Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)

Using sequential chains of regular n-gons in a row with one side touching, as for example, one triangle, two triangles, three triangles, and so on, students graph the length of the perimeter versus the number of n-gons and determine the functional relationship for different values of n. (MKR)

Outlines a lesson on the Fibonacci and Lucas sequences that captures student interest by presenting the opportunity for computation practice, mental mathematics, and proof for algebra students. Discusses an extension for solving simultaneous equations. (YDS)

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)

Describes students' generalization strategies and justifications as they engage in patterning activities. (YDS)

Demonstrates how to extend student awareness of a common computational pattern into the realm of algebraic thinking through carefully selected, sequenced activities and guided discussion. (YDS)

Describes how students can be guided to find an explicit rule for a pattern from a recursive rule. (YDS)

Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)

Presents a project that addresses several components of the Algebra and Communication Standards for Grades 9-12 presented in Principles and Standards for School Mathematics (NCTM, 2000). Describes doing mathematical modeling and using the language of mathematics to express a recursive relationship in the perimeter and area of the Koch snowflake.…

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)

The ability to use algebra in describing and analyzing real-world situations is becoming a basic skill for all students. The main focus of this book is on patterns, functions, and relationships. Information and ideas on how algebraic thinking can be developed in the years leading to a formal algebra course are included. K-8 teachers are offered a…

This book offers ideas to enrich instruction and help teachers explore the intrinsic beauty of math. Through dozens of examples from arithmetic, algebra, geometry, and probability, the symmetries, patterns, processes, paradoxes, and surprises that have facilitated generations of great thinkers are revealed. Activities include: (1) The Beauty in…

Presents a quilting problem that engages students at many levels, has multiple possible solution paths, lends itself to a variety of representations, and connects many mathematical ideas. (KHR)

Presents a lesson that teaches number patterns through the Vedic matrix found in Vedic mathematics from India. (KHR)

Presents a mathematics investigation in which students discover number patterns in physical structures and express their generalizations algebraically. (MKR)