Modeling (Some) Equations

An updated lesson app is out—this time, it's Algebraic Expressions—which features another simple interactive tool. The interactive module here focuses on modeling what many call one- and two-step equations (though I hate those terms).


For example, you can enter something like 5p = 100 (with or without spaces) to get a model you are almost certainly familiar with. Or you can enter something like 6x + 25 = 50 (or 50 = 6x + 25 or 50 = 25 + 6x, you get the picture). There are some restrictions, however, given that this is a more-or-less above grade level interactive (and given time pressures):

Equations must be of the form ax + b = c, using only addition and multiplication (with multiplication indicated by smooshing letters and numbers together, e.g., 5h not 5 * h).

The coefficient a, if it is present, must be a positive integer between 1 and 15 inclusive. So, 15x = 100 is cool, x = 100 is cool, but 16x = 100 won't work here.

The constant b, if it is present, must be a non-negative integer which is less than the constant c. (We don't want any negative solutions in the lesson.) So, 2x + 0 = 5 is cool, but 2x + 6 = 5 is not. This constant (b) must also be less than or equal to 100 (just for sanity in displaying the model).

Variables must be lowercase.

Likes and Dislikes

This would of course be much cooler and more useful without the above restrictions, but that's for another time. The fact that it draws the same kind of model every time is something I like. We keep the modeling but let technology do the part of the modeling that technology should do—the drawing part—while keeping the thinking part for the students. I also like the consistency of the model even when the left and right sides switch from the prototypical ax + b = c to, for example, c = b + ax. This can help reinforce that, yes, the same relationship is modeled even when the sides are "switched."

As you can discover when you play with the model, it is not drawn to scale. This is something else I'm inclined to dislike but actually like. The diagram remains abstract, requiring thinking, when it is not drawn to scale. And one more thing: I like that it draws itself. Better might be to change continuously as the equation is changed to show how changing equations affects the relationship, but that'll be for another time as well.

As always, the questions paired with the model, together, are what make anything like this valuable—not how flashy it is.