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Several Mathematical Problems Useful for Teaching

Several examples useful for teaching are considered in this article. Among those, using a content of the problem to build a meaningful solution, calculus in derivation, elaborating a new concept, extensions of the known rules, and interpretation of the results. The examples include algebraic problems, solution for quadratic equations and their systems, volume integration by the disk and shell methods, interpretation for the integral of distance by time, connections between the derivative and antiderivative of a function, some special features of integrals and double integrals. These examples help to a better understanding of the topics, and can be useful to instructors, and undergraduate and graduate students.