Math Home Search Dr. Math Open Box Problem Date: Open box problem I am not sure how to find the formula for the greatest volume box you can make from a sheet of cardboard with different-sized corners cut out of it.
Finally, there are differences in implementation between the above applet and that by Ortiz and Popovich. On one hand, the latter shows only the modifiable rectangle and a lot of textual in part, computed information, but no graph. I believe that a volume graph adds an essential dimension to the problem presentation, which might be especially important in middle school.
The second difference is the other applet displays, in my view, an enormous amount of information. In particular, the areas of the flaps provide no additional insight into the problem and constitute a distraction. The numeric value of the area of the base, while mildly relevant to the problem, is rather a side effect of computations and, again, does not help students gain an insight.
Thirdly, I am completely at odds with the introductory paragraph of their article: This problem can be solved using many representations: In this article, we demonstrate the use of applets as another way to present or explore possible solutions for this and other variations of this problem.
None of the above, applets including, provides a solution to the problem. Claims to the contrary are misleading. Some mathematical problems do not admit exact solutions and, if necessary and if possible, could be solved approximately.
Exact solutions to other problems can't often be obtained as exact quantities and may be presented by their approximations. Whenever mathematics models a practical problem, having an exact solution may not be even important.
It is still important to know the difference between solving a problem and finding an approximate solution.Thinking out of the Box Problem It’s a richer problem than we ever imagined he “box problem” has been a standard optimization exercise in almost every calculus textbook since.
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