The problem involves randomly breaking a stick into three pieces and using the pieces to form a triangle. The probability of getting a triangle is calculated using four different solution methods. Two unique problem interpretations are noted, and one solution method involves a BASIC program. (MP)

Presented here is an index which indicates the title and location of each activity by volume and page numbers. The majority of items relate to arithmetic, elementary algebra, and plane geometry, but material also covers such topics as statistics, probability, trigonometry set theory, topology, and modern algebra. (MP)

The harmonic mean is defined, and examples of problems viewed suitable for classroom exploration are presented. Such exercises provide many opportunities for students to engage in interesting nontrivial problem-solving activities and practice on many algebraic skills. Class discussion of the arithmetic, geometric, and harmonic means is suggested.…

The trick focuses on a theorem that the sum of the digits of the difference between any natural number and the sum of its digits is divisible by nine. Two conditions of using the trick are noted. The reason that the theorem works is established through a proof. (MP)

The proof is given that, if three equilateral triangles are constructed on the sides of a right triangle, then the sum of the areas on the sides equals the area on the hypotenuse. This is based on one of the hundreds of proofs that exist for the Pythogorean theorem. (MP)

A program written in PASCAL designed to find the number of binary trees possible for a given number of nodes is presented. The problem was found to be highly motivating and exciting for the group of introductory computer science students with whom it was used. (MP)

A science fiction approach is used to explore some unusual properties associated with the concept of infinity. (MP)

A variety of ideas for working with money are presented. Activities provide experience in counting nickels and dimes, counting money and making change, determining sale prices by computing the percentage off a base or regular price, and keeping a record of current balances in checking and savings accounts. (MP)

The activity described helps students develop facility in working with two-dimensional coordinate systems. Many students find the activity fascinating, so it can be used to motivate students to become involved in a number of explorations and to engender positive attitudes toward mathematics. (MP)

Seven workbook-oriented programs and one activity-oriented program were surveyed, and 106 different mathematics concepts were identified for kindergarten mathematics programs. Specific programs presented 31-58 of the concepts. Sixteen projects are described with uses that cover 87 concepts. They are suggested as supplements to any program. (MP)

The history of Hawaiian number systems is examined, and answers to questions regarding Hawaiian number words, including their origin and factors that influenced their development, are covered. A brief guide for pronouncing Hawaiian words is also provided. (MP)

A discussion of a contest between the German mathematician Adam Riese and a draftsman involving the construction of as many perpendicular lines as possible in one minute leads to a review of some interesting constructions involving circles. It is suggested teachers challenge their students with the historic contest question. (MP)

The use of a ruler with two parallel Straight edges as a tool in geometric constructions is presented, based on ideas that are fairly standard in high school geometry courses. The constructions are seen as potential challenges that provide opportunities for inventiveness by students. (MP)

Activities for calculating experimental and theoretical probabilities are presented. Worksheets designed for duplication for classroom use are provided. Suggestions are given for additional problems that could be generated from the original simulation, and answers to questions on the worksheets are included. The activities simulate parachute…

Activities designed to: (1) provide experience in determining the likelihood of events and systematically recording the results of a succession of events; and (2) provide experiences in reading and drawing logical conclusions from graphed data are presented. Worksheet masters designed for duplication for classroom use are included. (MP)