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

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)

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)

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

When a simple game was presented as a challenge to a primary-school girl, she solved the problem, and went on to generalize her solution. (SD)

Properties of a given array of numbers are discussed and some sample activity cards involving discovery of number patterns are presented. (MP)

Mathematical concepts occur spontaneously from many topics and can be developed in the framework of cross-curricular schoolwork. Consequently, students can gain knowledge of where mathematics arises and insight about its purposes. (Included are activities dealing with the reflectional and rotational symmetries of automobile hubcaps evolved from…

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)

The construction of tables of numbers is discussed as a learning activity that involves work in such things as reciprocals, calculators, formulas, patterns, discovery, prime numbers, and other types of numbers. (MP)

Students use a series of isosceles right triangles constructed on a geoboard to discover patterns and form generalizations. (MP)

Some number investigations on the multiplication table are provided by a sequence of four activity sheets. Beginning with examples of triangular and square numbers, the activities lead to the generalization. (MNS)