Programs (using Logo) developed by children to produce multiples, the Fibonacci series, and square numbers are presented, with graphical representations of functions introduced. Another investigation involves drawing a circle using turtle graphics. (MNS)

Five-frames are proposed as manipulative material to increase children's ability to identify the number of objects without direct counting. How to use frames and beansticks to construct basic facts without counting is discussed. (MNS)

Brief articles are included on dropping perpendiculars, working with rational exponents, and finding the square root with base 10 blocks. (MNS)

Included are brief articles discussing chain letters as an example of exponential growth, a box technique for factoring, and integrating the inverse of a function whose integral is known. (MNS)

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)

Some answers are given to questions that teachers ask about the preprimary mathematics program. A point of view is presented and a model provided outlining a scope and sequence for choosing experiences for children about five years old. (MNS)

Four worksheets for levels one-eight are included. Practice on addition, multiplication, fractions and decimals, and integers is provided through activities involving puzzling patterns. (MNS)

A "neat and general" divisibility algorithm for prime numbers is presented. Five illustrative examples are included. (MNS)

Five exploratory activities arising from work by sixth-grade students are described. They concern geometric ideas and number concepts, including fractions. Illustrations are included. (MNS)

An example is given for deriving mathematical content from a game. The game and eight activities are included for both basic and advanced versions. (MNS)

Different uses of numbers in natural language and mathematics is argued to have consequences for children's learning of numbers and for primary-grade textbooks. A study using particular properties of Hebrew indicates a crossing of the two language systems in children's reading of an arithmetic textbook. (MNS)

Four experiments are presented to support the theory that the rule system governing the law of large numbers is not tied to a content domain, and that it can be improved by formal teaching techniques. The experiments showed that statistical training enhanced everyday reasoning. Test problems and objective example problems are appended. (LMO)

This teaching guide contains material, for students in grades 6-9, in which a calculator is used in exploring and developing generalizations about quotient patterns generated from various polygons drawn on a hundred square. Includes suggested procedures and four ready-to-duplicate student worksheets. (JN)

Interpretation of rational numbers as fractions, ratios, percentages, and quotients of integers are discussed. Then coding conventions are noted, and equivalence classes are described. Finally, density and order are discussed. (MNS)

Some number investigations on the multiplication table are provided by a sequence of four activity sheets. Beginning with examples of triangular and square numbers, the activities lead to the generalization. (MNS)