Illustrated are the discovery and verification of new patterns in Pascal's Triangle. Discovery activities appropriate for students when they are learning to expand binomials are provided. (JP)

After prime factors of a set of numbers are listed, geometric shapes are used to find the prime factors of the least common multiple (LCM). (MNS)

Several ways to present two theorems (concerning a square matrix and a property of prime numbers) are demonstrated. One way for each theorem is more stimulating, better setting the stage for the proofs. Several methods of presenting proofs are illustrated, with the outcomes considered from the learner's viewpoint. (MNS)

How mathematics subject matter can be enhanced through the scientific reasoning method, how this integration can be achieved, adaptations needed for a modified approach, and resulting attainments are all considered. Prime numbers using the Sieve of Erastosthenes are the vehicle through which the approach is described. (MNS)

This guide is designed to aid the teacher in planning and teaching an eighth-grade mathematics course which should strengthen the student's understanding of the basic structure of mathematics through experience with and appreciation of abstract concepts. Thirteen units outlined are entitled: Numeration Systems; Natural Numbers and Zero; Integers;…

A concrete approach to prime numbers is presented using rectangles and triangles to construct a building for each number so that each story represents a pair of factors and the triangular-shaped roof represents the number. (MP)

Some benefits of helping learners think in prime numbers are detailed. Reasons for the decay of this ability are described, with short division presented as one activity which should be reintroduced in schools. (MNS)

Sorting activities for multiplication and division facts are suggested for developing concepts of prime factors. (MP)

The introduction of prime numbers in the intermediate grades should be handled with care or the concept will appear arbitrary, artificial, and unreal to the pupils. The approach suggested here is in the form of a game-like activity. A knowledge of multiplication and factors is a prerequisite. (BB)

The discovery method, according to the author, promotes logical thinking, is motivational in nature, makes learning more permanent, produces more usable knowledge, and gets students actively involved. A discovery lesson is characterized by the following: (1) the concept to be learned is not announced, (2) experiences and activities are developed…

An activity leading to the discovery of a property of primes is suggested for encouraging algebra students to make nontrivial conjectures. (MP)

Shares a coded version of the number line to provide concrete experiences for learning abstract concepts. Using the fundamental theorem of arithmetic, appropriate coded symbols are determined for the prime factorization of each natural number and used to study the concepts of greatest common divisor, least common multiple, square roots, and…