The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

Curiosities offer an interesting alternative to traditional methods of attacking problems. An illustrative situation is given, with graphical, computer, and analytical methods used to solve the problem. (MNS)

Presents several examples of investigations which demonstrate the following: (1) algebra is connected to other mathematical topics; (2) algebra is an effective tool for representing patterns and relationships; and (3) algebra is an effective tool for analyzing patterns. (DDR)

Some activities are provided to help students develop a conceptual understanding of perimeter, area, and volume, as well as developing skills in spatial visualization and formulating generalizations. (MNS)

Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

Briefly presented are suggestions on using exercises in number patterns in second-year algebra and factoring quadratics in a 10th-grade enrichment class. (MNS)

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)

Presents a methodology designed to strengthen the cognitive effects of using graphing calculators to solve polynomial equations using pattern matching, searching, and heuristics. Discusses pattern matching as a problem-solving strategy useful in the physical, social, political, and economic worlds of today's students. (DDR)

Describes a card trick that provides opportunities for students to discover patterns, work with variables, create tables, and ponder mathematics. Students at various levels of ability are able to enjoy the trick, and mathematical discourse is promoted within the classroom. (AIM)

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Explores algebraic thinking as children search for patterns while collecting, organizing, and graphing data and as they derive equations describing relationships found in the data. (ASK)

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)

This collection of activities resulted from a visit by the Polish author to the Teachers' Center Project at Southern Illinois University at Edwardsville in 1980. The set of 30 activity sheets involve blocks with various types of patterns depicted. Directions for using each sheet and questions to be answered are then given. Elementary school…

Presented are problem-solving experiences with area, volume, and algebraic expresssions resulting from data collection. Three worksheets are included for students in grades 7-12. (MNS)

Provided is a teacher's guide for a problem-solving activity that establishes a link between number patterns and geometry by focusing on the development of recurrence relations established when generating central polygonal numbers. Reproducible worksheets and a 3.0 BASIC program for the activity are given. (MDH)