Problem Solving Paradigm ( FORMAT FOR "WRITTEN UP" HOMEWORK ) Carter - Math 117 C – Fall 2002
You should use the procedure below for most problems that you attempt in class. However, when you “write-up” a
problem you will be documenting the process that you use in solving a problem.
1) DEFINE THE SITUATION. What is given? Use variables to represent the given information. Draw and label
a diagram if appropriate.
2) STATE THE OBJECTIVE. For what are you looking? What will the answer look like? Are units involved?
3) GENERATE IDEAS. Have you seen the problem before? Do you know a related problem? What formulas
or theorems might be helpful? What concepts are involved in the problem?
4) PREPARE YOUR PLAN. Choose your method. Gather pertinent information and formulas.
5) TAKE ACTION. Execute your plan.
6) REVIEW. State your answer in its appropriate context. Is it reasonable? Can you check your result? Does
your answer agree with any graphs or diagrams that describe the situation? Are you using appropriate units?
All six steps may not be appropriate for each problem or you may approach a problem in a different order. Do not
write down steps for the purpose of writing steps. However, when you do not know how to start a problem –
explicit use of the paradigm may help.
Remember, in a “write-up”, you are trying to communicate your thought processes and the mathematics that you
use in solving a problem. Write down enough information so that a classmate who doesn't understand the material
can grasp the concept by reading your problem.
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EXAMPLE - Two hundred yards of fencing will be used to enclose a rectangular plot. Express the area of the plot
as a function of the rectangle's width.
Define the situation.
We have a rectangle with a perimeter of 200 yards. Let L represent its length and W represent its width.
State the objective. W
Write an equation that shows how the area of this rectangle depends on its width.
L
Generate ideas.
The area of a rectangle is the product of its length and its width. In symbols, A = LW. The perimeter of a
rectangle is the sum of twice its length and twice its width. In this situation 2L+2W = 200. We can solve
this equation describing the perimeter for L in terms of W and substitute into our area equation.
Prepare the plan.
1) Solve 2L+2W = 200 for L.
2) Substitute for L in A = LW.
3) Express using functional notation.
Take Action.
1) 2L+2W = 200
2L = 200-2W subtract 2W from each side
2L = 2(100-W) factor a 2 from right side of the equation
L = 100-W divide both sides of the equation by 2
2) A = LW
A = (100-W)W substitute above expression for L
3) A(W) = W(100-W)
= 100W-W2
Review.
An equation relating the area of the above rectangle to its width is A(W) = 100W-W2. Since L and W are in
yards, A(W) will be in square yds.
