How I Teach Function Notation

I’ve found that function notation can be a challenging topic for my Algebra 2 Honors students. My first year, it was a constant struggle and they always looked so overwhelmed. So the next year, I totally revamped the way that I presented it and have had much greater success. My biggest goal is for them to realize that it’s really just a different way of writing things they already know about.

Teaching function notation in math can be tricky! Algebra students will love this activity while taking notes or filling in their foldables.

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.

How I Teach Function Notation - using hearts and smiley faces to make it painless

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!