For this topic we are going to be flipping the classroom, the topic is related rates. I would like you to take a look at the two videos that I have attached from Khan Academy on related rates. I would like you to comment on both listing for me what makes sense and what items that are hard for you to understand.
Also you and a partner from the class will be making a video to use to explain to the class how related rates work. I will be giving you the assignment soon.
Ladder problem
Cone Problem
Ladder Problem:
ReplyDeleteThings I understood:
The triangle/ Pythagorean theorem and how it was used.
Implicit differentiation.
I understood that dh/dt was how fast the ladder was sliding down the wall.
I understand why dh/dt was negative.
Things I didn't understand:
How he took the derivative. It was confusing. I understood the majority of this problem though.
Cone Problem:
Things I understood:
I understood how he got the volume.
I understood the algebra used after he got the derivative.
Things I didn't understand:
The way he took the derivative. I don't understand why he used h(t). I also didn't like that he used h(t).
I am not sure what was solved.
I understood the ladder problem real well. Having you explain the derivative to us in class is most likely the reason I could grasp what he was doing. The use of the Pythagorean Theorem made sense along with the rate being negative. On the cone problem, I started off understanding some of the things he was saying: Surface Area of the water= base, the ratio between the cone and water, and what we were having to do. However, when he started off writing the derivative, he lost me. I understood his verbal instructions but as far as seeing it written, I would start confusing myself. Another thing I didn't understand is why the diameter of the water is also h. His cone drawing with the water spout was surprisingly good!
ReplyDeleteLadder Problem: Things I understand: Pythagorean Theorem; how dh/dt was negative; how to take the derivative Things i didn't understand: Trouble understanding Implicit Differentiation; how fast the ladder was going.
ReplyDeleteCone: Understand: Understood how to find derivative: some of how to use the derivative(class helped a lot). Didn't Understand: got lost somewhere after finding the derivative.
Ladder Problem:
ReplyDeleteThings I understood:
The concepts
The equations
The theorems
Implicit differentiation
The problem
The solution
Things I didn't understand:
eh
Cone problem:
Things I understand:
The basic equations
The relations of radius to height
The derivatives
The rates
The problem
The solution
Things I didn't understand:
Why Khan felt it was necessary to show that h was a function of t in the final derivatives to further complicate the problem. I didn't think that it was necessary.
Respectfully submitted,
Peter Hellwarth
R E S P E C T, find out what it means to me.
ReplyDeleteI understood both problems going through them, but I feel like if you told me to do the cone problem by myself I wouldn't be able to do it without help. I guess the hard part is remembering how he related the volume to height using the cone formed by the water. Brain fried
Ladder:
ReplyDeleteI understood the idea, where to start, and the goal. The only thing I had trouble with was the idea introduction of Implicit differentiation.
Cone:
I felt very comfortable with this problem. I don’t think I could do it on my own quite yet only because of how he dealt with the derivative in relation to time.
I understood the ladder problem for the most part. The only thing that was somewhat confusing was how he took the derivative. I’m sure that if I watched it again though that it would make more sense. It completely made sense to me that the derivative of “h” was negative since the height was decreasing over time. As far as the cone problem, I understood some things before he took the derivative. After he took the derivative, I was lost. I remember the other day in class you were talking about derivate with respect to “t,” but for some reason it confuses me. I don’t know where all of the t’s are coming from. I feel like there are too many of them, and it’s throwing me off. The cone video was too long. I liked the ladder video better.
ReplyDeleteI still think that the clock on this thing is off. It is most definitely not 7:23. The clock on this thing is like three hours behind.
DeleteLadder:
ReplyDeleteI understood this problem for the most part. I got confused with the implicit differentiation and currently am not a fan of it
Cone:
I get the equations, I get the algebra, I know how I'm supposed to do the derivative but for some reason it never turns out right but then I see how it's done and I think that its really easy