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Since 1950, the Prisoner's Dilemma has intrigued economists and amused fans of mathematics. It presents a situation in which two players acting to their own advantage do not do as well together as two players whose actions oppose their individual interests--hence, the dilemma. Variations of the Prisoner's Dilemma have appeared in diverse circumstances, from television police dramas to analysis of political negotiations. Along with the scenarios presented here, we consider settings from the movie "The Dark Knight" (2008), students' take-home exams, and the Tragedy of the Commons in additional examples in an online supplement.

Starting with the classic Open Box problem, we present extensions of this problem that can be used in high school mathematics classes. We also challenge high school teachers to use this process of problem analysis in their own practice as a way to enrich the content of their lessons and as a means of individualized professional development.

This article presents several activities (some involving graphing calculators) designed to guide students to discover several interesting properties of Fibonacci numbers. Then, we explore interesting connections between Fibonacci numbers and matrices; using this connection and induction we prove divisibility properties of Fibonacci numbers.

Student who understand the connection between matrices and the Fibonacci numbers can use that knowledge in a wide range of activities like matrix multiplication, pattern recognition and proof by induction.

The Facts on File Geometry Handbook By Gorini, Catherine A

The article describes various activity programs for mathematics education that teaches students about Collatz conjecture.