Ploynomials which can be used to calculate the number of ways of coloring hexagonal patterns are presented. (SD)

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

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

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

A series of experiences with patterns in number pairs, each using a physical model. (MM)

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

Students examined patterns emerging when numbers placed at vertices in a braided pattern were summed. (SD)

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)

Using the notion of the difference between a number and its cube as a starting point, this article presents a wide range of mathematical activities at varying levels of sophistication utilizing numerical, intuitive, and graphical approaches. (JJK)

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…

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)

Presents lesson plans for activities to introduce recursive sequences of polygons: golden triangles, regular pentagons, and pentagrams. The resulting number patterns involve Fibonacci sequences. Includes reproducible student worksheets. (MKR)

The purpose of this article is to highlight and discuss the role of language as the link between experiences with number patterns and the emergence of algebraic notation. Discussed is a recommended approach. A sample of a written student response is provided. (CW)

Presents suggestions for developing algebraic concepts beginning in the early grades to develop a gradual building from informal to formal algebraic concepts that progresses over the K-12 curriculum. Includes suggestions for representing relationships, solving equations, employing meaningful applications of algebra, and using of technology. (MDH)