A compass can be used to draw a circle. But a compass is also a tool for comparing lengths. That is one way to view drawing a circle. The compass “finds” all points in the plane that are the same distance from a given point (the point marked by the sharp tip of the compass).
In each of the following constructions, start by posing the problem and seeing if some of the students can figure them out for themselves. If you are working with a group, somebody surely will, and then they will teach each other.
How can you construct an equilateral triangle? Start with a line segment as one edge of the triangle. Place the compass point at one end of the segment and swing it around in a circle. The second side of the equilateral triangle must be some radius of this circle. Repeat for the other end of the line segment. Where the two circles cross is the same distance from each endpoint of the segment as the segment is long.
How many degrees is each angle of an equilateral triangle? The three angles are equal; the angles add up to 180°; therefore each angle is 60°.
Try drawing a circle, then drawing an equal circle centered on some point on the original circle, then reposition the compass at the intersection points and repeat the process. (This is everyone’s favorite construction!)
It is interesting that exactly six equal circles fit aroung the original circle. This is because the first two circles reproduce the equilateral triangle construction; the angles of an equilateral triangle are each 60°; and 6 x 60° = 360°. For some kids this “flower” pattern is the lesson. Follow up by coloring it or extending the pattern by drawing circles at each of the new intersection points, etc.
Other spinoffs: Find equilateral triangles. Find a regular hexagons. Split the arcs to get a 12-sided figure (dodecagon).