The COVID-19 epidemic had caused one of the most significant disruptions to the global education system. Many educational institutions faced sudden pressure to switch from face-to-face to online delivery of courses. The conventional classes are no longer the primary means of delivery; instead, online education and resources have become the…

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)

This report illustrates a simple, short, yet relatively little known partial check on addition that elementary school pupils can be lead to discover, and later taught to understand. The process can also be used for subtraction and is viewed as more useful than the traditional check of casting out nines. (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)

Explores the use of computers for teaching mathematical models of transposition ciphers. Illustrates the ideas, includes activities and extensions, provides a mathematical model and includes computer programs to implement these topics. (MVL)

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)

Ways to combine the strengths of teacher and computer are suggested. Multiplication concepts and an algorithm for multiplication are taught in the same lessons. The computer is used as an electronic chalkboard to teach at a semiconcrete level. The computer program is included. (MNS)

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)

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)