We have so many strategies and tools for helping students become fluent in solving equations: stories about exes, friends, and enemies; step-by-step checklists; algebra tiles; hanger and tape diagrams; balances…. what if one impactful change could just come from tweaking our language?
When equations have variables on both sides, people often say something like “move the ‘x’s to one side” or “move the variables to one side,” but that description is quite misleading.
For example, let’s say we were solving
4x + 10 = 2x + 16. We could represent it with a hanger diagram like this:
If we follow the lingo and actually “move the variables to one side,” we’d get something like this:
6x + 10 = 16
But, of course, when someone says “move the variables to the other side” they mean for students to do this:
So let’s use language that accurately describes the algebraic reasoning we use when we subtract 2x from both sides.
I haven’t figured out lingo I absolutely love, yet. But I’ve experimented with “remove the variables from one side” and “eliminate the variables from one side” and the meaning is much clearer for students. I tack on things like, “To keep the equation balanced we need to add/subtract an equivalent amount from both side!” and, “We can subtract to remove a positive term and add to remove a negative term.” I also ask questions that go something like this: “Hm, it’s easier to figure out the value of x when we only variables on one side. For this equation, would you prefer to get rid of the 2x or the 4x?”
What phrases have you used to support kids in making sense of solving equations?
Quick Note: Because I’ve found hanger diagrams to be so effective in supporting algebraic reasoning and because it’s hard to find enough practice problems, I created 35 pages of scaffolded worksheets that (along with explicit instruction) support kids in moving from reasoning about hanger diagrams to reasoning about equations. You can find that 6-8th resource here on TPT.