The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)

Patterns emerging when two-digit numbers in various bases are operated on by squaring and summing the digits. (SD)

Three activities and patterns involving the addition table are described, each involving pentagons. (MNS)

Practice on computation is provided using new and novel situations, with discovery of number patterns a bonus of the computation. Activities with disguised addition and multiplication tables for whole numbers and integers are presented for varying levels. (MNS)

Presented are four activities which allow students to work with rhombus patterns. These activities encourage students to search for, test, and verify patterns and to also practice computation and work with ratios. Diagrams needed for each activity are included. (KR)