Conic Section Design with Desmos

If you haven't ever tried Desmos, go check it out now. Before you keep reading. Even if you think you hate graphing. You can't possibly walk away from it without being impressed with the fact that graphing can be cool- really cool!

So on to how we use it in my math classes, and more specifically for a recent project...

Desmos is a great way for students to explore how changing parameters in an equation changes the graph. This is its most common use in my class. Its sliders feature alone is worth its weight in gold to a math teacher and students!

However, there is so much more that one can do with Desmos. So for a concluding project for both the semester and our chapter on conic sections, we used math equations in Desmos to design and create art. My students were impressed and inspired by the amazing work others have done on Desmos and quickly set about to create their own with a few guidelines:

• Artwork does no have to be original (it could be a comic book character/ famous landmark/ logo) as long as it is not a copy of art already on Desmos.
• Use all four conic sections in the artwork.
• Some areas of the artwork must be shaded using inequalities.
• Work must not be similar to a classmate's.
• All the time given in class for this project must be used.
• Share the graph on Drive for your classmates and teacher to see.

My purposes were to practice the conic sections standards and reinforce inequalities and basic graphing techniques all while introducing students to the power of equations in design.

The results were fantastic! Here are some of my favorites:

[Under each image I have included the link to the graph on Desmos so those interested can see the equations and zoom in on interesting details]

1. "Maxine's Rainbow on Water"- The best part about this one is the black radiating lines around the rainbow. She wanted rays so she looked through artwork on Desmos until she figured out how to create these using sine curves in polar form! Since they only learned a little about sine curves and definitely never learned about graphing them in polar form, I was blown away!

   

   Link to view equations and zoom

2. "Calvin"- This is a really outstanding replica of a well-beloved cartoon character. If it looks simple, go look at the equations- all 31 of them!

   

   Link to view equations and zoom

3. "Dress"- Again, this student did an outstanding job finding and learning to use a complicated equation to make the star in the middle (actually 2 equations). Ever think you'd see "low level" math students using equations like this? Me neither...
   

   

   Link to view equations and zoom

4. "Surf's Up"- My favorite thing about this one is that it was created by a student who really struggled with translating what she was visualizing into the grapher. It was a real struggle for her so I was very proud of what she accomplished!

   

   Link to view equations and zoom

I was sooo impressed with all that my students did and can't wait to do this project again. This next time around promises to be even better. After introducing Desmos to my new class, one of the students seemed distracted for quite a bit. Upon going over to investigate, I discovered he had found the art section on Desmos (which my other class never found on their own) and was already playing with the graphs. He had discovered how to make circles and how to use the sliders to make a parabola look like a spinning jump-rope. He was full of questions about how to shade his graph and if there were shortcuts to typing some of the equations. Last semester's class didn't ever realize they could make moving pictures! 

If you want to see the objectives etc for the project, here is the link to the Google Doc. If you ever try it with a class, I would love to see what your students come up with so my students can be challenged with other's work. Any ideas on improving the project are always welcome as well!