A square lattice is used to generate classroom activities, such as counting the number of squares in a lattice of a given size. (MP)

Ways of finding the sums of some interesting sequences of numbers are discussed. Finding the patterns creates a challenge, but the patterns are not too difficult for average pupils to discover. Mathematical induction can then be used to prove the formulas. (LS)

Described are results obtained by students investigating double-diagrams, including discoveries of properties and accompanying proofs. (MP)

A problem concerning the generation of an array of numbers is posed. The author examines the use of this problem in several secondary-school and college classes. (SD)

An activity project is described which encourages students to question and experiment. Appendices provide examples of student results. (MNS)

Number sequence patterns for counting boundaries of familiar figures are extended to higher dimensions. (JP)

Students, using the materials provided, can determine the number of diagonals, number of triangles formed by the diagonals, and degree measures of interior and exterior angles of regular polygons. The activity is designed to lead them to general formulae for polygons with n sides. (SD)

Geometric concepts and theorems can be discovered by high school students using the materials described. Among the topics explored are Platonic solids and Euler's formula. (SD)

Details of an investigation into polygonal numbers are given. From a study of the tabled series, patterns are discovered both within and between the various polygonal series. From a study of these results and the corresponding figures, formulas are developed. (LS)