Beginning with a set of design cards and a rectangular grid, students can generate interesting and colorful designs using rotations, reflections, and translations. (SD)

Describes an activity in which students, grades 7-12, explore patterns and properties of repunits, an integer written as a string of ones. Includes extensions for exploring algebraic justifications. (MKR)

Completing these worksheets leads students to discover patterns in the distribution of even numbers and numbers obtained by successive additions of 9 (primary grades). Worksheets for intermediate grades involve counting the number of factorizations for integers, and addition of the first nine whole numbers. (SD)

Using these worksheets students explore patterns in numerical and geometric processes, and predict the outcomes when the processes are iterated further. (SD)

Five activities involving an array of numbers called an even triangle are given. Properties of the triangle are listed and some generalizations are proven. (MP)

Transformations are defined and described through many examples. Teaching aids and activities for teaching about transformations are suggested. (JT)

Paper squares, each divided into eight congruent triangles, can be used in a variety of activities introducing ideas related to symmetry, pattern, and geometric transformations. (SD)

A computer program is presented for the billiard ball problem. It can be integrated into a lesson on inductive reasoning and suggests several ways to do so. (MNS)

Patterns resulting from polygonal numbers are explored, with examples of triangular, square, pentagonal, rectangular, and other numbers. Tables and formulas to be developed are included. (MNS)

Three worksheets are given that use calculators to free students from computational restrictions and allow them to focus on the recognition of patterns and the application of numeration concepts in the development of their estimation skills. (MNS)

A mathematics unit which introduces number concepts through the use of patterns. All activities are based on the formation of patterns involving blocks or tiles of two colors. (RP)

Properties of the harmonic number triangle are listed, and ways of generating the elements of harmonic triangles are described. (MNS)

Presents three investigations related to the game Bulgarian Solitaire. Investigations ask students to find and represent optimal solutions to the problem, to identify cyclical solution patterns for different numbers, and to respond to questions involving the number and nature of the cyclical solutions. An appendix provides answers to questions.…

Describes learning activities in which fifth and sixth graders used spreadsheets to explore the shapes of numbers. Discusses creating spatial patterns with a computer draw program; examining number patterns in a spreadsheet; comparing square and rectangular numbers; and creating the multiplication times table. (AEF)

This booklet offers teacher instructions and student worksheets on number activities for gifted primary grade students. Three sections are included: (1) "moving numbers" which asks students to supply the missing member or members of addition and subtraction equations; (2) "number trails," which involve the completion of number…