Ideas for Desmos PD Day

On Feb. 16, I will be running a PD session for my department on how to use Desmos effectively in the classroom.

I would say more than half the department is coming with little to no experience with, and limited experience with the calculator.  I am planning on assuming no prior knowledge.  We will have 3 hours together.  Everything is still a work in progress, but I’m hoping to get suggestions and feedback!

So far, here’s the plan: Continue reading

Rotating a Function

You can pretty easily use parametric equations to rotate a function through any angle of rotation.

  1.  Define a function, f(x)
  2. Either choose an angle measure, a, or leave a as a slider and type in this parametric equation: (t·cos f(t)·sin a, t·sin a+f(t)·cos a)
  3. You’ll need to specify the values of t.  I generally use -20 to 20, because that will cover what is visible in a normal zoom.  If you want to zoom out quite a bit, though, you may want larger values as your bounds on t.
  4. If you want to animate the rotation, specify the bounds on the slider a.

Check out this example!  Click on the Continue reading

The Symmetry of Functions

As I work with students to analyze graphs, I’ve noticed that many of them have trouble distinguishing whether a function is symmetric about the y-axis or the origin.

I designed this activity to animate the reflection of a function about the y-axis and the rotation of a function about the origin.  I chose to illustrate symmetry about the origin as a 180° rotation rather than a reflection through the point (0,0).  I think this is easier for the students to learn to visualize in their minds.

To rotate the curve, I defined the rotation using parametric equations.  Desmos has a great learning demo on parametrics here


Here’s my activity:

Symmetry Activity

Feel free to duplicate it and try editing it to something useful for your classes!  (Remember, if you just click preview, you won’t be able to see anything in a hidden folder.  You’ll see it just like the kids will.)

Understanding Domain and Range

In my experience, students tend to get really mixed up and turned around when trying to identify the domain and range of a function based on its graph.

I have never had an excellent solution to this problem before Desmos rolled around.  But I created this activity to bring to life the ideas of domain and range.  Student feedback was overwhemingly positive about this activity.  Many students felt much more confident finding the domain and range after working through it.

Despite the fact that this was an effective activity, it did have a couple of hiccups, as is to be expected with the first run-through of any activity.  The link is to the revised version.


  1. Adding graphs* to the pages asking students what they got for the domain of the functions in Domain Challenges #1, #2, and #3, so students don’t have to click back to the previous page to check what they got. (Also adding graphs to the pages asking for range)
  2. Adding clearer instructions for what students should do on Domain Challenge #4 and Range Challenge #4.  Students got confused in class when we switched from interval notation (the better way of writing domain and range for the input boxes) to inequality notation.

*Quick tip: Don’t forget that you can copy entire slides!  This is particularly helpful if you want to add a screen where you use the same graphs, but maybe add a bit of text or an input box.  Once the screen is duplicated, you can then add input and/or text.  This is a lot easier to do than copying a graphing screen line-for-line.


New Features!

I am really digging the new features Desmos has rolled out.  My favorite two features are:

  1. You can now hide a folder of content on a graphing screen.
  2. You can easily add a graph image to a screen with text and/or student input.

Here are some ideas for ways to use a hidden folder of content:

  • Have students practice writing equations of lines, parabolas, piecewise functions, or whatever you happen to be working on!  Make a folder, write a function, and graph it as a dashed line.  Then write some text instructing the students to write the equation of the function.  It is easy to write an activity like this, and as students work, all it takes is the briefest glance at the teacher screen to see which students need intervention.
  • When you have lots of complicated formulas, it can be distracting for students to see lots of folders with all of the “background work” hidden.  I used to just make a folder labeled something to the effect of “hidden stuff” or “triangle” or, in the case of the example I’ve linked, “umbrella”.  Now I just hide the folder.  So easy!

I doubt you need help figuring out an effective way to use a graph alongside a question, but if you want an example of how I’ve used this, check out my last blog post!  Just remember