Introduces a room air-exchange activity designed to assess student understanding of the concept of volume. Lists materials for the activity and its procedures. Includes the lesson plan and a student worksheet. (KHR)

Presents a series of questions designed to help convince students that mathematics is useful, current, and newsworthy through solving systems of linear equations in real world contexts. (KHR)

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Reports findings from the team teaching of a course in mathematical problem solving designed for secondary and community college teachers to clarify the concept of ."ecessary and sufficient" conditions. Discusses assigned problems and students' incorrect interpretations. Student interpretations showed how simple mistakes can often lead to rich…

Describes the mathematical needs of electricians and in so doing, indicates where the trainers of electricians strike a balance between skills, understanding, and problem solving. (KHR)

Discusses how to help students avoid some pervasive reasoning errors in solving cumulative percent problems. Discusses the meaning of ."%+b%." the additive inverse of ."%." and other useful applications. Emphasizes the operational aspect of the cumulative percent concept. (KHR)

Presents an active way for students to learn about SAS, SSS, ASA, AAS, and HL in determining congruent triangles. (Author/NB)

Describes a combinatorics problem involving pizza toppings. Includes three activity sheets. (Author/NB)

The ability to transpose music into any key is assumed by musicians. Such was not always possible. Addresses the role of nth roots in tempering the piano keyboard. (Author/NB)

Uses the spot problem to illustrate the importance of inductive and deductive reasoning and the connections among algebra, graph theory, geometry, and combinatorics. (Author/NB)

Illustrates the varied mathematical reasoning involved when a geometric construction problem is solved with three different manipulative tools. (Author/NB)

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

Discusses ratio analysis by which investments may be evaluated. Requires the use of fundamental mathematics, problem solving, and a comparison of the mathematical results within the framework of industry. (Author/NB)

Presents a logical reasoning problem pivotal to the novel "Harry Potter and the Sorcerer's Stone" and discusses it at two levels. (Author/NB)

Describes the history of the unsolved moving sofa problem, presents one possible solution, and gives several suggestions for how this problem can be used in the classroom. (Author/NB)