Day 1:  Definitions

Objective: Have students understand the common definitions associated with circles such as radius, chord, and tangent, as well as the definition of a circle itself

Lesson:

Key Definitions:

- Circle:  the set of all points in a plane equidistant from a given point called the center of the circle - The interior of a circle is all the points inside that circle - The exterior of a circle consists of all points outside the circle
- Radius:  the distance, r, from any point on the circle to the center of the circle - Two circles with the same radius are called congruent circles - Diameter:  the longest distance across the circle, the length, d, of the segment passing through the center of the circle with both endpoints on the circle, d = 2r - Chord:  a segment having both endpoints on the circle
- Circumference:  the distance around the circle, the perimeter, 2*pi*r = pi*d
- Area:  the interior of the circle, pi*r2
- Central Angle: an angle with endpoints on the circle and vertex at the center of the circle
- Inscribed Angle: an angle with endpoints on the circle and vertex on the circle
- Tangent:  a line perpendicular to the radius which intersects only one point on the circle - The point of tangency is the point where the tangent line intersects the circle - Secant:  a line passing intersecting two points on the circle
- Two circles that intersect at one point are called tangent circles         - Two circles with the same center are called concentric circles

Begin the class by having the students discuss their ideas about circles. Have the students define a circle and its radius and diameter as well as area and circumference. Then begin going over the remaining key definitions with the students, having them discuss what they believe the definitions of chord, secant, and tangent to be. Finally, with the assistance of the students, write formal definitions for circle, radius, diameter, chord, circumference, area, tangent, and secant and then label these concepts on a diagram.

Activity: Have the students discover the value of pi. Have a large selection of circular objects such as jars or cans or lids of different sizes so that each group can have at least four different objects. Form groups of approximately four students, give each group a tray containing a ruler, string, and at least four circular objects. In their groups, the students will use the string and the ruler to find the measure of the circumference of the object and the diameter of the object. Then the students will find the ratio of the circumference to the diameter, and this should give the approximately the value of pi. Click here for a sample activity worksheet.

Conclusion: Discuss the activity with the class, having them conjecture as to why this activity produces the value of pi.

Developed by Katherine Huffman