A lesson for a sixth grade class that came out of an article in a Sunday newspaper is described. The instruction centered around an experiment in probability that was seen to provide an opportunity to add to pupil intuitive understanding of some basic notions. The lesson was viewed as worthwhile. (Author/MP)

People are noted as intrigued for centuries by interplay between algebra and geometry with many important advances viewed to have come down through some sort of linking of the two. Examples are given of advantages to learning and discovery that can be found in an investigative approach combining them. (Author/MP)

Five problems are given which are designed to challenge gifted students while giving them opportunities to use algebraic concepts. Solutions are provided. (MNS)

Three probability problems designed to challenge students are presented: Liars and Diamonds, Heads Wins, and Random Walks. Other statistic problems are suggested that could involve computer simulations. (MNS)

Problems involving multicolored cubes are discussed with examples of Instant Insanity and Rubik's Cube cited. Sections cover defining chameleonic cubes, producing such a cube, and extending understanding to multidimensional cubes. One theorem proved is that for each positive integer, every cube of that size is chameleonic. (MP)

A series of worksheets dealing with the Morse Code are presented. The material incorporates vocabulary knowledge, substitution, and patterns, and is viewed suitable for any student. The initial activities are followed by three optional challenges. Pupils can develop a basis for reflecting on mathematical symbols and words. (MP)

The mathematical nature of the product barcode that now appears on many supermarket goods is discussed. Particular attention is given to the nature and formula of a "check digit" used to verify that product numbers are correctly scanned. Several possible student activities related to this code and others are suggested. (MP)

Many students appear to enjoy mysteries at the same level that they hate proofs. It is felt that the solutions of the two can be so alike that their diagrammatic forms will coincide. One geometry and three mystery problems involving logic for solution are presented. (MP)

Describes techniques intended to provide the teacher (or student) with insights to the solution of the problems of constructibility of squares of area c and determination of the numbers of squares, and a method for the construction of constructible integers of area c. (DS)

A set of activities designed to help students discover properties about order-3 spirolaterals on square grid paper is presented. The materials are prepared on worksheets designed for easy duplication. The lessons can lead to investigations involving spirolaterals of many other orders and shapes. (MP)

A problem considered an interesting challenge to students with a good command of algebra and trigonometry is presented. (MP)

These exercises are designed to expose students to the nature and effects of inflation and consumption rates. Pupils are expected to see how long it takes for costs to increase to certain levels, and how quickly various growth rates can deplete a finite resource. Worksheets suitable for duplication are provided. (MP)

A problem that is seen to allow room for student discovery and exploration is detailed. A discussion starts with an examination of the generation of a general equation for the sum of a set of consecutive integers, and leads to an exploration of more complex sums. (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…

Three basic game types are identified and described (formation, chase, and elimination). Examples are given of each of these types, as well as a chase-elimination game and a formation-elimination game. The ultimate game is viewed to be one which would combine all three strategies. (MP)