In this lesson, students learn vocabulary for describing circles precisely (MP6). Students move from the informal idea of a circle as “a round figure” to the more formal definition that a circle is the set of points that are equally distant from the center, enclosing a circular region.

Students discover characteristics of a circle by examining examples and non-examples. They develop the idea that the size of a circle can be measured by its diameter, radius, circumference, or the enclosed area.

The last activity provides an optional opportunity for students to gain experience drawing circles with a compass (MP5). This helps prepare students for future lessons when they will use a compass to draw triangles with given side lengths. For classrooms that do not have access to compasses, a digital version of the activity is provided.

A note on using the terms diameter and radius:

A diameter is a line segment that goes from one edge of a circle to the other and passes through the center. A radius is a line segment that goes from the center to the edge of a circle. However, we also use the words diameter and radius to mean the lengths of these respective segments. Therefore, we will often use phrases like “What is the diameter of the circle?” to mean “What is the length of a diameter of the circle?”