By Tim Hickey, posted May 23, 2016 —

Cutting wood with a band saw is just plain fun. I have not found a trigonometry student yet who disagrees. This is one of the reasons that I have built the Trigonometry Miniature Golf project into my Trigonometry curriculum. The concept is simple, and I have seen a wide variety of versions of this  idea over the years in different geometry and trigonometry classrooms, such as the “Back Page: Virtual Miniature Golf” article by Edwards and Quinlan article (MT September 2015, Vol. 109, Issue 2). The current version that I use fits well into my unit on inverse trigonometry.

To begin the activity, students are given a handout with the layout of a miniature golf hole printed on it. They are given rulers and asked to draw the path of the ball that would result in a hole in one. The only condition is that the ball must ricochet off a wall at the same angle at which it hits the wall. I choose to not provide protractors to the students. The downside of this is that their angles will not be precise.

There are two upsides, however, to withholding protractors for this activity. First, doing so requires them to exercise their powers of estimation. Specifically, they must be able to draw the ball’s path in a way that reasonably meets the bouncing requirement, but I also make sure to ask each group to predict the exact measure of the angle in degrees and in radians.

Second, it lends itself to the topic of inverse trigonometry. After they have drawn the path of the ball, they use rulers to measure distances, then they write inverse trigonometric equations and solve for the angles at which the ball hits and bounces off each obstacle. Students are allowed to use calculators to find the angles and are asked to reflect on their estimated values. The first few times that I taught Trigonometry, I provided a few more golf holes and then moved on to the next topic.

But for my Trigonometry classes now, the fun is just beginning. Each group is tasked with designing and building their own miniature golf hole model. They are allowed to use any materials. Most of my students like to go to the woodshop so that they can use the various saws to make their models. This year, some designed and created their models using the 3D printer. In both cases, students bump into all sorts of interesting mathematical challenges and ideas and have a ton of fun along the way.

Providing opportunities for students to be creators and makers in the mathematics classroom is a path not only to deeper learning, but also to joy and inspiration. They might also pick up some woodworking skills along the way.

Tim Hickey is a Nationally Board Certified Teacher and the math department chair at Monticello High School in Charlottesville, Virginia.