I usually start by telling my students to put their pencils down, watch, and participate. This always gets their attention.

First, I tell them that I’m going to write an equation, but that it’s going to look strange. I write the first equation on the board. Then I say, “Ok, I’m going to change a few things.” and I write the second equation on the board.

I ask the students what the changes are. Someone always says, “You drew a heart instead of writing x.” My only response is, “ok”. Then, I write something like the next equations on the board.

Again, I ask about the differences between the two. At least one student will tell me that I just drew smiley faces and I barely respond.

Next, I write something like the next two equations on the board. They will tell me that the difference is an a instead of an x.

I continue this process with the equations below. I don’t simplify anything at this time. I just want them to notice that I’m simply replacing things.

Then, I tell my students that we’re changing gears for a minute. I put this picture up on the board and ask them to silently! see if they can figure out the pattern. I totally ripped this idea off of Druin at Stat Teacher. It’s such a great idea (go read it, really!).

After a few minutes, I ask if anyone wants to share. We have a discussion about what is going on and what the notation means. Then, we talk about how it relates to the problems we did before. I usually go back and simplify the answers from the previous problems and make sure everything is following along.

All of this takes maybe 15 minutes, but it makes such a world of difference for my students!