This is a very challenging set of student work to look at as a teacher. It’s tempting to just mark this up as “confused about how to deal with complex equations,” but just look at all the moving parts! There are so many things going on here, and so many things that all of these kids know how to do.

For example, each of these kids distributes — not entirely correctly, but they do distribute.

In particular, not every kid handles the sign correctly — a bunch of kids are during 0.2(d – 6) into 0.2d + something. That’s interesting, and a discrete algebraic move that we could focus on later.

And then there is the multiplication of 0.2 and 6. Unclear whether that’s a mistake these kids would make under calmer situations.

Every kid knows they’re trying to get all the variable expressions on one side, though some kids subtract or move the 0.4d rather than subtract it from each side. (It makes me wonder if they would’ve made the same mistake if the 0.2d was on the right side, as then it would be subtracting a smaller thing from a larger thing. Kids often have a harder time seeing subtraction if it involves creating a negative quantity.)

So much complexity here! I’m sure there’s more that I haven’t noticed.

Thanks Deb!