I wanted to show the kids how to figure out an unknown quantity by finding the equivalent value on the other side of the equation. First, we put an upside-down cup on one side of the balance, and I had the children weight the balance bar on the opposite side so both sides were in equilibrium.
I told the kids I would leave them room, and I wanted them to place the same number of pennies in each balance pan, but to put some of them in the left-side pan under the cup. When I came back in, I would have to figure out how many were under the cup.
When I came back in, I showed them that if I removed (subtracted) the six visible pennies from the side with the unknown, and then subtracted the same number from the known side, the two sides would be in balance again.
How might I figure out the number of pennies that were under the cup? By counting the pennies on the other side—since they balance, the number must be the same (pennies, fortunately, have a pretty standard weight).
Then I demonstrated how to write the equation and it’s solution on paper. I think I kind of lost them at this point, though—I’d like them to make the connection between the concrete and the abstract, but they’re all still at a pretty concrete stage, and the concrete understanding is what I am really aiming for.
For more balance scale activities, see Learning about mass using a balance scale, and Using a balance scale to demonstrate solving for x.