Students are given a worksheet in a dynamic geometry package. The construction, hidden from the students, is as follows: given two points A and B, construct the line through them. Take a third point, P, and construct H, the foot of the perpendicular from P to line AB. Students can drag any of the points. The problem is to determine the relationships among the points. Follow-up: When are two functions equal?
Students struggle with the standard definition of function. This exercise gives students a chance to explore the idea of a function without algebraic symbolism confounding the issue. They directly see covariation by moving one point and seeing how the others react.