The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…

Bethel Woods Center for the Arts is a performing arts venue that includes the Woodstock Festival grounds in Sullivan County, New York. The center is adjacent to the original preserved site where visitors can see the historic field where hundreds of thousands of rock music lovers gathered in August 1969. In this article, students analyze a…

University mathematics education courses do not always provide the opportunity to make connections between advanced topics and the mathematics taught in middle school or high school. Activities like the ones described in this article invite such connections. Analyzing concrete or particular examples provides a better grasp of abstract concepts.…

A geoboard-related extremal problem dealing with both concave and convex polygons is discussed and a proof is given of the solution. (MP)

Three activities that involve space perception, the concept of geometric equivalence, and Euler's formula regarding regular polyhedra are described. (JT)

The author shows how a rapid computational "trick" can lead to an investigation of Fibonacci-type sequences. (SD)

The origin of the magic square, its numerical concepts, and some procedures for its construction are discussed. (JT)

Four answers to a probability problem involving a perceived coincidence are discussed. (MNS)

The relation between the area of a rectangle and its perimeter is clarified by looking at patterns. Several examples involving rectangles with integral sides are presented. (MNS)

A familiar procedure for generating magic squares is reviewed. A surprising pattern is noted. (MNS)

Ways of finding the sums of some interesting sequences of numbers are discussed. Finding the patterns creates a challenge, but the patterns are not too difficult for average pupils to discover. Mathematical induction can then be used to prove the formulas. (LS)

An activity that offers computational practice, pattern recognition, and the formulation of generalizations is described. (JT)

A familiar Christmas song described as a second-year algebra problem is presented in "The Twelve Days of Christmas". Five strategies for solving inequalities are discussed in "Solving Algebraic Inequalities". (JT)