# Why I Love Julie Reulbach and Desmos

Transformations is something I have worked at over the years to have a solid series of activities and notes to help students comprehend how they work. (Side note, maybe I ought to look back at my blog more often. I had forgotten I had put together a couple of these things.) We are in round 1 of transformations. I am working with F.BF.3, which reads

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

The learning target this time is:

I can describe the transformation(s) that changed a graph of f(x) by replacing with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative). (LT20 for me)

I began with establishing the Parent Functions we were going to work with, as Rebekah Peterson had set up with her classes previously. We completed this in our interactive notebooks on the first day.

In the past, I would have done something like this to set up where the descriptions come from:

Yesterday, we did Julie’s Introduction to Transformations Marbleslides. It was my students’ second experience with Marbleslides and their first real experience with using Desmos Activity Builder in an instructional manner. My students were engaged with the activity. In one of my loudest classes, you could just about hear a pin drop as they begun the activity and worked through the first part on their own. WIN! For the most part, my students completed the notes that Julie had set up (and I adapted to fit in their interactive notebooks), although I did notice that some were caught up in working with Desmos and sometimes forgot to write down the notes.

Today was the day we were going to put it all together. Today was the day I had been thinking about and rethinking about over the last two weeks as I tried to best figure out how to help students put it together. I had started from some of Julie’s previous transformation activities which happened to come up when I read her post. Yesterday, as I was putting things together, it had dawned on me that I could use Desmos to create graphs that would be included in student notes so they would have a lasting record of how transformations work. I was pleased with that and went to bed pretty comfortable with how I set things up. I was still troubled with how I was going to explain the difference between horizontal and vertical dilations (compressions and stretches), but I had a basic idea of what I was going to do. The graphs were going to help.

As I explained how stretches and compressions worked, I used the graphs but I was physically illustrating pushing and pulling the graphs in the proper directions. That’s how it made sense in my head. About the third time through, I thought to myself that there has to be a way for Desmos to show this dynamically. And it does, with sliders. At the moment, the sliders go two ways and one way forward. I needed it to go one way backwards to show the horizontal stretches and the vertical compressions. Enter gifsmos. With a little bit of work, I got it to show what I wanted:

Horizontal Stretch:

Horizontal Compression:

Vertical Stretch:

Vertical Compression:

I was able to insert these into my notes and all I needed to add were arrows indicating the direction the stretching or compressing was happening. And, instead of me looking a little goofy showing the stretching and compressing, the graph and Desmos did most of the work, which was really neat.

(Update 12/7/2016:) Here is the blank PDF of my Smart Notebook file: