Demonstrates how students' power to recognize and express patterns and generality can be exploited in a variety of different ways that are connected to both arithmetic and algebra. Uses the Tunja sequence approach to teach multiplication of negative numbers and simplification of factors. (KHR)

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)

Patterns in modular arithmetic are discussed: (1) multiplication tables, and (2) diagrams obtained by joining points on the circumference of a circle. (MM)

Demonstrates how mathematics is a changing science through an in-depth look at the history of the development of logarithms. Serves as a reminder to continue to remember and appreciate the efforts and contributions of past mathematicians. (KHR)

Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)

Describes a credit-card-debt activity that allows students to increase their awareness of underlying mathematical concepts relevant to the world of commerce and personal finance through learning geometric and arithmetic sequences. (KHR)

Presents a brief definition and examples of residue designs while sharing some of the algebraic thought that a student used to form generalizations about the patterns discovered during the investigations of residue designs. (ASK)

An activity for grades 6-10 designed to allow students to explore a hundred chart to discover patterns is presented. Discussed are materials, objectives, and procedures. Three worksheets with answers are provided, and an extension activity is suggested. (CW)