Whether you teach middle school math, geometry or Pre-Calculus, circles are likely to be a subject.  Or you might be just touching on circles as part of your Pi Day celebrations on March 14th.  I am teaching pre-Calculus and we recently entered our trigonometry unit.  Let me start by saying I love trigonometry.  It is, for me, the perfect blend of algebraic logic and geometric principles.   I'm going to share what we did with Unit Circles, but be sure to check out the links at the bottom for a wealth of circle activities for different mathematic levels.

In the past I have rushed through unit circles.  Students have constructed radians, made quick connections and then we moved on.  Basically, students have memorized the circle.  I noticed that students rarely made the deeper connections about why trig functions are what they are, and the unit circle can help with this.  The unit circle helps students:

• visualize why trig functions are what they are
• find ratios
• stop memorizing (well, in the project we did)
• help for finding pythagorean identities.
We took a full week on the unit circle with a multi-step project.  By the end my students (in their words) "got it."

• Part 1: Students created three different unit circles, each highlighting one angle.  Students derived the points as well as the trig values.
• Part 2: Students created one larger circle that has all the angles and points.

• Part 3: Students created a design out of their circles.  The one shown to the left is from a series of "monster" circles.  Other students created wheels out of their circles and one even made stained glass windows.  It was great fun to give students a creative outlet and to see what they developed.
• Part 4: Students generated a table of relationships from the unit circle.  This is a handy reference tool.
We did this entire project in our interactive notebooks.  I thought about having students make poster boards so they could be shared easily, but I wanted each student to have a handy reference.  We shared the projects in small groups.  Students enjoyed seeing each other's creations as much as developing their own.