A discussion of some number patterns which arose from a consideration of the number of diagonals of a general polygon. (MM)

Several brief articles are included in this section. "Purple Puzzlers" are challenging problems for algebra students. "Linear Invaders" is a game to reinforce concepts of graphing lines. "The Diagonal Method" is used to prove that the real and natural numbers cannot be put into one-to-one correspondence. (MNS)

Details of an instructor's attempt to solve a problem in combinatorics taken from a textbook used by some of his students are presented. It is felt the material raises a number of significant points about problem solving and mathematics. Teachers are encouraged to put themselves in such situations. (MP)

Ideas are presented regarding: (1) unique learning activities for students who have difficulty with operations with signed numbers; (2) a mathematical inspection of a unique card trick that can be expressed as an equation; and (3) sketching of graphs of composite trigonometric functions. (MP)

Examples of student-developed methods for dividing fractions and dividing and multiplying whole numbers are presented. Both are selected to show mathematical creativity in general mathematics students which would often be overlooked. (MP)

Problems focusing on number theory that can make good use of the calculator in discovering and proving simple theorems are proposed. The focus is on the properties of subtracting the smaller of a three digit number and its mirror number from the larger in a process that leads to zero. (MP)

Described are activities and games incorporating a technique of "one step" which is used with children with learning difficulties. The purpose of "one step" is twofold, to minimize difficulties with typical trouble spots and to keep the step size of the instruction small. (Author/TG)

A special calendar chart is presented that can be used to find out what day of the week any date falls on during the 1980s. (MP)

Presents three number games for mathematics classrooms designed to improve the learning of number concepts. Game topics include determining products, arranging mathematical signs, and factoring. (ASK)

Discusses several solutions--correct and incorrect--for a "Food for Thought" problem from the May 2000 issue. Emphasizes the importance of proportional reasoning. (KHR)

Several problem-solving activities involving only 0-9 to be used with sets of ceramic tiles are presented. Finding specified sums, differences, or products is the object of most of the problems. (MNS)

Shares different students' solutions for a problem entitled How Much Film?, which appeared in the November 1997 issue of Teaching Children Mathematics. The problem has to do with how many rolls of film are necessary to take 687 pictures. (ASK)

Demonstrates examples, one of which is an extension of "guess and check," to include variables rather than numbers. The quadratic equation az2+bz+c=0, is solved by assuming a complex solution of the form z=x+iy. Explores the use of deMoivre's theorem in deriving trigonometric identities with other examples. (Author/ASK)