Rearranging Equations

To start solving multivariable equations for a variable, I have been using this task.  (Note:  For viewable files, you must download them in word.)

Here are the instructions:

 And here is an example of the cut-outs I give to each group of students:

The gist is that they have to decide which equations are derived from the "start" and explain what happened.

This is the students' first exposure to this in my classroom, so they must rely on their background knowledge solving one variable equations and with multivariable equations in the past.  Some students look for equations that have one solution in common with the "start" equation.  Some students using adding/subtracting/multiplying/dividing reasoning as we do in solving one-variable equations.  But this time I had a student use reasoning that was totally new to me, but also super-awesome :)

Her reasoning was based on comparing these equations to her prior knowledge of adding/subtracting from elementary school.  Consider the following set of equations "5 + 3 = 8" and "5 = 8 - 3"  In elementary school they were taught the relationship between these statements.  So my student used this reasoning to explain that "2x + 6y = 12" must bet the same as "6y = 12 - 2x"  ISN'T THAT AWESOME!

I feel that this is the impact conceptual understanding taught at all ages (in this case driven by common core) can be so beneficial to students.  Also can we just celebrate for a second that this student was 100% comfortable extending from numbers to algebra?  I think that is the epitome of deep conceptual understanding!

I'm excited to share this reasoning with my classes on Monday so that others can benefit from it.
-Kathryn