"Balancing" Equations

Here is a lesson that I taught a couple of weeks ago. I wanted to cement in the students minds that you must treat both sides of an equation the same to keep them equal or balanced. I always tell a story about “being fair” that whatever you do to one side of the equation you must do to the other side or it will get angry with you and give you the wrong answer. I should mention that this is a 6th grade math class and their first exposure to equations.

I made up a dozen of these scales with scrap wood from my shed over spring break and used pennies as weights. To calibrate them I had the students put paper clips in one side until they balanced (somewhat evenly).  I then used some items that I had multiple copies of laying around as the variables. The problems are a bit contrived but I was trying to show more than just addition in the equations.

One problem is that not all of my items were exactly equal to a certain number of pennies. For example the marble is closer to 2 1/2 pennies instead of exactly two pennies. I could tell my students were too used to “book problems” where every answer comes out neatly because they were easily sidetracked by the calibrating and the fact that the answers did not balance perfectly.

I used this as my first lesson and they did not all “get” it the first day. Some of my more abstract thinkers quickly found it easier to just “do the math” without the scales. What I thought was successful was that for the rest of the unit I had a mental image to refer back to to remind students that equations must balance.