Tables can be useful, particularly in organizing information so you see what you have to work with. When I teach the technique, though, I still find that students struggle with writing the equation in problems that differ just a little from examples they have seen, because they are stuck in a routine mindset, not thinking deeply about the meaning of the problem.

1. Math beyond fifth grade is not for everyone. For example, I do not drive. It is easy for someone with 10 years of driving experience to say: COME ON, DRIVING IS VERY EASY. IF I PASSED THE ROAD TEST, SO CAN YOU.

2. Maybe you should not switch applications a little bit. Why not simply switch the numbers within the word problems?

(When I first started teaching the topic from a book that emphasized tables, I found myself trying to follow a routine I could teach to students, depending too much on the table, and making silly mistakes because I was not actually thinking.)

It is not that students do not want to think their way through the problem. The problem is THEY HAVE NO IDEA HOW TO REASON THEIR WAY TO THE ANSWER. Schools today focus on TEACHING THE TEST. Students are taught how to pass standardized exams not how to learn. I was a per diem teacher in NYC for 8 years. Why per diem? Long story to share another day. Most students enter college not knowing how to reason.

So I recommend using the table

*only as a tool*. The steps I suggest for these distance problems are:

- Understand the problem, e.g. make a diagram of who moves where when.
- Write a template for the equation, expressing the condition that must be satisfied, e.g. "Amy's distance - Betty's distance = 10 miles".
- Make the table
*as a means to finding expressions to use in that equation*, e.g. Amy's distance = 35t, Betty's distance = 45(t-2).
- Fill in the template to make an equation.
- Solve the equation.
- Answer the question.