# Who Are You Calling Math Face? (How DO you turn that frown upside down?)

Awesome idea + powerful and GREAT tool + Sweet math wall = this year’s math faces.

Thank you Fawn, thank you Desmos, and thanks students for your cool ideas.

My students created their own “math faces” through graphing with linear equations, quadratics, conics, and a few trig functions.  They used Desmos.com (an online graphing calculator) to explore different facial expressions, and were asked to articulate the equations behind each feature of their graphs.  They practiced transforming linear and parabolic equations, and learned about restricting domain and range.  Students’ manipulations made subtle differences in their facial features as they figured out how to move eyes up, down or around a line of symmetry, or how to change amplitude or period of a sine function to make a thicker mustache.  I’ve done this project a couple of times now, and I am surprised each time how motivating creating a face can be for some students.

Desmos has created this beautiful classroom interface, which allows the teacher to see all of the student work at once, or filter students by things like who’s used an inequality or which students have restricted the domain or range.  This gives me an instant formative assessment where at a glance, I can easily target my advice or questions for students.    But even more importantly, students can see each others’ work, and share ideas in real time.  We spent about one hour as a full class on this, and then students were asked to complete a math face of their own over the next week.   I did this project early this past Spring with both Algebra 1 and Algebra 2 students.

I could see some students struggling with the transformations, but caring enough to work through the struggle.

I am very grateful to have discovered this task.  In my experience as an art teacher, differentiation is often natural and practically effortless.  A student can attempt to draw a portrait whether it is their first try or if they have been practicing for years.  There are different conversations I can have with students depending on his or her experience, but every one of them can approach the task  – and right from the start is set up for success.  Math teachers don’t often have this built in differentiation.  So often, our lessons are targeted to a highly specific set of procedures, for which students must be in exactly the right place in the Algebra sequence.  The low entry, high ceiling aspect of drawing with graphs makes it something we can return to with students again and again.