Function Family Picture Project

This was the final piece in our Function Families unit, after we sorted, compared, and folded.

FuncFam Hands

The goal: Write a bunch of equations, including at least one of each of the eight types we studied this year.

My resident kicked it off with a picture he made, using at least one of each type of function.


Students worked with their partner to write an equation for each function, name the type and define domain and range. Whatever they didn’t finish in class was homework–there were 20 functions total, so most had some work to do.

The next day, the project was introduced and students had the next two nights plus three days of class time to do it.

No source 😦 Please help if you know!

Students were given two minutes to draw, and he narrated the whole time:

  • S is starting with a periodic function.
  • You can’t steal, but you can borrow someone else’s idea and make it your own.
  • Just start drawing–you don’t have to keep everything. I had a rocket ship on mine when I started, and then the boat showed up.
  • H has a logarithmic and exponential already.

The goal was to create a sense of urgency here to prevent paralysis–the student staring at their paper for 15 minutes while they wait for inspiration to strike. It mostly worked–there were very few students with a blank paper after that.

Here’s the sketch the student above started with:

Function Families Hands Sketch

They were given the rest of the period to start getting their picture together, and near the end we reviewed domain and range*. They were told to start writing their functions, but that we would review the harder ones in class the next day.



For the rest of the two days of class time, we started out with a Do Now of writing a function that was trickier and then they had the rest of the period to work. The overall assignment was a function list, including domain & range, a reflection, an artistic rendering and a sketch with each function labelled.


This project was a ton of fun, and a great review going into finals. It was also so gratifying to see how well my resident put all of this together and led the class. He has been hired for my school and next year, and will be taking my place in Honors Advanced Algebra (I’m moving to Algebra 1). He’s going to be great, and I’m so proud of how well he has done.

*This is a HUGE HUGE win for domain and range, which has been a source of trauma and stress ever since Piecewise Functions. No drama this time. Not even commentary in the reflections. Silence. They get it. They totally get it. Awesome!


Comparison Matrix: Function Families

One of the teachers at our school leads a PLC as well as some whole-school PDs around literacy skills. She tries really hard to share strategies you can actually use in ALL content areas (you know the drill, they show you something, tell you it can totally be used in math, but they aren’t sure how and have no examples. Sigh.)

Our latest strategy was the comparison matrix, and it seemed like a great fit for Families of Functions.


We weren’t sure if our students had seen this structure before, and function families are a huge and wide-reaching topic, so my resident wisely took half a period to intro the concept.

Criteria Option 1 Option 2 Option 3 Comparison

This is the basic concept (files below), and we started off with cell phones. First students were given two minutes to brainstorm some criteria they could compare the phones on, and fill those in down the left side. Then they had about five minutes to talk through filling in the columns for each type of phone.

We called on a couple of students, several of whom were hilariously into it. “Well, this network is 4G, and this is only 3G, so I think the wifi is important, but it really depends on what you want it for.” ….Um, an example? Although next time I’d totally have them look at something I did need compared–they did a good job!

Then we introduced the “Comparison” column and talked through good ways to make a comparison, and how its more than a list.

Once we were set on the overall concept, we got to work. Each pair of students received one of four versions of the comparison matrix, comparing three types of functions.


They had two days in class to work on the comparison matrix and got some amazing work back.



We both loved overhearing student conversations during this project–so interesting to listen in on what they’ve learned and how it all fits together.

I don’t know why the first page is blank, but I couldn’t seem to fix it. Just scroll down.

Have you ever tried a comparison matrix before? I had never heard of it.

Function Family Foldable

…say that five times fast!


I don’t have a file to share for this one, because we went low-key. Its handwritten. My resident put this together, and I encouraged him to do it by hand because you’re much less likely to want to shoot yourself than when you make one electronically.

They turned out great though, and the students are referring to them left and right as they work on their projects. A lot of students made gorgeous and detailed ones, but this student sits fairly near my desk in my first period (and gets there early) so I took pictures of her cover and interior pages.

LinearAVFF QuadPolyFF ExpLogFF RadicalPeriodFF

(I have no clue why the last one is smaller).

Finals start on Wednesday–almost there!

Families of Functions

[I know everyone else is all schools-out-for-summer, but I don’t even start reviewing for finals til tomorrow!]

In our Honors class, we are wrapping up the year with a major review of Families of Functions. My resident has taken over the majority of my load and definitely took the lead on all of the great stuff below.

We started last week with a card sort matching function, name, graph, domain & range. The next day brought a much more intense card sort with all of the above PLUS transformations. Students used that to fill in a graphic organizer with basic information about each function.

Adapted from here, I think.

Both card sets were found online, although we would adapt them a little if we did them again. It was a good intro over the first two days, until we moved on to the Comparison Matrix, up next. (And coming after that, a Foldable and a project)

What’s your favorite card sort activity? Leave a link below if you have one!