This textbook takes the learner from the basic definition of slope through derivatives, integrals, and vector multivariable calculus. Each section is composed primarily of examples, with theoretical introductions and explanations in...

Making a clear connection to algebra concepts helps learners understand the definition of a derivative. The lesson begins with looking at limits of simple linear and rational functions, and leads to the definition of the...

Local linearity isn't the first thing that comes to mind to start off an AP® Calculus course. A scholarly article discusses one possible beginning to the AP® Calculus course: investigating and introducing derivatives through activities...

Of course, calculus can help you build the largest box possible. Scholars play a digital game to gain familiarity with situations where optimization would be appropriate. After gaining a solid conceptual understanding of optimization,...

Derivatives are useful for many things — they can even keep track of particle motion. An informative lesson plan provides an introduction to the idea of the second derivative in particle motion. Class members determine the...

The inverse of matter is anti-matter, so the inverse of a derivative is an antiderivative. The lesson introduces antiderivatives and indefinite integrals to the class along with the notation for integrals. Groups work together to find...

Finding the critical numbers of a function can be extreme. The lesson introduces the Extreme Value Theorem to the class with a graph. Pupils then have an opportunity to practice determining the values using an algebraic function.

To work through the complexity of coordinate geometry pupils make the connection between the coordinate plane and the complex plane as they plot complex numbers in the 11th part of a series of 32. Making the connection between the two...

What if I can no longer justify area by counting squares? Lead a class discussion to find the area of a rectangular region with irrational side lengths. The class continues on with the idea of lower approximations and...

As part of an investigation of transformations of exponential functions, class members use Newton's Law of Cooling as an exponential model to determine temperature based on varying aspects. The resource makes comparisons between...