Activity Overview
What is the difference between a parameter and a variable? This activity introduces the notion of a parameter through two pairs of parametric equations that result in the same Cartesian equation, highlighting the additional information provided by the parameter. Variable isolation and animation support visual and conceptual development models for understanding the mathematics concepts in this activity.
Objectives
Understand the difference between a parameter and a variable and the additional information provided by a variable in the case of parametric equations.
Vocabulary
Parameter, variable
About the Lesson
Students begin by exploring the relationship between x and t. The parameter t is changed using a slider and x is naturally plotted along the x axis. The y variable and its relationship with t is then explored and finally the two elements brought together with the joint coordinate being plotted as t is changed. This relationship is then explored by changing the relationship between x, y and t, however the same end result is produced providing evidence that the parameter provides additional information that a standard Cartesian equation cannot.