Problem-solving template

In past courses, I've tried off and on to have students use a problem-solving template that my colleague Prof. Mankey developed. The basic idea is to give you a general structure for solving problems by compartmentalizing the problem-solving process. Break it down into fairly general steps that most problems have (though not always in the same order) so you have a guide for how to start and finish problems.

The template is not something you will be required to use when solving problems, but if you're having trouble with the homework, it might help. Details below the fold ...

There are six sections to the template, which you can find here:

Find/Given: state what you are supposed to find, and what is given in the problem. Usually trivial.

Sketch: this should be something that helps solve the problem, not just a picture. If you are given a function, sketch its graph. If you have a physical situation, draw a picture with rough dimensions noted to help clarify the geometry a bit better. Particularly with problems involving circuits or point charges, this will be an obvious thing to do.

Relevant equations: list all equations you will (or might) need to solve the problem, such as F=qE or x=vt.

Symbolic solution: without plugging in any numbers, algebraically solve for the variable of interest. This is supposed to be a general solution, in the next step you plug in the numbers you have. Your answer should (in most cases) be an equation, solved for the quantity of interest. You don't want to plug in numbers until you absolutely have to, because it makes troubleshooting later on vastly more difficult. I've ranted about this before.

Numeric solution: now use the previous result, plug in the numbers and units/conversions, and state the numerical value of the quantity of interest. Include the proper units and significant figures or error margin. By waiting to plug in numbers, you can easily check that the symbolic solution has the right units, and trace the origin of any mistakes.

Double-check: Just what it sounds like, find a second method of solving or estimating the answer of the previous step to confirm that your methods are correct. Two usual ways to do this are to make sure the units of the answer are correct, and to make a "ballpark" estimate (order-of-magnitude).

The point of the template is to help you learn good problem-solving techniques that can serve you generally. It seems painful when the problems are easy, but it pays off considerably when things get more involved (soon).

If you are interested, I'll solve a few example problems in class using this method, which should give you an idea of how & why it is useful.