group Small Group Activity
Students draw the 3D graphs of equations using three variables. They make choices for drawing a stack of curves in parallel planes and a curve in a perpendicular plane (e.g. substituting in values for \(x\), \(y\), or \(z\). )
In this small group activity, students determine various aspects of local points on an elliptic hill which is a function of two variables. The gradient is emphasized as a local quantity which points in the direction of greatest change at a point in the scalar field.
This small group activity using surfaces introduces a geometric interpretation of partial derivatives in terms of measured ratios of small changes.
Students work in small groups to identify locations on their surface with particular properties.
The whole class wrap-up discussion emphasizes the equivalence of multiple representations of partial derivatives.