What it is: A packet which contains all of the functions we will be studying during the year, with space to fill in features of each function. Each function has the same features listed to help students look for similarities between different functions.

How it came to be:  At my first ever TMC I went to a morning session all about Algebra 2 run by Glenn and Jonathan. During that, Glenn shared this “Describe Functions” worksheet he gives his students for every function they look at over the year, and it’s really stuck with me. The last couple times I’ve taught Algebra 2 I’ve wanted to do it, and this past year my co-planner Kat was game. She by far did most of the work with formatting this, and was a fantastic thought partner for all of it.

When we use it: At the beginning of the year in our “Tools of Algebra 2” unit. It’s after we’ve introduced all of the different vocabulary, and we have them complete it for a linear function (Constant function is pre-filled as a model, as below). Then we come back to it during every unit once we’ve introduced the basic graphs for the new function (generally we start with graphs then move to equations).

What works well: Kids have some sense of where we’re going for the whole year starting in September. They can flip through the packet and see some of the crazy functions and be curious about them. Kids knew what a sine and cosine function looked like all year, and so it felt less crazy when suddenly we had waves. It also allows us to preview certain vocabulary earlier in the year (like asymptotes) even though we don’t get to them until December. When we get to new functions kids can fill in a lot of information already, and then we can have really interesting debates about equations for asymptotes and domain and end behavior. Plus it allowed us to tie every function back to transformations with (h, k) form, creating a better through-line for the content. It also served as a great reference material for them throughout the year. When we did a Desmos graphing project at the end of the year, kids also said they used their roadmaps a lot to figure out what different functions they could use, which then also helped them review for the end-of-year tests.

What we want to improve:  The information included was really awesome, but because it was spread out over 6 pages the connections weren’t always obvious. We’re discussing trying to move everything to one page to make the connections easier, but I’m not sure if that’s physically possible without cutting out some of the content. For example, the “other graphs in the family” section would have to go, but that’s maybe ok because they didn’t do a great job with it even though they’d seen several examples. I think this was partly because when we’d give them time to fill this out, we’d also go over the answers, but we never went over those graphs. Because those weren’t explicitly given to them, they didn’t fill them in. I also wish that, when talking about symmetry, we’d gone with “Odd/Even” instead of just “Yes/No” because that distinction was something they really struggled with later in the year.

File:  .docx file,  pdf version

Also, a link to Kat’s blog just to shout-out her awesome work.