031: Math Masterpiece PBL

Project based learning is hard. Anyone who tells you differently has not done a high quality projects that leads to deeper learning. The reason in implementing project based learning so difficult is that the mindset has to change. There is a massive upfront preparation phase of mapping out the project with all the necessary elements, determining the authentic audience, how to weave in experts, and figuring out the final place for the project to reside. This all requires an invested time and energy focus months ahead of time. It requires the teacher(s) to do the the project, map things out, and have all bases covered knowing things will change and adapt based on the development of the students.

However, I have yet to meet an educator or student who has been part of a quality project that has not been changed for the good after completing and being part of a quality project.

As we explore projects I think many people would agree that math is probably one of the most difficult to create a high quality learning project, let alone integrating it with other subjects.

Recently, my wife who teaches 8th grade algebra and pre-algebra completed a project that was a pivotal moment for her, the students, and the school where she teaches. I know this seems quite dramatic, but it is true. Let’s cut into the project(pun intended).


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She was trying to find a way to enhance her math instruction and learning. Her department is already doing some great work to get to this point. They don’t use a textbook and essentially have created their own curriculum from scratch and other resources to enhance instruction. They also have a powerful PLC established where the teachers and instructional coaches have some high quality conversations about data, instruction, and how to constantly improve.

The general challenge of this project was to create art using the Desmos website by creating vertical and horizontal lines and lines with positive and negative slopes as well as multiple other functions that allowed students to create their desired masterpiece. This may not seem like much, but have you ever tried to create a minion or logo of your favorite team or coffee using nothing but math? I thought so!

Students were also given the parameter of a minimum of 75 lines. As students began to brainstorm and come up with their designs they had to have approval of their plans from the teacher. Once they were good they were given time to write their “code” to bring their art to life.

Students had to think. They had to teach one another, brainstorm, and do additional research as their ideas developed. How do I stop the line from going on endlessly? How do I create a curved line? What if I want to do this? or that? Many things were left open for them to explore and solve on their own. This is where the power in learning took place.

As they began to finish their designs the prints were then formatted to be cut in a vinyl cutter. Students would email the teacher their Desmos graph. From there the grids and all backgrounds would be removed within the software.

Art with all grids

Art with all grids

Remove all grids and lines from background

Remove all grids and lines from background


Clean background

Clean background

Choose the "Image" option

Choose the “Image” option

Save this file and load to your vinyl cutter

Save this file and load to your vinyl cutter

We use the Silhouette Cameo to do all of our cuts. It is a very easy to use vinyl cutter that makes great cuts and is very easy to learn.

For the sake of costs(vinyl is not the cheapest) students images were printed within a 5 x 5 in square so we could get 4-6 prints per 12 x 12 inch vinyl sheet. This was also large enough to see all details and small enough to add to computers, cars, and more.

Once they were all printed, students were given a day or two to pick all the pieces out. We had them do this part because it is their design and they understand what they want to be removed. Keep in mind that allowing students to do this will lead to mistakes. We had to cut several more than once. Students had a hard time understanding what to pick and what to leave. I would suggest having examples to show them so they can understand negative space.

In the end all students were able to take their designs home. However, this was the not the end. She decided to host her own exhibition during the day. We went back and cut out  about 40 of them again for a display. We placed colored cardstock that matched the vinyl behind it.


We also made a poster of every single design(even the ones partially completed) using collage.com because we needed a site that would allow us to upload over 100 images. After several various exhibit design layouts(some were amazing) time got the best of us and she ended up with this very nice looking display at the front of the building.


(If you are interested in other layouts reach out to me)

The next step was to have the students own the learning. This is something that they have not had to do before. She invited staff to her room for a showcase day. She also emailed a letter to all parents inviting them to the school. For her exhibition day, staff and parents came during the class period. The students took on the role of the teacher and taught the adult how to write math equations and formulas to make simple shapes. This allowed them to showcase how difficult their own art was to create, gave them a sense of pride by how the adults struggled and really gave everyone a chance to bond over math. So often parents see kids doing work, but have no concept of what they are doing or how to engage with the content. My wife teared up several times watching the kids and parent interact.


This Sway has a massive amount of images to help you understand what was all created.

Despite the kids and teacher being super nervous, it turned out to be a glorious day. Since this project has ended(just a few weeks ago) she has already developed and launched a bigger and more massive project and is already sketching out plans for another project.

Just when you think you cannot do a project or thinking that pbl does not fit your curriculum, I challenge you to think again. It can be done. It is simply a matter of putting in the time, effort, and planning. It is finding people who can help you. It is removing the mental barriers you have placed on yourself as well as the limitations you have placed on students by deciding what they can and can’t do.

Nothing is impossible once you decide it is not.

All documents for the project can be found here

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One thought on “031: Math Masterpiece PBL

  1. I was one of the staff members that visited her room that day. I was amazed with what the students accomplished and their ability to explain and teach the process to some of us who have been away from any type of formal math class for a very very long time. I was most impressed with Amanda’s excitement and emotion. She had me tearing up as well. A very lucky bunch of students to have such a dedicated teacher.