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 \(z\). )

Students use their arms to act out stationary and non-stationary states of a quantum particle on a ring.

Students use their arms to act out two spin-1/2 quantum states and their inner product.

Students consider the dimensions of spin-state kets and position-basis kets.

Students are asked to "find the derivative" of a plastic surface that represents a function of two variables. This ambiguous question is designed to help them generalize their concept of functions of one variable to functions of two variables. The definition of the gradient as the slope and direction of the "steepest derivative" is introduced geometrically.