you're leaving with the keys to your future in your hand.

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

Just to have a laugh or learn some math,

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

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

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

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

Student Voices Episode 4: Justice, Lawrence, and Richard

First an update on this podcast: While we have received few comments on this or any of our class blogs the number of times the audio files have been downloaded is remarkable ...

Episode 1: Jessie 2440 downloads

Episode 2: Tim_MATH_y 1766 downloads

Episode 3: Chris, Craig, Graeme 1367 downloads

Thanks to all our listeners. We might get one more published during this school year but this may be the last until September. In any case feel free to let us know your thoughts about what you heard; every comment is appreciated.

In this episode of Student Voices Justice, Lawrence, and Richard talk about how they put together their Developing Expert Voices project and what they learned in the process: how they they best learn math, how it can best be taught, and many other incidental things like team work and organizational skills.

They have titled their project with one of my favourite reminders to all my students: Mathematics is the Science of Patterns. If you watch any of the video content they created you'll hear several "in jokes", listen for them. Without any further ado, here is the podcast. A copy of the poster they made for their work is below.


(Download File 12.2Mb, 25 min. 30 sec.)

Photo Credit: Shadow singer by flickr user EugeniusD80

Today's Slides: June 4

Here they are ...

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Introduction to Anti-Derivatives (sounds like some sort of medicine)

So, on the previous class, we were introduced to anti-derivatives..


At the beginning of the class, we were asked to find the derivatives of the above functions. Needless to say, we found it difficult... NOT. It's 2x for all functions. And then we were given the derivative, f ' (x) = x and were asked to find the parent function. We were quite stumped at first, but then managed to figure it out. We had to go back to a previous lesson since we were asked whether if given a constant and a function and if we had to find the derivative of the function, does the constant play a role? No, it doesn't. Anyway, we were asked to find the parent function of the derivative f ' (x) = x. If x is the derivative, then obviously the parent function is x². But the derivative of x² is 2x and the derivative we want is x. So we figured, we have to multiply 2x by 1/2 to get x. From that, we got the parent function, which is 1/2x². Mr. K then asked us, what about if I give you the derivative x²? What would be its parent function? We then thought about it. If x² is the derivative, obviously the parent function is x³. But the derivative of that function will give us 3x², which we don't want since we're given the derivative x². So we thought multiplying 3x² by 1/3 would give us x². We reckon that the parent function is 1/3x³. From that we came up with a rule for all power functions, which is:

f ' (x) = xⁿ -------> f (x) = xⁿ⁺¹/n+1 + C, where C is the constant. I'll explain later.


We then made anti-derivative rules for almost all derivative rules we remember. Mr. K said that the anti-derivative rules for the product and quotient rule are much more complicated and we won't be taking it until First Year University Calculus, so yeah.


Now this is where I explain the C part in the rule:

f ' (x) = xⁿ -------> f (x) = xⁿ⁺¹/n+1 + C, where C is the constant

We can't really find C not unless we're given a point in the graph. C is basically the y-intercept, but if we're just given the derivative and asked to solve for the parent function, all we can do is find the parent function and then + C, not unless we're given a point in the graph.

Then we were just given a practice problem, which was pretty straightforward.






The next scribe is etimz, or Ethan.

Today's Slides: May 23

Here they are ...

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BOB

Well, another test. This unit hasn't been so bad for me, I understand most of it. Hopefully I do well in the test. I do have a couple of problems with differentiating implicitly but it's nothing practice cannot solve. Otherwise, I'm good to go.

Good luck.

BOBBOBBOB!

What can I say? Well for one, this unit was simple the second time around =). I really think that I'm going to do well on this next test and yeah, hopefully I don't stumble on something that I haven't yet seen or tried to do. As always, the solution is practice! Hmm, I think the best place to start review would be to go through the past slides, and then see if I have any muddiest points.

This bob was short and straight to the point. I hope everyone remembers to bob and and and! Good luck on the test Wednesday I believe!