When I was in a high school physics class, I was introduced to GFS. That acronym stood for Given, Find, Solution. Our teacher added to it.

He changed it to GFAS. The A stood for Approach. I’d like to build and add to that.

I’d like the A to actually stand for Approaches. And I’d like to add another letter, R, which stands for “Results.” But we need to add one more letter, as well.

The last letter I want to add is P. P stands for Problem. A problem is what we start with.

PGFARS unpacks to Problem, Given, Find, Approaches, Results, Solution. The reason why we have a formula is that we have a problem. Whenever we have problem, we start with what we know.

What we know is what’s “Given.” Find doesn’t refer to just finding the ultimate solution, it refers to finding what we’re solving for, the unknown variable, often referred to as “x.” My teacher’s inclusion was Approach…which is refined to Approaches.

When we’re trying to solve for the unknown variable, we hopefully have multiple approaches we can take. We need to enumerate them. And we also need to record the results.

One of the reasons why we need to record our results, or show our results, is to show our work. We need to see if we’ve made an error in our calculations. And once we see we didn’t, we can move on to the next approach.

One of those approaches will result in a solution. And I’ve found it’s easiest to find a solution when we define our problem, note what’s given, or what we know, about the problem, and show our work through multiple approaches. A good result is often the result of a good formula, like PGFARS. Solve away!