UPDATE – I recently posted more info about this project, with a rubric and more examples, at this post.

One of my favorite math projects takes place during our unit on conic sections in Algebra II. In the project, students are challenged to manipulate equations of conics and graph them using software to make pictures. I started with this project 12 years ago when a colleague, who has since retired, introduced me to his ideas. Back then, we used a DOS program which could only graph in black, cyan and magenta. We were happy if we saw a tree made from a hyperbola and a parabola leaf line.

The project grew new wings with a program called Math Toolkit, which allowed for finer graphing and the ability to save work. Later, we started using Print Screen to grab the graphs and move them into MS Paint. The projects grew more intricate, and many kids took off with their creativity.

This year, the Desmos online calculator brought the project to a new level. Students this year could work on their equations at home, save work, and work with their teacher during time allotted in class. Thanks to Kevin for working with his class to share their creations.

First up is Kristin. Her project moves from Desmos to Paint. Then un-needed pieces are removed, and the final product emerges.

Next up is Matt. Here are his graphs after the axes and grid were removed….

Any ideas what the finished product will be?

Did you guess yet?

OK, so you just want to see it…ok….

What I love most about this project is when students discover how the conics behave, and experiment with them without fear. In the next example, Connor wanted to tilt his ellipses and researched on his own how to make that work using trig functions (did I mention that these kids haven’t had trig yet?).

In some years, I have had students peer-assess their work by creating an art gallery of their work. Giving each student 5 star stickers, I had students select their favorites. Contact me if you would like any of the instructions or rubrics I have used for this project in the past. Thanks again to Kevin and his Algebra II class!

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These are awesome! I would like rubric, etc. Thanks! I can think of lots of interesting things to do with Geometry. I’m going to have a harder time ‘amping up’ Alg 2. Here’s at least one thing I can do.

Thanks Melissa! Bob, Kevin, and their students did an amazing job 🙂

If you coordinate a similar lesson in your classroom, please let us know – we’d love to feature your projects too.

-Team Desmos

I would love to get the rubrics etc. from you and try using this great project with my flipped Alg 2 and Math Analysis classes next year. 🙂

very nice! I have done similar projects using TI-Nspire. Have you considered making the students use Domain restrictions for each graphed relation? In the examples section of the Desmos calculator, there are some examples to help you with the syntax. Just a thoght.

Pat, thanks for your comments. The problem with domain restrictions here is that the majority of what the kids are graphing are not functions. In my quick check, I was not able to locate syntax for restricting domains for non-functions.

To those requesting instructions and rubrics, I will try to have them up via drop box later today.

Hi Bob – first, thanks again for sharing your students’ work. We absolutely love their creativity and feel so proud that we were able to be a part of it 🙂

We just updated our support page (support.desmos.com) with a brief tutorial on how to restrict domains for non-functions. You can find the post at: http://support.desmos.com/knowledgebase/articles/83355-how-can-i-restrict-domains-for-non-functions-

Please let us know if it helps. And, if you have any other ideas on how to improve the calculator feel free to send them our way.

Thanks again!

Team Desmos

Reblogged this on Mr. Siderer's Weblog and commented:

Math meeting art is always an interesting topic. Let creativity reign!

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This sounds like a great project! Could I please have your rubrics etc. ? Geometry projects I find easy to come up with. Algebra 2, not so much. Thank you for your help.

I agree with everyone else. This is a great project! 2 questions for you… 1. could I get a copy of your rubric? and 2. How do you keep your students from just going in to the Desmos graph gallery and copying one that is already there?

The skimpy rubric I have for this project is given here. I have not changed it since the advent of Desmos, but it is on my to-do list: https://dl.dropboxusercontent.com/u/68005919/Conic%20Sectins%20Drawing%20Rubric.doc

As for copying, I don’t do anything to stop kids from hunting, and have not run into this problem. But what I would do is provide class time to have them start the project, circulate and discuss as you see projects evolve.

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These are great! A far cry from the TI-83 “drawings” my kids did just 4 years ago. I have a bank of conics applets that may be helpful for getting to know the curves. They are at http://ggbtu.be/c4091/m38856/ylyy. One set requires flashlights! Thanks for sharing 🙂

This is amazing! I’m teaching Precalc for the first time this year and really wanted a way to incorporate Desmos into the course. I will definitely be using this project when we do our conics unit. I also really like the idea of making this an overarching theme in a course from your video. Thanks!

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