Calculus

This lesson walks students through a classic optimization problem involving building a (lidless) box from a sheet of paper. The lesson uses a worksheet in The Geometer’s Sketchpad.

Students will explore some classic optimization problems using The Geometers Sketchpad. This lesson has students begin by exploring a pattern, then has them extrapolate their findings into a generalization about inscribed shapes. Extension questions are included.

This is a fun problem that has students investigate how many triangles they can create out of rods of various lengths. Students use the triangle inequality, and look for a pattern in their solutions.

Students find the area of an annulus and find that the result is unexpectedly intuitive.

A second problem to investigate the concept of linear programming

Students use the idea of volume of a cylinder to figure out the length of a single fiber of cotton candy.

A worksheet with five common optimization problems.

This lesson will explain the concept of a limit from various points of view.

This resource is a list sorted by subject and individual lessons that include web pages for students to obtain extra practice.

This course is divided into two semesters and is designed to acquaint you with calculus principles such as derivatives, integrals, limits, approximation, and applications and modeling. During this course you will gain experience in the use of calculus methods and learn how calculus methods may be applied to practical applications. Upon completion of this course you will: be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal understand the connections among these representations understand the meaning of the derivative in terms of a rate of change and local linear approximation and be able to use derivatives to solve a variety or problems understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems understand the relationship between the derivative and the definite integral as expressed in both parts of the fundamental theorem of calculus