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)

Methods of finding algebraic expressions to fit number patterns are explored. (DT)

Mathematical patterns obtained by using rectangles and inductive reasoning are discussed. (DT)

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)

Three examples are given illustrating the use of the calculator in problems where determining patterns and making conjectures are stressed. (MP)

Worksheets for duplication are provided for this activity designed for students in grades 6-10. The objective of the activity is to have students discover generalizations about the patterns formed. (MK)

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)

Students use a series of isosceles right triangles constructed on a geoboard to discover patterns and form generalizations. (MP)

Describes an investigation-based, lecture-free first-year algebra course in which students are responsible for compiling their own textbooks. Discusses the purpose and procedures of the activity. Includes student worksheets. (KHR)

Presents a project used to help students make connections between linear and exponential models and between arithmetic and geometric 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)

Presents three teaching ideas: (1) investigating patterns in the sum of four numbers in a square array, no two from the same column or row; (2) using three-dimensional coordinates to generate models of three tetrahedra; and (3) applying the K=rs area formula for a triangle to other polygons. (MDH)