Identifying the larger (L), smaller (S) and difference (D) of two real numbers, and then selecting the appropriate relationship between L, D, and S can help students solve algebra word problems. (SD)

Algorithms for generating random numbers are discussed along with disadvantages. A program for a programable calculator is given that overcomes those disadvantages. (MP)

Presents an example of mathematics from an algorithmic point of view, with emphasis on the design and verification of this algorithm. The program involves finding roots for algebraic equations using the half-interval search algorithm. The program listing is included. (JN)

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

Common mistakes pupils make when adding fractions are categorized and analyzed. (MP)

The article presents a general test for divisibility that includes composite numbers and shows that such a test can be used to determine divisibility by several numbers simultaneously. (MK)

An algorithm for multiplying natural numbers is described. The algorithm provides a chance for some unusual drill and might serve as an enrichment topic. (MK)

The teacher's guide for the second unit of this SMSG series covers the two chapters in Unit 2 of the student text on algorithms and flow charts and on problem formulation. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed,…

One hundred seventy-six seventh grade students underwent a recorded interview where each was given a set of computational exercises and asked to say aloud his thinking as he worked them. The most frequently used strategies in computations with whole numbers and fractions are described in detail, an analysis of the nature of wrong answers is…

When two methods of transforming numbers from one base to another were taught sequentially, the first interfered with learning of the second. (SD)

The patterns of the coefficients in the expansion of (x + y +z)n are discussed, and a recursive property is developed as a generalization of the Pascal triangle. (MP)

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

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)

Considered are what discrete mathematics includes, some parallels and differences between new math and discrete mathematics (listed in a table), and lessons to be learned. A list of references is included. (MNS)