Equals as Balanced Objective
Pretend you are holding a jar of peanut butter. Now pretend to take the lid off. Did you turn the lid to the left because it “felt right” to turn it that way or did you think “lefty loosy, righty tighty” and consciously turn it that way? If the former, you relied on kinesthetic knowledge—knowledge that is stored in the brain but is so connected to the body that it feels like it is stored in the body. (This is the kind of knowledge athletes seek when they practice the same thing over and over again.) If the latter, you were using a goofy but commonly used phrase to help you decide which way to turn the lid. Either way of knowing is sufficient for getting the lid off, but for this objective—knowing that “equals” means “balanced” or “is the same as” in mathematics (unlike on a calculator where it means “get the answer”)—both ways of knowing are required.
Elementary school students should develop a literal feel for when an equation or number sentence is balanced and, when balanced, know that whatever is on one side “is the same as” whatever is on the other side regardless of appearance. They should also learn not equals (≠), less than (<), and greater than (>) to the same degree.
Elementary school students should solve enough problems on a math balance to feel comfortable flipping an equation about the equal sign, like rewriting 7 = X as X = 7. The payoff in algebra is huge. Without this fluency with equals, just reversing the sides of an equation is a