The Ten Commandments
(of solving problems)
Carefully thinking through the important variables and concepts is the most difficult task of solving problems. Many students will complain that the math is too difficult....simply not the truth....but the math becomes the scapegoat when the answer doesn't work out. (It is a bit like blaming the car for taking you the wrong place...instead of looking at the driver!) Getting a firm grasp on the correct concepts becomes the crucial first step in solving the problem. You can help to reduce errors in mathematical solutions and in your thinking by following some important steps that force you to slow down and truly understand the question being asked. A sample problem is worked out below this list of "Commandments" to help you out.
Thou shalt....
I. Read the entire problem carefully before you do anything...twice if necessary. II. Divide the information given in the question into : a. given information b. unknowns to be answered c. special considerations to remember as you answer the question
III. If the problem is not clear, try to pick out key words and phrases that identify the conditions under which the problem will be solved.
IV. Visualize the problem. Make a drawing, diagram, chart, map, etc. to help you 'see' what is happening.
V. Label all the information and make sure everything is accounted for. (Notice how the first 5 steps don't even get to the solution yet!)
VI. Identify the concepts & relationships (formulas) that apply to the problem.
VII. If the problem involves numbers, solve the formulas algebraically first.
VIII. Fill in the information and come to an answer.
IX. Check to see that the solution is as simple as possible and is not missing any important information (like units if it needs them.)
X. Ask yourself: Is this solution reasonable?. Try it out if necessary or make a good approximation in your mind as a quick guess.The hope of the preceeding list of "Commandments" is that you see the usefulness in all areas of problem-solving. Broken down quickly, it is always a good idea to:
(1) Write out what you know (2) Write out what you don't know (3) Get a clear picture in your head and on paper (4) Identify all the conditions to watch for (5) Solve the problem (6) Check the reasonability of the solution.
It
should be noted that all this is a very important part of being a good
student in any course. When you struggle, there are many resources
available to help you learn. Most important is your desire to want
to be a good student. Learning how to solve your own problems
is a crucial life skill.
Missy Target is learning how to bow hunt so she can go hunting for da' Big Bear. She pulls back on the bowstring 40 cm and lets go. The arrow accelerates as the string recoils and the arrow takes off with a speed of 60 m/s.
(a) Calculate the acceleration of the arrow as the string pushes it forward.
Solution
