Learning activities are given for instruction in the skill of associating numbers with sets of dots, a skill intermediate between counting and higher number concepts. (MP)

Describes an activity in which students, grades 7-12, explore patterns and properties of repunits, an integer written as a string of ones. Includes extensions for exploring algebraic justifications. (MKR)

Presented are the mathematical explanation of the algorithm for representing rational numbers in base two, paper-and-pencil methods for producing the representation, some patterns in these representations, and pseudocode for computer programs to explore these patterns. (MNS)

This booklet offers teacher instructions and student worksheets on number activities for gifted primary grade students. Three sections are included: (1) "moving numbers" which asks students to supply the missing member or members of addition and subtraction equations; (2) "number trails," which involve the completion of number…

A visual model of fractions, the tower of bars, is used to discover patterns. Examples include equalities, inequalities, sums of unit fractions, sums of differences, symmetry, and differences and products. Infinite sequences of numbers, infinite series, and concepts of limits can be introduced. (DC)

Practice on computation is provided using new and novel situations, with discovery of number patterns a bonus of the computation. Activities with disguised addition and multiplication tables for whole numbers and integers are presented for varying levels. (MNS)

Activities with triangular, square, pentagonal, hexagonal, and octagonal numbers are briefly discussed. (MNS)

The relation between the area of a rectangle and its perimeter is clarified by looking at patterns. Several examples involving rectangles with integral sides are presented. (MNS)

A familiar procedure for generating magic squares is reviewed. A surprising pattern is noted. (MNS)

Simple patterns both in mathematics and music are discussed. Several activities using standard instruments and handmade devices are described. (MNS)

Several experiences with palindrome numbers are given, each leading to the "Law of 11." Conjectures for the reader to consider are included. (MNS)

Advocated is developing intuitive ideas of limits whenever the opportunity arises in elementary mathematics. Examples are given for geometry, fractions, sequences and series, areas, probability, graphing, and the golden section. (MNS)

Stresses that powers are all based on geometric progressions which start at unity. Various patterns are discussed. (MNS)

Developing numerical relationships with calculators is emphasized. Calculators furnish some needed support for students as they investigate the value of fractions as the numerators or denominators change. An example with Logo programing for computers is also included. (MNS)

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)