Instructions are given for making a flexagon; the possible transformations of the flexagon by flexing and turning are shown to form a non-abelian group of order 6. (DT)

Worksheets provide activities with a modified number line and involve ordering numbers, number facts, and estimation. A suggestion for a bulletin board display is included. Two problem posters are also provided. (DT)

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)

Chains made up of alternate arrows and numbers are used to represent the result of repeated applications of a function. A collection of problems based on these arrow chains is provided. (DT)

Mathematics exercises involving the number of electoral votes, the apportionment of representatives, and population data are described in detail, with solutions given. (DT)

A Math Rummy card game, a stock market enrichment activity, and a puzzle in logical reasoning, all used with seventh and eighth graders, are described; directions for constructing a clock with suggestions for its use at the first grade level are given. (DT)

Notes on De Morgan's rules; a perpetual calendar; the use of coloured rods; a balance problem; a graphical approach to natural logarithms; a problem in geometric probability; and the parallelogram law of forces. (MM)

Discussed are some applications of Euler's Formula N plus F minus E equals Z, where N, F, and E are respectively the number of vertices, faces, and edges of a planar figure. In particular, the Four-Color Problem is proved for the special case of five countries. (CT)

Five solutions to the problems of constructing an equilateral triangle within any triangle and having the vertices on the sides of the given triangle are presented and a generalization is made. (CT)

The author examines a well known number trick, in other number bases, and finds that equivalent results arise. (CT)

This material shows how to use basic techniques, principles of counting, and geometry to count squares on geoboards. The methods are elementary in that the proofs are easily conceptualized. A discussion of other approaches illustrates that easily stated problems may lead to very difficult and sophisticated methods. (MP)

A procedure for generating the "nth" term of figurate numbers is given. (MNS)