This discussion of cyclic patterns that appear in repeating decimals includes the use of the calculator in discovering the patterns. (MP)

Repeating decimals are used as a source for geometric patterns. Ways for generating patterns focus on dividing a circle into certain numbers of equal parts and interpreting the decimal expansions of certain fractions in terms of connecting sequences of points. Suggestions for possible expansions are given. (MP)

Three examples are given in which students create their own Logo software to explore the topics of number patterns and operations, fractions, and decimal parts in measurement. (MNS)

Presents an activity that involves drawing pictures to collect data, conjecturing a recurrence relation, and solving the relation using geometric series and partial fractions. (MKR)

Mechanical devices offer an alternative to computers to explore mathematical concepts in different curricula areas. Described is the discograph, a series of pulleys and wheels, that can be used to teach mathematical principles in pattern drawing, locus, rotation in geared systems, gearing, rotational symmetry, regular plane figures, decimal, and…

Uses pattern blocks to model basic parts-of-a-whole fraction concepts. Suggests that students reflect these models in oral, written, pictorial, and symbolic representations. (MKR)

Explores the number problem of writing an expression for each of the unit fractions using any digit exactly four times. Includes tables of expressions for unit fractions. (MKR)

Uses spatial visualization to make connections among Zeno's paradox, geometry, fractions, infinite series, and limits. (YDS)

Describes two activities for developing computational skills, discovering patterns, checking answers, and factoring quadratics and equivalent fractions. Provides worksheets for the activities. (YP)

Activities designed for use with middle-school students to help them discover intriguing number patterns and practice their arithmetic skills with fractions are presented. It is felt that work with repeating number patterns should be both fun and instructive for middle-school and prealgebra students at all development levels. (MP)

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)

The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…

Discusses 4 numerical patterns occurring in the decimal expansions of 2 raised to a negative exponent. Includes two row patterns, one diagonal pattern, and a pattern in the sum of the digits of the expansions. Conjectures are presented for each pattern and subsequently proved. (MDH)

Discusses the collaboration between a university and local school district in the use of calculators to help students discover patterns and to estimate quotients when dividing decimals. (MKR)

Presents a series of five activities that introduce division of fractions through real-world situations. Discusses problems related to resurfacing a highway, painting dividing stripes on a highway, covering one area A with another area B, looking for patterns, and maximizing the result of a division problem. Includes reproducible worksheets. (MDH)