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.

Download (PDF, Unknown)

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

Download (PDF, Unknown)

While this accomplished what I wanted (students had to explore how the rules were determined), it was rather time consuming. I had already kind of decided that I may not have students graph every piece by hand and then this gem of a post came from Julie Reulbach about an activity she put together in Desmos Activity Builder. (Go ahead and read it, I’ll wait while you do.) As I read it, I thought about the notes I had done in the past and was planning to do something with when I got there a month or so later. And Julie had already done it for me (without even knowing I needed it!)! YAY!

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.

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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-stretch

Horizontal Compression:

Vertical Stretch:

Vertical Compression: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:

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The next I see my classes are Thursday, so I will be sharing the gifsmos with the other three classes that didn’t get to see them. Hopefully that helps some more students.

What I what I truly appreciate about what Desmos has done is that it is has taken away what appears to students as the heavy lifting – the creating of the graphs. Students can focus on what is happening to the graphs rather than the act of determining the points and plotting them. Both of these can be rather time consuming and by the time students are done with this, I believe that they have lost focus on what is really the issue I want them to grapple with in this case, which is how the graphs change and the description of those changes. Julie took the ideas behind something I have previously done (and in all honesty, had not shared with her) and created a series of activities in Desmos’ Activity Builder that not only allowed students to explore how the graphs change, but then allowed them to try to create equations to show they understand how those changes appear in equations. What I had done on paper took most of 2 class days (50 minute periods). Julie’s activity took about 30-40 minutes in class to complete and was way more elegant and was definitely more effective.

I am so glad that I have taken the time to work with Desmos more in my Algebra 2 class this year. I think that it has helped enhance my students’ understanding of the material. I know I’ll continue to use Desmos in my classes this year.

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