The Building Painted Cubes Task is a groupworthy algebraic task. Students build cubes using linking unit cubes, search for algebraic patterns, and report findings on posters. This task can create spaces for students to see themselves as doers of mathematics.

Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

This paper describes kindergarten children's engagement with two patterning activities. The first activity includes two tasks in which children are asked to choose possible ways for extending two different repeating patterns and the second activity calls for comparing different pairs of repeating patterns. Children's recognition of the unit of…

Pattern generalisation has become an important feature of mathematics classrooms around the globe. Sometimes these activities focus purely on given numerical terms, but the use of pictorial or figural patterns is now becoming part of the standard repertoire for such generalisation exercises. From a pedagogic point of view, the investigation of…

Introduces students to nonperiodic tiling and allows them to construct their own sets of kites and darts through a series of explorations, conjectures, and discoveries. (ASK)

Argues that mathematics is, to a large extent, the study of patterns. Presents an activity in which students search for patterns in the Fibonacci sequence and Pascal's Triangle. (ASK)

Presents responses to the pattern problem that appeared in the November 1998 "Problem Solvers" section of this journal. (ASK)

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)

Describes a model using a group of fifth-grade students to better understand the assessment standards. Discusses the activity, the lesson on tessellation, and instructional decisions from the perspective of the assessment standards. (ASK)

Five activities involving an array of numbers called an even triangle are given. Properties of the triangle are listed and some generalizations are proven. (MP)

Presents a problem that requires solving a card problem by exploring patterns that will lead to a logical solution. Involves students in developing and analyzing their own algorithms as well as discussing their reasoning with peers. (ASK)

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 problem suggested for students in grades one through six concerning the concepts of grouping, reasoning, and pattern finding. Discusses the student problem-solving process. (ASK)