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)

The use of dice and dominoes in the classroom is discussed as leading from counting activities to pattern recognition and discovery learning. (MP)

Activities suitable for use with primary school students are described. The author offers advice concerning expectations of the students, use of the vocabulary of probability, integration of activities with other classroom work, and related topics. (SD)

Playing with number patterns can lead students to discover some divisibility tests. (JT)

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)

Having students find and cut out of graph paper the 12 pentominoes can provide an enjoyable exercise in perception, discovery, and double checking. The pentominoes can then be used to illustrate informally several geometric concepts. (SD)

Elementary School Teachers were instructed on finding number patterns in a figure in one of three groups: individual discovery, group discovery, and expository. They were tested for recall, retention, and transfer. The expository groups did better on recall, but group discovery was more effective for retention and recall. (SD)

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)