Describes a group project that involves geometry and falls into an area of mathematics known as operations research, which is crucial to making decisions in business and industry. Includes problem statements and project assessment guidelines and illustrates solutions. (KHR)

Describes an activity designed to help students connect the ideas of linear growth and exponential growth through graphs of the future value of accounts that earn simple interest and accounts that earn compound interest. Includes worksheets and solutions. (KHR)

Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)

Investigates the idea of the center of mass of a polygon and illustrates centroids of polygons. Connects physics, mathematics, and technology to produces results that serve to generalize the notion of centroid to polygons other than triangles. (KHR)

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Focuses on Pierre Varignon (1654-1722), who established the central place of mathematics in schools of Western Europe and his parallelogram theorem. (KHR)

Demonstrates how students' power to recognize and express patterns and generality can be exploited in a variety of different ways that are connected to both arithmetic and algebra. Uses the Tunja sequence approach to teach multiplication of negative numbers and simplification of factors. (KHR)

Examines textbooks and classrooms from antiquity through the 19th century in search of historical precedents for mathematical communication in the form of dialogue between teacher and student. (KHR)

Presents a quilting problem that engages students at many levels, has multiple possible solution paths, lends itself to a variety of representations, and connects many mathematical ideas. (KHR)

Presents the problem of points and the development of the binomial triangle, or Pascal's triangle. Examines various attempts to solve this problem to give students insight into the nature of mathematical discovery. (KHR)

Describes an investigation-based, lecture-free first-year algebra course in which students are responsible for compiling their own textbooks. Discusses the purpose and procedures of the activity. Includes student worksheets. (KHR)

Describes an investigation of polygons and their properties in which students apply very basic understandings of geometric properties. (KHR)

Describes an activity connected with mathematical definitions that illustrates the process of gradual refinement as a way to understand and construct knowledge. Presents a gradual construction of a specific geometry concept that was the result of interaction between participants in a mathematical discourse. (KHR)

Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)

Examines existing research literature which suggests that introducing computing tools can help students focus on the relevant aspects of a problem, function at higher levels of geometric understanding, distinguish between drawings and constructions, and develop and reason about conjectures on the basis of generalization of patterns. (KHR)