At The Academy at Penguin Hall, we love to see our students excited about learning. When students in Sherry Cook’s Precalculus class couldn’t stop talking about their most recent creations, we knew it was something that needed to be shared. While math might not be everyone’s strong suit, students in Precalculus managed to master functions, transformations, and domains in a fun, artistic, and memorable manner.
The class started with the following problem statement:
“How do we as mathematicians create an informative, public, artistic showcase that uses a variety of functions, transformations, and domains as our medium?”
With that in mind, the class began with an exploratory phase of studying functions. In order to better remember what different functions look like, the class created a “function zoo.” Animals in a zoo are grouped by certain common attributes like habitat or physical characteristics. In their function zoos, students had to consider functions and decide how best to group them for their “zoo visitors”. From there, students began experimenting on Desmos, an online graphing calculator. They were able to see how slight alterations to function equations affect the function’s expression on a graph, learning about transformations through direct application. “Learning here happens through use,” said Veronica Sanchez, a Precalculus student. “We don’t just study the material in a book. I don’t ever wonder about when I’ll use what I learn now.”
After exploring the basics of functions, Ms. Cook, who heads the Math & Science Program at APH, asked her students to pick a design that they would then recreate in Desmos, using functions. Students chose a variety of designs, ranging from buildings to penguins to Mickey Mouse. Many of the students decided on designs that held some significance to them. Ms. Cook provided students with a rubric including expectations for the target number and types of functions that needed to be included in their designs. While students initially considered the rubric as the bare minimum of what they needed to achieve, they soon became motivated to surpass the requirements set out in the rubric and design spectacular pieces of art. Students who started out with linear functions expanded their repertoire to include many more complex functions. One student even shaded a portion of her design using a cosine function with domain restrictions.
Kathryn Ward, another Precalculus student explained it well by saying, “If our design didn’t look exactly the way we wanted it to, we were able to figure out what to change in our equations. What started as focusing on art and making the functions fit the design later changed to focusing on the functions with the art being secondary.”
The end results clearly showed a strong understanding of functions, transformations, and domain restrictions while masterfully incorporating the necessary components into a wonderfully creative piece of artwork. Students had the option to submit their designs to Desmos for consideration as a staff pick in the Desmos gallery. We are proud to say that the Desmos staff selected one of the Precalculus pieces to showcase! We can’t wait to see how our students continue to grow in their skills and abilities, whether in math, art, a combination of the two, or something completely new. Check out this incredible artwork from our students at The Academy at Penguin Hall, the only independent, all girls, college preparatory high school on the Northshore.