### Summary

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?

### Snapshot

**Engage**

Students will brainstorm prior knowledge related to circles and triangles.

**Explore**

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

**Explain**

Students will determine the relationship between pi and circumference.

**Extend**

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

**Evaluate**

Students will reflect on their learning and feelings of learning.

### Materials

Rulers

Protractors

String

Scissors

Colored pens or pencils

Copies of the Explore Circle handout (one for each student)

Copies of the Circle Knowledge student handout (one for each student)

### Engage

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

### Explore

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.