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

This activity is designed to help students recognize and extend rectangular patterns and to use patterning to formulate rules for "nth" cases. Three worksheets are included. (MNS)

Introduces students to nonperiodic tiling and allows them to construct their own sets of kites and darts through a series of explorations, conjectures, and discoveries. (ASK)

The author's experience in leading activities related to the Mobius strip to a fourth-grade class is discussed. (SD)

Similar rectangles are the basis of a set of activities using newspaper. Topics arising include infinite series and Pythagorean theorem. (MP)

Three theorems for Pythagorean triples are presented, with discussion of how students can amend their ideas about such numbers. (MNS)

Some activities are provided to help students develop a conceptual understanding of perimeter, area, and volume, as well as developing skills in spatial visualization and formulating generalizations. (MNS)

Deriving all Pythagorean triples from simple patterns within an addition table is presented, with formulas included. (MNS)

A series of lessons in which the concept of symmetry is informally developed is described. Rotational and reflection symmetries are examined. Pictures and sample worksheets illustrate the article. (SD)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

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)

Using the two posters in this article, students are to search for patterns as a way of counting different types of squares and cubes obtained from a larger square or cube that is printed on the outside edge or surface. (MP)

Described are activities for thinking through patterns using toothpicks, paper strips, wooden cubes, and people patterns; thinking with attribute items such as geocards, namestrips, and treasures; and thinking with geometric materials such as geoboards and dot paper, cubes, and simple puzzle pieces. (MNS)