What is a Radian?
Equipment list
String (cut to various lengths: 3 ft, 4 ft, 5 ft, or 6 ft)
Measuring tape
Tape (or chalk for outdoor surface)
Chalk (optional, for drawing on pavement or gym floor)
Explanation
Objective: Help students discover what a radian is by physically measuring how many times the radius fits around a circle.
Group Setup:
Students form groups of 3.
Step-by-Step:
Measure the Radius
Each group cuts a piece of string to a specific length (assigned or chosen).Draw the Circle
Tie chalk to one end of the string.
One student holds the other end at a fixed center point.
Another student walks in a circle, keeping the string taut, to draw the full circle.
Mark the Radius
Draw a straight line from the center to the edge (this is the radius).
Measure in Radians
Starting at the point where the radius touches the circumference, lay the string (the radius length) along the curve of the circle.
Mark each segment until you've circled back to the starting point.
Record Results
Count the number of segments.
Students should observe approximately 6.28 segments, representing 2π radians around the circle.
Concept Reinforcement:
This activity provides a kinesthetic understanding that the circumference = 2π × radius, and that one radian is the angle created when the arc length equals the radius.
Variations
Assign different string lengths to groups and compare results.
Bring the activity outside for more space and a break from the classroom.
Progression
Begin with physical measurement to build intuition.
Transition to calculating radian measures mathematically.
Introduce arc length and sector area formulas.
ASK ID 2025-04-30-004-E