# Equations & Art – Winter Fun with Technology

It’s that time of year – countdown until winter break.  As many teachers know, this is often a difficult time to get students to focus and learn, so often we try to keep them engaged with ‘activities’, often that are NOT connected to the subject (i.e. watching ‘holiday’ movies). One thing in math that you can do to both engage, challenge, and still keep learning at the forefront is to do some art with math. Winter-related is always fun (i.e. snowflakes, snowman, ornaments etc.). Often plotting-points on grids to create images is the go-to type of activity, but I also suggest that you take advantage of the technology you might have in your classroom (graphing calculators for MS/HS students, or math software, like ClassPad.net). You can do both plotting points using technology tools as well as more advanced creations, exploring how equations and domain/range constraints can create some interesting ‘winter creations’.

I have been having a bit of fun this morning playing with equations – linear, conic, parametric, parabolic, and plotting points to come up with some winter images. I’ve shared several images here – done both in ClassPad.net as well the graphing calculator, CG50. What you can do with students is challenge them to come up with their own creations. Maybe limit them to only linear equations and inqualities, or only parametric equations, or they have to use a combination. In the process of creating and exploring, students are really deepening their understanding of what the different coefficients in an equation/inequality do to impact the graph. And they can play around with different forms of the equations/inequalities, since some forms control the shape/movement of the graph more efficiently. For example, I like the slope intercept form of the linear in my creations because I can control the slope. I like the standard form of the circle because I can control the center. You will note also that in some of these images, the axes are showing, and some are not. I created them with the axes but then turned them off once I was completed. I also played around with my window/scale.  All of this is using mathematics and trying to really manipulate the domain, range, and using the right equations to create the shapes I wanted. A nice review and extension of prior knowledge and in the process of being creative, students are deepening their understanding of the equations and their graphs.  Here’s a link to all the ClassPad.net examples below (free CP.net usable activity):

Parametric equations only example (the Classpad.net GIF uses a slider to change the snowflake):

Snowman using circle equations, linear equations with limited domain, and parabolas with limited domain. Snowflake with circle equations, linear equations with limited domains, plotted points and parametric equation. Christmas Tree with plotted points, polygons (using geometry tools). 