My students amazed me with their attention to detail with the Linear Programming art assignment. The objective of the assignment was to use linear programming to make an art piece, but I also wanted students to have the option to challenge themselves and be exposed to other types of functions. I introduced the students to sliders so that the students would have the structure and confidence to work with unfamiliar functions. Here are a couple of examples of their work.
Alexandra pays great attention to details and was motivated to make an eye. Her process was so methodic and her conversations with her peers and me about the functions she needed to use focused on the attributes of the graphs you only wish your students would eventually notice. She played around with ellipses but noticed that she could not get the crease of the eyes. She was explaining her problem and I suggested using parabolas and was able to discuss cusps that occur in graphs. In her write up for the assignment she was able to reflect on the different aspects of the functions she used. In her reflection she wrote:
“I was finished with the eye very soon after I started working on it, and I decided that I wanted to challenge myself even more. I attempted to draw eyeliner on the eye and draw an eyebrow as well. I experimented with parabolas and modified some equations and added sliders to figure out the correct equations and finally they turned out the way I wanted them to.“
Lily wanted to work do a character with more than just linear lines and choose Carl Fredricksen from the movie Up. The emotion and facial expression she captured only using functions is true to the character. In Lilly’s reflection she discussed her use of different types of equations and use of sliders.
“I had reached a point where I knew I had to start putting in my circles, parabolas and ellipses. …. I realized that my hesitation to begin using the equations for circles, parabolas and ellipses was because I felt that the equations were a bit intimidating. …. more values are involved; the more numbers there are, the more intimidating the equation becomes. ….. The use of sliders made creating equations and graphing lines go much more smoothly and much quicker, making work more efficient and less time consuming, allowing me to complete it on time.”
The assignment and the graphing tool desmos provided a situation for the students to take risks, explore different types of functions and be motivated to find equations that would best work in their art piece.