Assessment Problem:

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?

Mathematical Issues:

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.

Domain:

Patterns & Functions

Theme:

Functions

Common Core Standards:

F-BF: Building Functions

Technology:

Geometer's Sketchpad, Geogebra

Research References:

Falcade, R., Laborde, C., & Mariotti, M. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317-333.