In my Calculus class, we have been studying applications of derivatives...
First derivatives and all of the great information that come with them.
Second derivatives and their special qualities.
We have been curve sketching, asking questions different ways by looking at graphs and determining where the first derivative is > 0 or where the 2nd derivative is > 0. Fun stuff.
Then we came to Optimization problems.
I used Dan Meyer's Taco Cart problem to kick it off. (Find the problem here:
http://threeacts.mrmeyer.com/tacocart/)
What a great way to start Optimization!!!
The class came up with the main questions that need to be answered. As a class, we figured out the easier ones first. Then came the set up for the optimization problem... went SO smoothly. Everyone was on board. The rest of the lesson and problem set up was great! Hopefully that will carry over to the test.
(unlike when we did related rates... usually during class, I will give/show an example to model how to think about a problem, then I have the students work on a few problems on their own or in small groups, so the students feel some frustration and THINK through the set up... when we did related rates, I gave the students the option to a)have me go through the problems for the whole class or b) to do our usual work... they chose option a). It was one of the most painful lessons that I have ever taught. UGH... what was extremely eye-opening was that when these students were tested on problems VERY SIMILAR to what I did in class, they did horridly... I mean really, really, really poorly. They thought that the problems were 'easy' because they felt that they understood the problems as I did them.)
First derivatives and all of the great information that come with them.
Second derivatives and their special qualities.
We have been curve sketching, asking questions different ways by looking at graphs and determining where the first derivative is > 0 or where the 2nd derivative is > 0. Fun stuff.
Then we came to Optimization problems.
I used Dan Meyer's Taco Cart problem to kick it off. (Find the problem here:
http://threeacts.mrmeyer.com/tacocart/)
What a great way to start Optimization!!!
The class came up with the main questions that need to be answered. As a class, we figured out the easier ones first. Then came the set up for the optimization problem... went SO smoothly. Everyone was on board. The rest of the lesson and problem set up was great! Hopefully that will carry over to the test.
(unlike when we did related rates... usually during class, I will give/show an example to model how to think about a problem, then I have the students work on a few problems on their own or in small groups, so the students feel some frustration and THINK through the set up... when we did related rates, I gave the students the option to a)have me go through the problems for the whole class or b) to do our usual work... they chose option a). It was one of the most painful lessons that I have ever taught. UGH... what was extremely eye-opening was that when these students were tested on problems VERY SIMILAR to what I did in class, they did horridly... I mean really, really, really poorly. They thought that the problems were 'easy' because they felt that they understood the problems as I did them.)
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