Tracing Parametrics, Chains of Events, and Constructing a Pentagon

Last week I attended a PD session by Suzanne Gaskell, an art teacher at the high school where I teach.  She presented on a work of art she has created and calls the Kavad of a Sacred Geometer.

This work of art is a wooden box that tells the story of ancient geometry and its relation to various sacred traditions.  After her presentation, she instructed us on how to perform some interesting constructions, including one I had never done before, the regular pentagon.

It inspired me to create an illustration of the construction for a regular polygon using Desmos.  Here’s what I came up with:

Pentagon Construction


First skill: how to trace a parametric curve.  Prior to creating this, I didn’t know how to make a parametric curve trace itself out.  Here’s how to do it: Continue reading



Show Fake Names.JPG

You can now hide student names by clicking on the little dude with the hat in the corner!  Desmos will (temporarily) change the names of the students to the names of famous mathematicians.  Now you can show the class what they’re all working on while keeping the students’ identities hidden.  Love this new feature!

Using Restrictions in Innovative Ways

Let’s talk restrictions.  So helpful, so amazing.  I’ve seen people use restrictions in some very creative ways lately, so here’s the lowdown on cool ways to use restrictions.  Make sure to scroll to the end to see an Angry Birds activity that makes extensive use of restrictions.

First, the classic use: restricting x and/or y.

You can restrict just the x values, or you can restrict just the y-values, or you can stack restrictions.  Desmos even knows the difference between AND and OR:

Here, I’ve shown a graph with x > 0 OR y > 0
In Desmos, type the restrictions in the same bracket, separated by a comma: {x>0,y>0}

BTW, this is super helpful if you want to do something like this:

Restriction by List 2

Here, I’ve shown a graph with x > 0 AND y > 0
In Desmos, type the restrictions in separate brackets: {x>0} {y>0}

The team at Desmos has also made it possible to place restrictions on both x and y at the same time in an implicitly defined inequality.  Here is one example:

Link to Desmos: see how this is done!

Second: restricting parameters.  This allows certain aspects of the graph appear or disappear depending on a certain parameter.  It also can be used to make whole images appear or disappear.  Here are some of my favorite examples lately:

Here I built upon a graph that Desmos had featured, and set it up to turn on tangents by sliding a point on the graph.  This technique is awesome for building teacher activities where you want to make a graph into an interactive exhibit (i.e. students can’t access the expression list, just the  graph itself.)  Check out the graph here.

For another example, here is a tweet by Stefan Fritz showing a fantastic Angry Birds activity he created that gives students feedback as they work through the clever use of restrictions on parameters.  Here’s the link to the teacher activity for anyone who wants to use it!  Such a fun activity!


Sinusoidal Fun

Link to some totally rad sinusoidal picture graphs I’ve been working at lately.  The first 3 pictures have movement!

Turns out sinusoidal curves can be amazing for creating really cool animations.

All 4

These pictures were part of a nerdy Valentine to my husband.  (Valentine? Yup!  These pictures are Desmosified versions of some of our favorite things!  And, he’s nearly as nerdy as me, so it’s cool.)  I already showed them to him because I was too pumped up on Desmos-ing to wait until the 14th to share them with him.

I hope you enjoy!

Peace out Desmos world!

Simple steps toward real learning.

Today’s adventure: The Golden Arches Challenge.

After 10 years of teaching, it should come as no surprise to me that kids are expert at gaming the system to their educational disadvantage.  They commit to memory exactly and only what they need to for a test.  When it comes to applying knowledge in new and creative ways, students often stumble and don’t know where to begin.

This is a huge problem with math education, and much of the blame lies with over-paced curriculum, over-committed kids, and teachers, myself included, who have historically enabled this behavior from students by giving assignments and assessments with lower-order thinking skills and predictable questions.  In my own classroom, I am working to change this and Desmos has been an invaluable tool in this pursuit.

Where can we make changes? Continue reading

Riemann Sum Activity Launch Pad

Desmos is the perfect outlet for creativity in graphing.  Students are engaged, concepts become clearer.  Desmos is everything you always wished a graphing calculator could be.  It’s dynamic, easy to use, and FUN!  And the graphs are just so incredibly beautiful.

If you haven’t tried it yet, head on over to and try Custom Activity Builder.

Besides brainstorming ideas for creative activities, the one really time consuming part of creating an activity is making more complex graphing screens.

It is out of this desire for a quick start to the creation and design of an activity that Continue reading