The Mathematics of Turtle Art

I’ve been working on an updated project guide for Turtle Art (coming soon), and it’s inspired me to do a follow-up to my previous Turtle Art post, and talk a little about why we like Turtle Art to begin with.

We use Turtle Art not only as an introduction to programming, but also as a tool for helping students explore mathematical concepts. Asking a student to draw a shape using Turtle Art doesn’t necessarily demonstrate much mathematical thinking, but once students discover that they can make the turtle turn at right angles by entering “90” into a right command block (indicating the turtle should turn right 90 degrees), teachers can start a discussion on angles. “Great! You’ve figured out that to make the turtle turn sideways, it has to turn 90 degrees. How many times does it have to turn to make a square? Four? So, how many degrees does a square have?” Then, as students develop an understanding of area and perimeter, we can ask them to use Turtle Art to prove their comprehension. “Draw two shapes with the same area, and different perimeters.”

We’ve found Turtle Art particularly useful in engaging students in learning about the Cartesian coordinate system. As students experiment with changing ‘x’ and ‘y’ values to move the turtle, teachers can challenge them with questions like, “What do we have to enter to put the turtle back in the center of the screen?” Again, once students have a basic understanding, teachers test their comprehension with challenges like, “Draw a shape in each of the four quadrants.”

The programming element serves as a method for driving the curriculum, and as way of demonstrating the students’ understanding—all while providing them with a fun and engaging creative outlet.



David is the documentarian and professional development coordinator for the Creativity Lab. In 2014, he received a BA in creative writing from Louisiana State University, with focuses on short fiction and screenwriting. In partnering with New Orleans-based independent film company, Asymptote Pictures, his work has been featured in film festivals across the country. He likes his espresso maker, and vegetarian tacos.