A lesson taught by an American teacher to Chinese students is described. The lesson was a "Silent Lesson in Mathematics" (SLIM) presentation concerning the guessing of functions. (MK)

The topics of angle construction, angle trisection, and regular polygon construction with only a straightedge and compass are discussed for angles with integer measure. (MP)

A method is developed for finding the equations of two circles that intersect at points with integral coordinates. Such equations are useful for the introducing systems of quadratic equations. (MP)

Two units are developed that provide the student with experience in constructing auxilary lines that are often needed in formulating geometric proofs. (MP)

An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

Methods are discussed for transforming sets of data so that properties of the scale used to obtain the data are preserved. A list of suggested activities is included. (MP)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

A mathematics department head's experiences with developing and supervising an open classroom department are related. (MP)

A unit on programing is discussed in terms of limitations due to lack of hardware and benefits resulting from using a microcomputer in the classroom. (MP)

Models and diagrams are described that demonstrate certain geometrical theorems and relationships. The use of models is suggested as preceding the more formal proof. (MP)

A detailed proof is given of a theorem that characterizes the vertex sequence of any convex polyhedron and establishes the existence of only 13 Archimedean solids. (MP)

Some reflections by a teacher include personal satisfaction, relevance of mathematics, reasons for teaching, and the unique contributions of mathematics. (MP)

An example is given of a class of problems whose solutions require the use of a scientific calculator in order to plot the graphs. (MP)

A technique is given for solving problems involving a balance scale and a number of coins which are to be sorted in a certain number of weighings. (MP)

A number of questions are posed that can be answered with the aid of calculus. These include best value problems, best shape problems, problems involving integration, and growth and decay problems. (MP)