Common Core Standards: Math
7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
This standard is pretty self-explanatory, but we'll give it a go.
Students must be able to write and solve single-step equations with nonnegative rational numbers. It might sound pretty basic—and in many ways, it is—but it's also kind of monumental. For the first time in their lives, students are solving real, algebraic equations all the way through.
Okay, so it's not the first time in their lives. Students have solved for unknown values a million times before; they just didn't know the nitty-gritty algebraic steps of what they were doing. Well, now, they will.
In order to successfully solve one-step equations in one variable, they'll have to know how to isolate a variable. More specifically, they'll need to know to perform inverse operations to both sides of the equation in order to get the variable they want all by its lonesome. If we have x + p = q and we want to solve for x, then subtract p from both sides. If we have px = q and we want to solve for x, then divide both sides by p.
Since we're only dealing with one-step equations at this point, there's no need to tell them about performing inverse operations in reverse-PEMDAS order. Of course, if you've got a class full of overachievers, then feel free to start delving into more complicated equations. And maybe throw in some multivariable calculus while you're at it.
Remember, too, that p and q should be nonnegative rational numbers. That means you're free to give 'em all the fractions and decimals in the world—but a simple negative sign might be too much for them to handle. Students haven't fully developed their understanding of negative numbers yet, so for now, keep things positive.
Don't forget that we want students to do more than just solve these equations; they've got to write them and use them to solve real-world problems. That means students need to practice their English to Algebrese translation skills, as well as interpret the answers they get according to the context of the problem.
If students can write and solve these types of equations in response to a real-world problem, then they've satisfied this standard.
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