Sage is an open-source software package that can be used in many different areas of mathematics, ranging from algebra to calculus and beyond. One of the most exciting pedagogical features of Sage (http://www.sagemath.org) is its ability to create interacts--interactive examples that can be used in a classroom demonstration or by students in a…

In one school, algorithmic development has been infused in the mathematics curriculum. An example of what occurs in mathematics classes since the teachers began using the computer is given, with two students' conjectures included as well as the algebraic justification. (MNS)

Described is a computer program that uses an interesting matrix method to generate Pythagorean triples. Program listings and output for two programs are included. (MNS)

Microcomputer programs that help students calculate permutations and combinations are developed. Listings of five programs are included. (MNS)

The progression from simple interest to compound interest leads naturally and quickly to the number e, involving mathematical discovery learning through writing programs. Several programs are given, with suggestions for a teaching sequence. (MNS)

Presents three problems, each with a computer solution in BASIC programming language: (1) finding sum equals product for three-digit numbers; (2) finding cases of improper cancellation that give a correct answer; and (3) finding perfect numbers. Some suggestions for further investigation are included. (JN)

Described is a simple algorithm that can be used for the input, arithmetic manipulation, and output of large integers in their exact representations. Three BASIC programs are included that apply this method to the problem of multiplication of large integers, computation of factorials, and the generation of palindromic integers. (MNS)

Two relevant applications of mathematics and computer science are presented: International Standard Book Numbers (ISBN) that appear in textbooks and universal product codes that appear on grocery products. A computer program is included. (MNS)

Abundant and deficient positive integers are investigated, with a computer program listed. (MNS)

Included in this section are brief articles on an algebraic puzzler, periodic decimal fractions with computers, and the arrow method of teaching logarithms. (MNS)

Programs are listed for integer powers and fractional powers, with discussion of how to use them in instruction. (MNS)

How the computer can become an integral part of mathematics learning at the junior high school level is discussed in terms of mathematics processes. The rationale for activities involving programmed processes and examples of them are given. (MNS)

Suggested are investigations of rational numbers and their decimal representations where a computer generates the data for explorations. Conjectures and two program listings are included. (MNS)

Brief articles are included on exploring mathematical patterns, with two computer programs listed for finding happy numbers; a simple periodic function in trigonometry; and comments on humorous student errors. (MNS)

Activities to extend the core curriculum through the study of the periodicity of rational numbers to help students develop calculator and research skills are presented. Four worksheets are included, to be used as discovery activities. A computer program is listed, as well as examples of periodic pictures. (MNS)