Geogebra/Desmos Functions Resource Page

I came across this resource page that I made for a presentation back in January.  I thought it was going to continue to get filled out, but I had to move on to other projects.  I wanted to share this in case it inspires any summer learning, and I hope the resources can help give an idea of how dynamic graphing software can enhance the student learning experience for functions.  A lot of these links are to pre-made Desmos or Geogebra pages by other authors, and some I created on my own.  I linked to blogposts for a few of the activities as well to give a better idea of how the activity was used in class.



You can also open this document in Google Drive and make your own copy at this link.  I've spent a lot of time over the past couple of years thinking about how to use Geogebra (and now Desmos) to improve student understanding of functions.  Most of the textbooks that I've used in Algebra and Algebra II in our district don't go very far beyond "graph this function" for practice problems in these sections.  Geogebra and Desmos offer us a chance to change the task and the types of questions that we ask when teaching functions.  

For the project above I included links to sliders, flashcards, and transformation activities when I could find/create them.  Students can play with sliders when first being introduced to a new function type to help them attend to the structure of the function with its parameters, and they can build on the background knowledge from previous function types.  Flashcards can be used to review vocabulary, and to check for understanding of the values of the parameters.  More on Geogebra Flashcards here.  Transformation activities or "other" activities mostly consist of Geogebra pages where students will find the equation for a given function.  

Though I haven't used all of these pages, the ones that I have used in Algebra II and Pre-Calc facilitated richer conversations, and overall better understanding of functions and transformations in my own class.

Piecewise Functions for Trig/Math Analysis

We are about to start functions and transformations in trig/math analysis, so I made some piecewise functions in Desmos to use for the intro.

The above function is named f(x).  Below is what I entered to graph the function.  

Then we can view transformations of f by typing the transformation on an input line to the left of the graph.

You can show or hide each graph by clicking on the colored circle to the left of the equation.  Below is 2f(x).

And f(2x).

Here are the links to the Desmos graphs.  Graphs 3 and 4 include questions for students to answer.   Hope some of you can use them!

Piecewise 1

Piecewise 2

Piecewise 3

Piecewise 4 

All of these functions were taken from Calculus AB free response questions, hence the link back to the website.  I also made a table of values to use for by-hand practice.

Watch this video by Meg Craig for a fantastic demo of how to use the table above.  Scroll down to the embedded video to view.

Desmos Lessons

Desmos is a free, easy to use online calculator.

Desmos has also partnered with educational professionals such as Dan Meyer to develop classroom activities.  Teachers can sign up for a Desmos account on the classroom activities page.  This account will allow you to see what each student in your class is doing as they work through one of the five classroom activities.  If you have time, check out the demo for their newest lesson, Central Park.

If you've tried any of these lessons, please let us know.  If you'd like support using any of these lessons in your classes, I am happy to help.