Resolución De Problemas

Problem-Solving StrategieS
NCTM’s Principles and Standards for School Mathematics recommends that the mathematics curriculum
“include numerous and varied experiences with problem solving as a method of inquiry and application.”
There are many problems within the MATHCOUNTS program that may be considered difficult if
attacked by setting up a series of equations, but quite simple when attackedwith problem-solving
strategies such as looking for a pattern, drawing a diagram, making an organized list and so on.
The problem-solving method that will be used in the following discussion consists of four basic steps:
FIND OUT

Look at the problem.
Have you seen a similar problem before?
If so, how is this problem similar? How is it different?
What facts do you have?
What do you knowthat is not stated in the problem?

CHOOSE A STRATEGY

How have you solved similar problems in the past?
What strategies do you know?
Try a strategy that seems as if it will work.
If it doesn’t, it may lead you to one that will.

SOLVE IT

Use the strategy you selected and work the problem.

LOOK BACK

Reread the question.
Did you answer the question asked?
Is your answer in thecorrect units?
Does your answer seem reasonable?

Specific strategies may vary in name. Most, however, fall into these basic categories:
• Compute or Simplify (C)
• Use a Formula (F)
• Make a Model or Diagram (M)
• Make a Table, Chart or List (T)
• Guess, Check & Revise (G)
• Consider a Simpler Case (S)
• Eliminate (E)
• Look for Patterns (P)
To assist in using these problem-solvingstrategies, the answers to the Warm-Ups and Workouts have
been coded to indicate possible strategies. The single-letter codes above for each strategy appear in
parentheses after each answer.
In the next section, the strategies above are applied to previously published MATHCOUNTS problems.
Examples of relevant problems from this year’s MATHCOUNTS School Handbook also are included for
each section.MATHCOUNTS 2006-2007

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MATHCOUNTS 2006-2007

Compute or Simplify (C)
Many problems are straightforward and require nothing more than the application of arithmetic rules.
When solving problems, simply apply the rules and remember the order of operations.
Given (63)(54) = (N)(900), find N.
FIND OUT

What are we asked? The value of N that satisfies an equation.

CHOOSE ASTRATEGY

Will any particular strategy help here? Yes, factor each term in the equation into primes.
Then, solve the equation noting common factors on both sides of the equation.

SOLVE IT

Break down the equation into each term’s prime factors.
63 = 6 × 6 × 6 = 2 × 2 × 2 × 3 × 3 × 3
54 = 5 × 5 × 5 × 5
900 = 2 × 2 × 3 × 3 × 5 × 5
Two 2s and two 3s from the factorization of 63 and two5s from the factorization of 54
cancel the factors of 900. The equation reduces to 2 × 3 × 5 × 5 = N, so N = 150.

LOOK BACK Did we answer the question asked? Yes.
Does our answer make sense? Yes—since 900 = 302 = (2 × 3 × 5)2, we could have
eliminated two powers of 2, 3 and 5 to obtain the same answer.
Example

Problem #5 of Warm-Up 3 is a good example of a problem that can be made easierby
simplifying the expression before plugging in the value given for the variable.

Use a Formula (F)
Formulas are one of the most powerful mathematical tools at our disposal. Often, the solution to a
problem involves substituting values into a formula or selecting the proper formula to use. Some of the
formulas that will be useful for students to know are listed in the Vocabulary andFormulas section of this
book. However, other formulas will be useful to students, too. If the strategy code for a problem is (F),
then the problem can be solved with a formula. When students encounter problems for which they don’t
know an appropriate formula, they should be encouraged to discover the formula for themselves.
The formula F = 1.8C + 32 can be used to convert temperatures between...