Some functions on digits of positive integers are presented as possible sources for useful investigations by students, particularly through the use of calculators and computers or in the writing of small proofs. The material is designed to encourage students to conduct their own investigations. (MP)

Geometric construction problems are recommended as sources of stimulating exercises for mathematics classes. (MP)

A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

Presented is a method for finding two triangles that have five pairs of congruent parts, yet fail to be congruent. The solution is thought to involve some creative insights that should challenge both the teacher and students to recall and analyze all the congruence axioms and theorems. (MP)

The problem of finding the maximum number of right angles a polygon can have, given the number of sides, is discussed in detail. (MP)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

An open-ended data-analysis activity, prompted by a Royal Mail advertisement, explores the claim that the real cost of first class postage has fallen below the inflation rate. The activity provides realistic exercises in both arithmetic and statistical indices, and in logical interpretation of, and deduction from, the data. (JJK)

These worksheets suggest activities through which secondary school students may be introduced to the ideas of simulation. All can be played as games to give students a feel for the situation modeled; most use coins or dice and a few use random digits. Directions are detailed for each of the 17 worksheets, with variations suggested for many. (MMS)

Presents examples of questions and answers arising from a hands-on and exploratory approach to discrete mathematics using cuisenaire rods. Combinatorial questions about trains formed of cuisenaire rods provide the setting for discovering numerical patterns by experimentation and organizing the results using induction and successive differences.…

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

Eight activity packages, designed to teach students mathematical topics which are inappropriate to teach through a paper and pencil approach, are presented. The materials were created so that students: (1) can follow the instructions with little supervision; (2) are physically engaged in the activity, either measuring, counting, drawing pictures…

Problem solving is viewed as an ability required throughout life, and how we function is seen to be directly related to how well we solve problems. In this document, the issue of a steady decline in students' abilities in the area of mathematical problem solving is confronted and a program designed to teach students the necessary skills in this…

This book is intended for use as a student guide. It is about human problem solving and provides information on how the mind works, placing a major emphasis on the role of computers as an aid in problem solving. The book is written with the underlying philosophy of discovery-based learning based on two premises: first, through the appropriate…

These documents are three separate sets of student problems and teaching guides geared towards calculators. Series A is designed for pupils from ages 10 to 13; "B" is structured for 13 through 16, and "C" for 16 through 19. The materials are designed to provide activities for investigation and exploration of number properties and patterns that are…

Presents two worksheets that ask students to count and classify the triangles that can be formed with a given total number of toothpicks or a given number of toothpicks for one side of the triangle. A third worksheet asks students to identify patterns observed during the investigations. Provides reproducible worksheets. (MDH)