Authentic Lessons for 21st Century Learning

My Unit Is a Circle

The Unit Circle / Trigonometry

K20 Center, Alexandra Parsons | Published: September 18th, 2020 by K20 Center

  • Grade Level Grade Level 11th, 12th
  • Subject Subject Mathematics
  • Course Course Precalculus
  • Time Frame Time Frame 1-2 class period(s)
  • Duration More 90 minutes


This lesson is intended to introduce the unit circle, leading into the concept of radians as a unit rather than degrees. This lesson is intended to introduce the concept at the beginning of the unit, but it could also work as remediation if students are just not getting it.

Essential Question(s)

How are units connected but also separate?



Students will brainstorm prior knowledge related to circles and triangles.


Students will investigate the relationship between the radius and circumference of a circle.


Students will determine the relationship between pi and circumference.


Students will insert special right triangles into the circle and determine the relationships.


Students will reflect on their learning and feelings of learning.


  • Rulers

  • Protractors

  • String

  • Scissors

  • Colored pens or pencils

  • Copies of the Explore Circle handout (attached; one per student)

  • Copies of the Circle Knowledge handout (attached; one per student)


Put students into pairs (using the Elbow Partners strategy is super easy and quick, but any grouping strategy will do) and have them get a fresh piece of paper wherever they take notes.

Set a timer for 5 minutes, and tell students they need to Tell Me Everything about:

  • Circles

  • Special Right Triangles


Pass out a copy of the Explore Circle handout to each student. Students also need a ruler, string, scissors, and a protractor.

  • Tell students to carefully determine the exact center of the circle and draw a straight line representing the diameter.

  • Once the center and the diameter are denoted, tell students to cut a piece of string the length of the radius.

  • Starting from one point of the diameter, tell students to lay their string around the circumference of the circle, making a small mark where it ends. Have them repeat under they have gone around the entire circle.