Clock Buddies is our favorite first-day-of-class activity. It starts as a nonthreatening icebreaker activity that helps students learn one another's names, but it soon asks students to find their own strategies for solving a real-world scheduling problem. Even highly math phobic students work with others and succeed. Students gain insight from…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) propose a new vision for the mathematics classroom with updated content standards and Standards for Mathematical Practice (SMP). These practices are founded on NCTM processes (Problem Solving, Reasoning and Proof, Communication, Representation, and Connections) and abilities…

"Mathematical Lens" uses photographs as a springboard for mathematical inquiry and appears in every issue of "Mathematics Teacher." Recently while dismantling an old wooden post-and-rail fence, Roger Turton noticed something very interesting when he piled up the posts and rails together in the shape of a prism. The total number…

The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…

Research shows that the greatest gains in student learning in mathematics classrooms occur in classrooms in which there is sustained use of high cognitive demanding tasks throughout instruction (Boston and Smith 2009). High cognitive demanding tasks, which this article will refer to as rich tasks, are mathematics problems that are complex, less…

Most high school mathematics teachers completed a mathematics history course in college, and many of them likely found it intriguing. Unfortunately, very few of them find the time to allow much, if any, mathematics history to trickle into their instruction. However, if mathematics history is taught effectively, students can see the connections…

This article illustrates how the arithmetic series 1 + 2 + 3 + ... + n is pervasive in mathematical contexts as a powerful problem-solving tool.

The article describes the harmonic mean and explores situations for using it. Activities that involve hands-on practice for students are provided. Students learn to recognize which mean, harmonic or arithmetic, is appropriate.

This article discusses divisibility tests for any prime number.

Solution of, and commentary on, a problem suitable for use in the secondary school mathematics classroom. Topics from arithmetic, algebra, and number theory appear in a unified way. (FL)

A list of the basic competencies in mathematics set by the Vermont Board of Education is given and discussed. The basic competencies are grouped as follows: numeration, measurement, money, arithmetic, and reasoning. (MP)

Presents a collection of problems focusing on: (1) squares in arithmetic and number theory; (2) squares in geometry; (3) topics blending arithmetic and geometric aspects of squares; and (4) squares and Logo. A sample student worksheet (with answers) is included. (JN)

Example of magic tricks that can be used as an integral part of various lessons in arithmetic and algebra are given. Their mathematical basis is also discussed. (MNS)

Presented is a problem involving a real-life situation involving simple ideas, computation, and a proof. A variety of other situations in which this type of problem may be applied are discussed. (CW)

Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)