Another answer to the "When are we going to use math?" question. Calculus provides mathematics answers to questions sometimes we didn't even know we were asking. http://www.dummies.com/how-to/education-languages/math/Calculus/Practical-Applications.html has a whole list of problems that are answered with Calculus mathematics.
Sure, anecdotal or observational information could be substituted for the mathematics, but the mathematics will stay constant even when situations change. For instance, calculus finds maximums and minimums very quickly, and thus will define the dimensions of a box based on the total area of a sheet of cardboard, through relating volume to surface area.
In this case, the math is faster and less expensive in time and materials than simply building boxes until you come to the maximum. Thus, in order to understand this application, you must understand calculus and how surface area would confine volume, since both are related to the dimensions of the shape involved (rectangles). So this is one example of how the math we learn in middle school relates to the math learned later in life.
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