We'd tried scales, number rods and a few other gadgets, but Neal just wasn't quite catching on to the mysteries of algebraic equations. It all looked like a jumble of numbers and signs that weren't particularly connected or sensible. I was beginning to wonder whether I'd have to put the The Life of Fred: Algebra away and go back to arithmetic for a while.
Then our big tabby walked, or shall I say, sauntered, across the room. Brain flash! We'd use Tom Sawyer and Zahra to get the concept across.
We'd been over and over about the fact that doing the same thing to both sides of the equation leaves it equal. That's one of the basic rules that we use to find the weight of our kitties as well.
To find the cats' weights, we weighed Neal first, then weighed the chosen kitty. We drew a diagram showing the weight of Neal and the kitty on one side (in this case, 115 lbs) and the weight of Neal and the kitty as Neal + x (with x as the cat's weight) on the other side. To find the weight of the cat, we subtracted Neal's weight (100 lbs) from both side, leaving only the weight of the cat on either side: X = 15. Thus we proved that Tom weighed 15 lbs. (Zahra prefers not to have her weight disclosed.)
Neal went back to his equations and solved them easily.
Some kids really need to understand why before they can proceed with a new task. They can't follow a list of rules without knowing the reason behind them. This is actually a very good thing, though it isn't provided for very well in modern education. Kids who learn this way can often go much deeper into a subject than someone who would rather skim the surface.