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:
ReplyDeleteWhat I understood: The use of the Pythagorean Theorem.
Taking the derivative.
How they solved the problem to get and answer.
I actually understood this problem shockingly well. I doubt I'll be able to do it, but I understand it.
What I didn't understand: Chain rule.
Implicit Differentiation
Cone Problem:
What I understood: The volume of a cone.
What they were trying to find.
How they found volume.
What I don't understand: How they found the area of the water surface.
Just about everything else. I understood what they were trying to find but after they found the volume I was pretty lost.
(Tonto bob = Baumer)Ladder Problem:
ReplyDeleteUnderstood: Pythagorean theorem, the derivative equaling the rate of change(duh), why the final change was negative, and the general way the problem was solved.
Did not understand: why they put "2"s in the equation when solving, but I might have jus not payed attention to something
cone problem:
ReplyDeleteUnderstood: how the height was actually a function of time, substituting in the known values after the equation is written to make it cleaner, how they found their known values, volume of a cone,
Did not understand: the point when he just removed the "constants" from the v= equation and took H^3 out.
Ladder problem:
ReplyDeleteI understood the Pythagorean theorem, taking the derivative and how it equals rate of change, the concept of the problem, and overall how they came up with the solution. I kind of understand chain rule now, but still not entirely. I did not understand implicit differentiation though.
Cone Problem:
I understood the volume of a cone, substituting in the values and finding the values, and where they found what they were trying to find. I didn't understand anything really after finding the volume. This question, I thought, was more complicated than the ladder problem, so there was quite a bit that I didn't understand.
Ladder Problem:
ReplyDeleteWhat I understood- I understood about taking the derivative and using the measurements to solve the Pythagorean theorem. I did not understand the implicit differentiation.
Cone Problem:
ReplyDeleteI understood about using the volume equation and plugging in the numbers with the derivative involved. After the volume was found I didn't understand how to use it to find the answer. The Cone problem was harder to me.
Ladder Problem:
ReplyDeleteI understand how to set the problem up and use Pythagorean theorem to find values of the variables. I know how to do the chain rule and take the derivative. I know why you have to use implicit differentiation, but the way the guy did it kind of confused me. I think he used double differentiation or something?
Ladder Problem:
ReplyDeleteI understood the pythagorean theorem, how to take the derivitive, finding h and plugging in x and y to get the end result. I did not understand the chain rule completely or implicit differentiation.
Cone Problem:
I understand the height and the diameter of the cone are the same, how fast the water is pouring in, how to find the volume and what we are trying to find.
I don't understand what he was doing with the volume after he found it. I kind of understood it doing it along with the video but i probably couldn't do it by myself.
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ReplyDeleteCone Problem:
ReplyDeleteI understand how to set the problem up and substitute things we know for unknowns. I get how to use the volume of the cone in the problem and that the height and diameter are equal to each other. After that part I get really lost. Why can you just take the constants out when taking the derivative? I would need some help if I tried doing a problem like this on my own.
Ladder prob: i knew how they got the equation and how they did all the implicit differentiation kind of. (still kind of confuses me a little).
ReplyDeleteCone prob: I know how to get the volume and thats about it. I know this late, sorry...
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ReplyDeleteLadder problem I understood the Pythagorean theorem, some what of how they got some of the equations. I didn't understand implicit differentiation at all.
ReplyDeletecone problem- I understand now better how these kind of problems are solved. I get all the substitution. I do not understand very well how to do implicit differentiation with the chain rule
ReplyDelete