Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)

Presents an extension of Pick's theorem for simple closed polygonal regions to unions of simple closed polygonal regions. Students are guided to discover Pick's theorem from sets of data including numbers of boundary points and numbers of interior points. (Author/MKR)

Explores applications of the Fibonacci series in the areas of probability, geometry, measurement, architecture, matrix algebra, and nature. (MDH)

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)

Describes activities to be used with fifth and sixth graders to improve students' spatial sense with respect to three-dimensional shapes. Includes the use of cubes, triangular prisms, tetrahedrons, and square pyramids. (MKR)

An activity that shows how mathematics can be used to model events in the real world is described. A way to calculate the area of the sun covered by the moon during a partial eclipse is presented. A computer program that will determine the coverage percentage is also included. (KR)

A variety of suggestions for making the mathematics curriculum more meaningful and interesting to students are described. Activities that incorporate real-world situations are provided for verbal items, common and decimal fractions, estimations and rounding off numbers, large and small numbers, geometry, probability, and statistics. (KR)

The simple physics behind the mechanism of the toy are explained. Experimental and mathematical steps are given that help in understanding the motion of the doll-pair. The geometry of the setup is described. (KR)

Examples and solutions to these problems are presented. Figures for which different equations are necessary are presented. The use of the geoboard for this exploration is emphasized. (CW)

Various methods for solving the problem of finding when the hour and minute hand of a watch have the same direction are explored. The relationship of these problems to the educational environment and the maturity of the student are discussed. (CW)

Discussed are the geometric patterns formed when two geometric patterns are superimposed. General moire fringes, circular and line gratings, physical applications, and projects for students are described. (CW)

Discusses how different meanings can be given to the proof at different levels and branches of mathematics education. (ASK)

Rich and stimulating instruction in geometry can be provided through playful activities with mosaics such as pattern blocks or design tiles. Presents an intriguing mosaic puzzle to describe activities at various developmental levels and how the activities can help develop children's geometric thinking. (ASK)

Presents interesting activities to develop mental imagery and the ability to transform these images. Concludes that using images facilitates mathematical thought in numerical and geometric settings. (ASK)

Compares students of average ability in three high school geometry classes that utilized computer software in varying amounts. Reports that using computer software may not be beneficial when teaching certain topics in geometry and that using computer software did improve student interest and participation. Contains 13 references. (Author/ASK)