One mental block to solving problems is the fear of taking a risk: making an attempt at a solution before you know if it will in fact solve the problem. I try to encourage risk-taking with younger students and easier problems. For example, if you are asked to solve for given this equation: , the next logical step is to subtract from or add to both sides.

Some students inexperienced in algebra may begin by dividing both sides by . I won’t stop them from trying this approach. As long as it is legal to divide both sides by we should give it a try and see if it brings us closer to a solution.

The we proceed to solve for :

We see that we can reach a solution, but it introduces some ugly fractions. Only after pursuing this path do I then suggest the more elegant fraction-free solution.

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## Published by mathproblemsolvingskills

I coach students preparing for MathCounts and the AMCs, and I teach using curricula published by Art of Problem Solving.
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