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)

Presents alternative equation-solving procedures that emphasize an examination of the steps or operations necessary to perform a calculation, followed by the inversion of those steps. The approach is especially attractive to students with limited mathematical skills. (Author/MKR)

Shortcuts to use when performing operations with the calculator are given. Algorithms discussed include reciprocals, powers, parentheses, infinite series, and synthetic division. (MP)

The calculator is used to explore the distributive property of a unary operator over a binary operator. This is an extension of an earlier paper. The emphasis is on student discovery of the property for various combinations of the operators. Instructional material contained in the report include a reference sheet of questions for potential…

Solutions to difficult equations are illustrated with numerical techniques that can be used easily on calculators. Flowcharts and programs for computers and calculators are included. (MP)

Investigating properties and characteristics of unary operations is shown to be facilitated by using calculators. Several avenues for instructional exploration are suggested and examples given. These include questions relating to relations, inverses, commutativity, distributivity, and iterations. A discussion of the calculator algorithm for…

A program in BASIC which decomposes fractions is provided. Activities related to student use of the program are listed. (SD)

Topics covered include alternate methods for finding LCM and GCF, imaginative word problems, and a primes-breakdown method of factoring quadratics. (MP)

A classroom photography activity is outlined that motivates learning of mathematical topics such as estimation, geometry, ratio, measurement, and algorithms. (MP)

The algorithms for finding cube roots is approached by slicing a cube. (SD)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

The calculator is used to investigate properties and characteristics of certain unary operations. These include how a number is related to the number resulting from a unary operation and the result of two unary operations. A discussion of the calculator algorithm to accomplish a series of unary operations is given. Record sheets to summarize…

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)

Presents cooperative computing activities in which each student plays the role of a switch or processor and acts out algorithms. Includes binary counting, finding the smallest card in a deck, sorting by selection and merging, adding and multiplying large numbers, and sieving for primes. (16 references) (Author/MKR)

Presents the algorithm to approximate square roots as reproduced from the 1579 edition of an algebra book by Rafael Bombelli. The sequence of activities illustrates that the process of understanding an original source of mathematics, first at the algorithmic level and then with respect to its mathematical validity in modern terms, can be an…