The material presented is designed to help students explore geometric patterns involving Fibonnaci numbers and the golden ratio, and to aid in review of basic geometry skills. Worksheet masters intended for duplication are provided. Suggestions are made of possible classroom extensions to the initial activities. (MP)

The Mayan system of numeration, which used 20 as the base, is discussed. The material presented has been used to stir the curiosity of students in different systems of numeration. It has been helpful in promoting a speedier and better understanding of base 10. (MP)

Some patterns in prime numbers and their implications for general theorems are presented. Much of the material is taken from "The Strong Law of Small Numbers," an unpublished paper by Richard Kenneth Guy. (MP)

The Spirograph, a device used for artwork and designs, is utilized to explore the mathematical topics of symmetry, ratio, divisibility, and modular arithmetic. A worksheet for each topic is included along with pedagogic information and extensions and also the answer key. (JJK)

Properties of a given array of numbers are discussed and some sample activity cards involving discovery of number patterns are presented. (MP)

It is noted that students sometimes have the misconception that square roots of integers are evenly spaced. The difficulty seems suited to approaches with calculators and computers, and is viewed arithmetically, graphically, and algebraically. It is suggested that differences between roots of successive pairs of consecutive integers be examined…

Mathematical activities suitable for reproduction as worksheets are suggested. These activities are adaptations of the classic tower puzzle and are intended to help students discover patterns, make generalizations, and use the strategy of solving simpler problems in order to solve a more difficult one. (MK)

The nature of an investigation into numbers termed Nearly Isosceles Pythagorean Triples (NIPTs) is detailed. The exploration, even though it is stated to have no practical value, is defended as helping pupils see the beauty of patterns in mathematics. Two questions regarding the pattern of generating NIPTs are noted. (MP)

This is a not-so-serious discussion of accidental patterns involving chance patterns between mathematics and natural laws and accidental patterns involving the numbers "pi" and "e." (Author/SA)

Patterns generated by the set of natural or counting numbers are discussed. Included are quartic, odd, square, and triangular numbers. (MK)

Number sequences are useful complements to traditional drill and practice. Described is an activity in which the basic rule, add the tens digit to five times the ones digit, is used to generate a sequence of numbers. The dialogue between teacher and student discussing characteristics of emerging patterns is given. (MDH)

Provided is a set of six activities demonstrating how mathematical connections can be made using the concept of rectangle. The activities relating rectangle to factoring whole numbers, prime numbers, and calculating the area of rectangles, triangles, parallelograms, and circles, are also connected to each other. (MDH)

Discusses the problem of how the stars on the American flag would be arranged were another state added to the Union. Presents solutions using linear equations based on conditions given in the problem. (MDH)

The use of clock arithmetic patterns to make geometric patterns is presented as a tool to instruct students in the understanding of multiples in different systems. (MP)

The construction of tesselations as a mathematics activity for young children is presented. (MP)