When teaching multiplicative and additive comparisons using equations, should I leave the problems like this: 10 + y = 20 Missing an addend, so we should subtract 10 from 20 to find the missing addend. 10 x y = 20 Missing a factor, so we should divide 20 by 10 to solve for the missing factor. OR Should I show them how to isolate the variable. My kids will get the first way no problem because I have hammered that subtraction is inverse of addition, occurs when we are missing an addend, and division is inverse of multiplication--use when missing a factor. I'm thinking isolating variables is more middle school-ish, not elementary-ish? I can't find in my curriculum map anything about isolating variables--but I don't want that to show up the EOG having not shown them.

By isolating, do you mean something like y=10? That is how I have been teaching variables to my 4th graders.

Well, we're not common core, but I teach them more in terms of thinking what number would make sense in the blank. I don't teach them how to isolate the variable, though they are able to understand how to do it at a basic level (which is all that is expected of them with our curriculum). I did have one discussion with them about how they could rewrite 10 + __ = 20 so that the missing part is on the right hand side, but that was only a brief conversation, as I have a brighter crew... I actually teach them to think of subtraction in terms of addition, as they often have so many problems subtracting, that if they think in terms of adding on, they can have much more success. That's just another extension of algebraic thinking being developed at that age. I don't know if that helps you, as I don't have a common core perspective! but I get the sense that our curriculum is similar to common core.

My third graders can handle isolating variables. I don't think it's too advanced for 4th grade. Start by having them fill in the blank (10 + blank = 20, so blank=10), then just swap out the blank for a variable. They've been doing stuff like that since kindergarten... they've just never known the variable aspect to it

Yes they can do that, I mean should I show them this: 3 x b = 36 and then draw the line under 3 and cross out on the left hand side and then draw the line under 36 and divide, isolating the variable b to the left side of the equation--b = 36. If I show that to my first core they may all just have a stroke. If I leave it as 3 x b = 36, we are missing a factor so we divide 36 by 3 to get 12, they'll get it with no strokes involved. I know it is virtually the same thing, except to my students--it won't be the same thing. I don't think they're ready for it. If I need to show them this, I will wait until later in the year.

I do like gr3teacher, and my kiddos love it when I explain that they are doing algebra (and have been since kindergarten)!