Since there are six times as many students as teachers, the value of P has to be less than the value of S. That should be a flag that your intuition is off. The check you did to see if your intuition was correct is exactly the type of critical thinking that can assist a student in setting up formulas. Playing with numbers we know can lead to being able to write a formula to solve problems with any set of numbers. First, though, we have to master things like basic math facts. I think this is why the questions that were marked wrong bother me so much. To me, they seem to intimate that there is only one way to think when it comes to solving math problems. The truth is, there are many ways to think … and whether I think of the problem in terms of three fives or five threes, I am thinking correctly. Don’t dis my thought process. 