Taking Risks

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 x given this equation:  3x-2=2x, the next logical step is to subtract 2x from or add 2 to both sides.

3x-2=2x

A_{2}: 3x=2x+2

S_{2x}: x=2

Some students inexperienced in algebra may begin by dividing both sides by 3.  I won’t stop them from trying this approach.  As long as it is legal to divide both sides by 3 we should give it a try and see if it brings us closer to a solution.

3x-2=2x

D_{3}: x-\frac{2}{3}=\frac{2}{3}x

The we proceed to solve for x:

S_{\frac{2}{3}x}: \frac{1}{3}x-\frac{2}{3}=0

A_{\frac{2}{3}}: \frac{1}{3}x=\frac{2}{3}\rightarrow x=2

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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