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)

It is noted that students sometimes have the misconception that square roots of integers are evenly spaced. The difficulty seems suited to approaches with calculators and computers, and is viewed arithmetically, graphically, and algebraically. It is suggested that differences between roots of successive pairs of consecutive integers be examined…

This note describes five repeating patterns (networks of polygons) which have been found to produce an immediate creative response when pupils are asked to colour them as they like. (MM)

This is a not-so-serious discussion of accidental patterns involving chance patterns between mathematics and natural laws and accidental patterns involving the numbers "pi" and "e." (Author/SA)

Explores the close relationship between pattern formation and traditional geometry using the LOGO programing language with the specific example of joining squares, corner to corner, to form a closed ring. Includes the LOGO programs utilized, as well as color illustrations of the interesting and eye-catching patterns generated. (JJK)

Repeating decimals are used as a source for geometric patterns. Ways for generating patterns focus on dividing a circle into certain numbers of equal parts and interpreting the decimal expansions of certain fractions in terms of connecting sequences of points. Suggestions for possible expansions are given. (MP)

This set of transparency masters of mathematical puzzles has as its intent the development of logical and perceptual skills. The puzzles include patterns, magic squares, and counting problems. Solutions and follow-up suggestions are provided on the back of each page. (MP)

Eight teaching ideas involving circular shapes and patterns are described for grades one through eight. (JT)

Examined are the three regular tessellations and derived semiregular tessellations whose regular polygons meet at common vertices. Included are BASIC computer program listings that explore the various combinations of regular polygons that can form regular or semiregular tessellations. (JJK)

This compilation is drawn from the IDEAS section that has been a feature of the "Arithmetic Teacher" since 1971. The contents are arranged in the following categories: Computation, Fractions and Decimals, Developing Number Patterns, Using Flowcharts, Problem Solving, Geometry, and Metric Measure. All selections are reprinted just as they…