This is the sixth volume of a series produced by the State Education Department of the University of the State of New York. Mathematics objectives and sample items included were originally developed by four local school districts and are not intended to be official or comprehensive, but an aid to teachers in constructing curricula and making…

The uses of geometry in everyday life, in various professions, and in other areas of study are discussed. The role of geometry courses in high schools and elementary schools is summarized. (MP)

Examples from some area tasks indicate that misconceptions about linear measurement can be carried over to area measurement; children will occasionally count points rather than length units or area units. (MP)

Two experiments involving geometry, statistics, and integers are presented. Practical problems of using individualized instruction are discussed as well as long-term benefits to students. (MP)

The author outlines a possible approach to the discovery of Euler's Theorem that results from a search for a classification of polyhedra. (MN)

The author investigates the construction of angles (using Euclidean tools) through a numerical approach. He calls attention to the surprising impossibility of constructing the conventional units of angle measure--the degree, minute, second, radian, and mil. (MN)

An application of the formula for finding the sum of an infinite geometric series is described through the use of Pierre Fermat's method for finding the area under a curve. (JT)

Ploynomials which can be used to calculate the number of ways of coloring hexagonal patterns are presented. (SD)

Presented are examples from geometry that are designed to investigate whether situations fit Euclidean geometry. Diagrams and activities are provided for examples. (RH)

Discusses the need to include symmetry as an important topic in the mathematics curriculum. Describes how symmetry might be developed conceptually and its relation to geometry, algebra, group theory, and physics. (JM)

Presents a problem, modified from a familiar situation, that would be suitable for high school students to investigate. The problem involves the properties of an array known as the odd triangle, which is made up of the odd counting numbers. (JN)

The Fibonacci sequence of Pascal's triangle is considered in pyramids and in the fourth and n dimensions. Four theorems are presented. (MNS)

Presents six mathematical problems (with answers) which focus on: (1) chess moves; (2) patterned numbers; (3) quadratics with rational roots; (4) number puzzles; (5) Euclidean geometry; and (6) Carrollian word puzzles. (JN)