Problem Solving Strategies
By: Rebecca Sawady
How can you solve a problem when you don't even know where to begin? In this article, I will highlight one strategy you can use to approach a challenging problem (and by challenging I mean a problem that really makes you think!).
Strategy #1: Look for a Pattern
Many mathematical concepts can be thought of as looking for underlying patterns, understanding what those patterns are and why they exist, and then applying those patterns to new situations. When you have a problem that seems either impossible or impossibly tedious to solve, one strategy you can use is to look for a pattern that will make solving the problem more interesting and efficient.
Take this problem from the Art of Problem Solving Pre-Algebra book: What is the 2010th letter in the sequence below?
ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC... (Problem 15.1)
The first step to solving this problem would be to find the basic pattern in the sequence. In this case, that would be ABCDEDCBA. You could then write this pattern out enough times (keeping track of how many letters you have written down) to figure out what the 2010th letter would be. But this would be tedious and not all that interesting.
Look at this student's strategy for solving the problem:
Notice how the student recognized the underlying pattern in the sequence and used that to find the 2010th letter without having to write the pattern out 224 times!