September means PEMDAS season.

I give this substitution problem every year in my summer Algebra I refresher class. The mistake they almost all make, is a classic PEMDAS problem.  So I teach order of operations rather strictly as illustrated in the example below.  Here are 2 things essential things I teach them:

1. Do only ONE level per line (M/D and A/S are the same level).  Put the letter(s) you are doing next to each line.
2. Do NOT drop parenthesis until the M/D line (i.e. leave them in the

Here is a typical PEMDAS mistake students make:

PEMDAS typical student mistake

This is the big mistake, of course, because they try to do multiplication and exponents on the same line. They see the double negative (because they naturally look for patterns) and we’ve taught them to zealously “replace them with 2 + signs! (it’s not shown here but I typically see the the 2 plus signs in step 2)

Here is how I teach them PEMDAS:

PEMDAS – the fool proof method

Notice the mistake is gone because they don’t use the negative sign outside the parenthesis until step 4.  It’s difficult to get them to stick with this method at first, so be sure to practice it often with them.  As always, I try to integrate this topic throughout the year – and I remind them of the rules each time.