I love teaching Algebra and Pre-Algebra. This Spring I had a student who was having a difficult time with the concept, and I finally came up with a plan.
OK, here you go. In this box (on the plate, whatever) are 28 M&M's. Some are loose, some are in baggies. There are 5 baggies, and the same amount of M&M's is in each bag. How many are in each bag?
Then we go through the process of removing the loose M&M's. Do we still have 28 M&M's in the box? NO! we took out 3, so we subtract 3 from both sides, the visual image and hands on experience makes processing the formula a no-brainer, now we have 5 baggies and 25 M&M's. The student can easily solve the remaining portion of the equation.
We did about half a dozen problems with different candy (with pre-session parent approval) and the conditions are, if you get the answer correct, you can keep the candy. Then the student was easily able to also do problems that included subtraction. When questioned about the concept behind the formula, the student was able to clearly and easily explain the "why I solved the problem this way" and also was able to retain the formula for use in the classroom. R