The evolution of Archimedes' method is traced from its geometrical beginning as a means to approximate pi to its modern version as an analytical technique for evaluating inverse circular and hyperbolic functions. It is felt the web of old and new algorithms provides considerable instructional material, and ideas are offered. (MP)

An unusual algorithm for approximating square roots is presented and investigated using techniques common in algebra. The material is presented as a tool to interest high school students in the logic behind mathematics. (MP)

A model of the division algorithm is described which relates step-by-step to the standard algorithm. Use of the model in instruction requires the distribution of a special worksheet. The focus of the instruction is on students sharing some amount of money equally among several friends. (MP)

Typical instruction of the division algorithm fails to justify why one brings down a number during the process. The construction and use of an aid is described which can be used to help explain the process of division to students. The aid emphasizes place-value aspects. (MP)

Five problems on the generation and study of prime and related numbers are discussed. Solutions to the problems posed will be in next month's presentation. (MP)

An approach to teaching pupils the long division algorithm that relies heavily on a consistent and logical approach to estimation is reviewed. Once learned, the division estimator can be used to support the standard repeated subtraction algorithm. (MP)

Interesting mathematical questions that require computations involving fractions, percentages, and decimals are presented. The material is designed for students in the middle school grades, but many of the ideas could be used with higher or lower level pupils. (MP)

The discrete mathematics topics of trees and computational complexity are implemented in a simple reliability program which illustrates the process advantages of the PASCAL programing language. The discussion focuses on the impact that reliability research can provide in assessment of the risks found in complex technological ventures. (Author/JJK)

The trick focuses on a theorem that the sum of the digits of the difference between any natural number and the sum of its digits is divisible by nine. Two conditions of using the trick are noted. The reason that the theorem works is established through a proof. (MP)

An example of a lesson involving calculators that focused on calculator use is given. An examination of the traditional algorithm by the students led to student-directed investigations. (MP)

A subtraction algorithm that does not involve borrowing is presented and called the residue method. It has been taught in junior and senior high school classes and preservice and inservice classes for teachers. The method has helped in classes where arithmetic in other bases is presented. (MP)

The factors which have a major impact on the success in producing effective readable text in both the content as well as to the way it is presented are outlined. A discussion of the objectives of the learner and the characteristics of the text that facilitate student learning is presented. (KR)

An organized series of steps designed to help students solve related rate problems often found in beginning calculus is presented. Two example problems are taken through five steps of solution. (MP)

Described is a way to use knots to relate a three-dimensional object to a two-dimensional representation of the object. The results are used to produce an algorithm or rule to explain a general case. Included are examples, diagrams, procedures, and explanations. (KR)

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)