# Longer Activities

- The Crusty Loaf of Bread: An Exploration of Area of a Surface of Revolution This write-pair-share activity for Calculus II students involves a hypothetical hemispherical loaf of bread with a 12-inch diameter that has been sliced into twelve one-inch-thick slices.
- How Much Work is Required: Intuition vs. Mathematical Calculation This classroom activity presents Calculus II students with some Flash tutorials involving work and pumping liquids along with a simple question concerning the amount of work involved in pumping water out of two full containers.
- Mathematical Curve Conjectures In this write-pair-share activity, a six-foot length of nylon rope is suspended at both ends to model a mathematical curve known as the hyperbolic cosine.
- Partial Derivatives: Geometric Visualization This write-pair-share activity presents Calculus III students with a worksheet containing several exercises that require them to find partial derivatives of functions of two variables.
- Riemann Sums and Area Approximations After covering the standard course material on area under a curve, Riemann sums and numerical integration, Calculus I students are given a write-pair-share activity that directs them to predict the best area approximation methods for each of several different functions.
- U.S. Population Growth: What Does the Future Hold? Students are presented with a ConcepTest, a Question of the Day and a write-pair-share activity involving U.S. population growth. The results are quite revealing and show that while students may have learned how to perform the necessary calculations, their conceptual understanding concerning exponential growth may remain faulty.
- Volumes of Solids of Revolution This write-pair-share activity presents Calculus II students with a worksheet containing several exercises that require them to find the volumes of solids of revolution using disk, washer and shell methods and to sketch three-dimensional representations of the resulting solids.