# Function Family Picture Project

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

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.

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:

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!