Lenape Regional High School District Discovering Radians In Geometry you learned how to measure angles in degrees. Using degrees there is no relationship between the size of the circle (the radius) and the 360° around the circumference. To accommodate this, there is a measurement called a RADIAN which relates directly back to the radius of the circle. We will use the following activity to discover what a radian is.
Pick up the following materials
 A bag of candy
 a compass
 a ruler
 a blank sheet of paper
(some of the bigger candies will need multiple sheets taped together)
 A protractor
Choose 7 pieces of candy and place them side by side on the paper. This will represent the radius of your circle. Use the ruler to draw the radius. (Make sure that you have enough space on your paper to form a circle – this may require taping paper together.)
Use the compass to draw your circle with the radius that you just discovered. Center the circle on an x-y coordinate plane.
Starting where the circle meets the positive x-axis, wrap your 7 pieces of candy around the outside of the circle, placing the diameter of the candy directly on the circle.
Make a mark on the circle at each endpoint of the 7 pieces. This distance is ONE RADIAN. Draw the a line back to the center of the circle from where you stopped (making a central angle). Then start again from that point.
Continue until you can no longer fit the candy on the circle.
How many (complete) times were you able to fit the pieces of candy around the circle? How many pieces of candy fit in the small segment that was remaining?
Express the number of times you could fit the candy as a: Mixed number
Improper Fraction (unsimplified) Decimal
Do you recognize any of these numbers?
(simplified)
~3~

Follow up questions
1.) How many radians are in 1 circle?
2.) Calculate how many degrees are in 1 radian.
Measure the size of each radian with your protractor. What did you get?
3.) Consider the distance around a circle. We call this the and its formula is . How does that compare to what we just discovered as a radian?