Lessons for first-grade students deal with the numbers five and six. How groups of five and six differ is the focus of the comparing and counting activities. (MNS)

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)

Ten examples of when the sequences of key presses given in calculator instruction booklets are either inefficient or lead to an incorrect answer are given. (MNS)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

The Mayan system of numeration, which used 20 as the base, is discussed. The material presented has been used to stir the curiosity of students in different systems of numeration. It has been helpful in promoting a speedier and better understanding of base 10. (MP)

Examples of four interviews are presented to serve as sample evidence in support of more comprehensive diagnostic procedures in assessing reliably and validly the weaknessess and strengths of learners. The search for computational errors is seen to go beyond standard paper and pencil tests. (Author/MP)

Ways in which bead strings can be used for reinforcement and concept development are noted. After discussion on how to make bead strings, the material looks at: (1) prenumber concepts; (2) more than, less than; (3) conservation of number and numerals and numerousness; (4) addition and subtraction; and (5) place value. (MP)

This discussion deals with the question, are there integral rectangles such that a box of maximum volume is obtained by removing an integral-sided square from each corner? An equation to solve the problem is generated and a table of values presented. The material appears suitable for beginning calculus students. (MP)

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)

Three studies of college students found a sex difference in the correlation of memory scanning rate, short- and long-term components of free recall, and word recognition with memory span. Findings are discussed in terms of prior work and a theory presented to account for the obtained sex differences. (Author/RD)

Masters of three worksheets are provided which require students to name selected polygons, compute areas of triangles, rectangles, squares, and trapezoids, and compute cost per square unit. (MK)

Three alternative methods of finding averages of two numbers are presented. (MP)

An introductory multiplication lesson, used successfully with second graders, is detailed. The method takes advantage of prior knowledge acquired in a geometry unit of study. The lesson is seen to have potential for other grades teaching multiplication for remedial work, and explaining the commutative law. (MP)