(Vectors will appear in bold)

1.  Draw a carefully labeled sketch of the physical setup.

2.  If the problem has been stated in terms of numerical values, you should replace these with letters.  List what you are using for each value.  Fully solve the problem algebraically and substitute numbers in at the end of the solution.

3.  Attack the problem from first principles.  Substituting into some formula can't lead to as much understanding as an approach from fundamentals.  It is also less likely to be correct.  This means that when you have an acceleration and need to find the velocity or position, you must do the integrals.  When you are working out a mechanics problem involving forces, explicitly list the forces on each object in the problem and apply F= m a to each piece of the problem; let the algebra glue the pieces back together for you.  For some types of problems you will start from a form of the work-energy theorem or a conservation law.  Especially don't just look through the book to find a formula that you can plug into -- that shows you nothing.

4.  Use some words to explain what you are doing as you go.  Also states what assumptions you are making.  This would be a good way to start the problem, stating what the basis of your solution is to be.  It's not necessary to write paragraphs, but I require a few sentences scattered through the solution.

5.  Analyze the solution:  Check special cases of the parameters entering the problem; see what happens if one of the parameters gets very big or very small.  Try to show that your answer is wrong!  This requires that you have done the problem algebraically as mentioned in item 2 above.  Check dimensions.  When there are numbers, substitute them at the end and see if the result is plausible.

6.  Use vector notion properly.  Vectors are not equal to scalars.  Components of vectors are not vectors, they are numbers.  The equal sign is not just a bit of punctuation.  it means exactly and only what it says, so you can't set a vector equal to a scalar any more than you can say that the population of Miami is two million miles per hour.

The above rules are simply the way that people experienced at solving problems always work.  They take practice, but when you are used to them you will be able to solve complex problems far more readily than you would with other, less structured approaches.  You can, especially with some of the simpler problems, get a correct result without such a systematic approach, but a major part of this course is learning how to solve problems effectively and efficiently.

Because human nature is what it is, to make you pay more attention to the rules as a long-term investment, there is going to be a "tax" applied to your score when the rules are not followed.  The tax is going to get stiffer as the semester moves along.