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)

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

The following ideas are shared: (1) a low-stress subtraction algorithm that eliminates the traditional borrowing process, and (2) an approach to graphing circular functions that looks at the process of modifying simple functions as a series of shifting, sliding, and stretching adjustments, with its biggest advantage viewed as its generality. (MP)

Symbols and shapes used in flowcharting are defined, reasons for incorporating flowcharts into instructional activities are listed, and eight different flowcharts are presented. (DT)

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)

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)

Upper elementary school students created their own algorithms for finding products of whole numbers. The algorithms were similar to familiar ones for finding products involving 9 and 11. (SD)

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

An approach is suggested to the use of sets of practice exercises that is more like the actual use of computation by adults and may be more effective in attaining accuracy and speed. (MP)

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

Helping teachers to build a strong bridge from concrete experiences to algorithms is the focus. A detailed sequence of activities is described. (MN)

Instructional sequences are presented for teaching two-digit multiplication and division with one- and two-digit divisors using a base-oriented approach. (MN)

A teaching sequence provides a guide to instruction on initial concepts of fractions, equivalent fractions, and addition with fractions. (MN)

Instruction on properties of whole numbers, the meanings of operations on whole numbers, symbolic representation and algorithms for completing these operations is discussed. Many activities appropriate to each of these topics, and suitable for primary school children, are presented. (SD)