# Math + Art + Desmos… Connections.

“I love math and art, and I’m glad that I was introduced to Desmos, a way to use both subjects at the same time.” – Marianna, Grade 10

Drawing with graphs has been a powerful way to motivate students’ interest in understanding how equations relate to functions, and how manipulations of equations lead to transformations from a parent function.  I jumped on to Fawn Nguyen’s Des-Man project as soon as I saw the idea, and have done some incarnation of this work each year.  Each time I’ve guided students through this process, it’s gotten better and deeper, both through the development of my own approach, and from improved tools like the Desmos Des-Man interface (…which I’ve heard is currently “in the shop” undergoing some improvements) and more recently tweaks to this idea like the “Winking Boy” challenge, created by Chris Shore (@MathProjects), and posted on the Desmos Activity Builder by Andrew Stadel.

This year’s work was definitely the strongest yet, and I owe the major improvements to my reading of  Nat Banting’s post, which extended this project to another level for my students. In the past, I have asked students to create a graph, which had features of a face or a building or a plant.  This year, I asked my grade 10 students to choose a graphic, photo, or work of art, which they had to replicate using only equations.  I asked that they choose an image that was meaningful to them for some reason, and then helped to guide them to something that was challenging, but that they could accomplish – a natural moment for differentiation, built in to the process.  In the earlier versions of this project, students had been motivated by trying to make their face look angry or happy or sad, but they didn’t have a specific place where their equations had to end up. Asking kids to commit to re-creating something forced them to be purposeful and deliberate in every choice.

They took the responsibility of recreating their chosen image seriously, and honestly, their work exceeded my expectations. There were regular exclamations of satisfaction echoing around the room as we worked on this. They persevered. They definitely attended to precision. They argued with each other about the best equations to use. They reflected about how to make the best use of Desmos. They practiced the habits of mind of successful mathematicians.

When we shared the in-progress work for some peer feedback, kids were actually applauding each other when their work came up on the screen.  Not because I reminded them to be a supportive audience, but spontaneously.  Seriously.  And when they saw the staff creative picks at Desmos, they asked me whether they might be able to submit their work.  The whole class was taking pride in creative math work.

I asked that students reflect in writing on their learning during and at the end of the project.  I haven’t asked for students to do enough writing in math so far this year, so when they seemed to be really struggling with this, I made a fill-in-the-blank “reflection assistant” to scaffold their thinking and writing, and to give them some ideas about what to include in their written analysis.

A few highlights from their reflections:

• “I was quite surprised that I could replicate a drawing by using graphing.  If somebody asked me to do it last year, I would say that it is a “mission impossible.”   However I was able to do it.”
• “As my piece of art, I chose the logo of the football club Barcelona because I am a big football fan and FC Barcelona is a club worthy to be recreated through the use of quadratic equations in vertex form. In addition, the logo was an appropriate challenge for me, containing easy and smooth curves but also difficult shapes, like letters or circles. When the project was assigned, I was skeptical that it was possible to recreate an artwork, just by using equations. But now that I am done and a proud owner of a recreated art piece, I strongly believe that it is possible (obviously).”
• “I found out that desmos is a really good tool to practice and sharpen your understanding on any equation and in my case it was the vertex form of a quadratic. Desmos allows you to experiment and find new ways to fix the problems or even work more efficient in order to surpass the problems in the first place. I am proud of the detail and sharpness of my work in general. I tried really hard to make the whole piece smooth and detailed. In order to do so, I zoomed in a lot and by doing so, I identified minor mistakes and was able to fix them.”
• I chose “Pumpkin Pepe” as the subject of my project because it provided the right level of challenge for me and it was really fun to do. Overall, I really liked this project because it solidified my knowledge of graphing equations and has made me more comfortable using parabolas. I found that my understanding of quadratic equations really improved while I worked on this project because before, I wasn’t sure which variable shifted the parabola which way, but now I understand.
• “I found that my understanding of parabolas and linear equations really helped me improve, and made me more confident during my work on this project. At first parabolas seemed to not make any sense to me, but now I feel like I really understand the way they work. Now I have the capability make connections with all these equations in the real world.”

Here are the project guidelines, the rubric, some peer editing forms, the “reflection assistant,” and a .pdf, which has a range of student work.  My rubric borrows from the I.B. Math Internal Assessment Guidelines, as one of my tasks as a grade 10 teacher at my school is to do some specific preparation for the I.B. program in grade 11.  Thanks in advance for any feedback on this project, and on the guidelines and rubric.

Desmos Drawing Project Guidelines and Rubric

Desmos Peer Feedback

Desmos Drawing Project Reflection Assistant

Desmos-art-project-student-work-2015-16-updated

## 6 thoughts on “Math + Art + Desmos… Connections.”

1. Donna MacKinnon

What a great way to formally extend this activity and to encourage kids to challenge themselves. I have had some students do amazing pieces of art, but others a fairly simple attempt. The idea of replicating helps because they have a clear goal. Really like your reflection sheets too. Thanks for sharing. I will add this structure the next time I do desmos art. Thanks for sharing.

1. Nat Post author

So glad that you can use some of the ideas. I really found that having to be deliberate about copying something – and kids choosing something that they cared about made for much stronger thinking and work. Thanks for your comment.

2. Dana Bjornson

Hi there,
Thank you SO MUCH for making this post. After seeing Desmos art on their site, I looked into turning this into a project for my Gifted Math 10 class and your work not only got me off the ground— it launched me!!! I have now completed two courses with the project and things are going really well. It becomes a labour of love for the students, without question. I set my minimum number of equations to 75, so some students do not actually finish their work, sadly. On the plus side, some students double or triple the minimum and often those who do not finish, are those who chose very challenging pieces of art. Here is a link to our class blog from last semester, if you want to check it out. Please ignore the flashing reflections. Some of these “monkeys” like to monkey around with the code and I haven’t had the time to figure out how to get rid of the flashing! http://esqmath10c2019.weebly.com/desmos-art-reflections
Again, many thanks!!!! Dana

1. Nat Post author

Wow. What a nice comment. I’m so glad that this work was useful for you and for your students! Thank you for writing to let me know. And your students did some Amazing work! Some of the choices they made were very ambitious. We definitely have to be careful in coaching them as to how much time we want them to spend on this project. I think that they gain a ton of practice with transforming graphs, and that this is time well spent because they have an accomplishment that they are proud of and will remember – and this is time building positive relationships with math. But this year, I’m trying to keep students under 6-8 hours or so total for the project. Please keep in touch to share what your students do next. And stay tuned here where I’ll share this years’ work soon.