Topics covered in the first chapter of Unit 8 of this SMSG series include square roots, operations with radicals, operations with real numbers, and the structure of the real number system. The second chapter deals with measurement of area (for rectangular regions, other polygons, and circles), volume and surface area, computation involving…

This workbook along with a set of transparent 2" x 3" cards was developed for use with underachieving seventh and eighth grade boys. It is designed for a 14 week term or less. The format uses the cards extensively to learn about fractions and operations with fractions. The cards have circles etched on them and the circles are divided into varying…

Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

Use of graphs in studying greatest common divisors, least common multiples, and other concepts can illustrate patterns related to the definitions of these concepts. (SD)

A mathematics teacher who avoided students' questions about zero, notes that children are able to interpret this concept and any system of numeration in a language that they have made up and can understand. (AM)

Some benefits of helping learners think in prime numbers are detailed. Reasons for the decay of this ability are described, with short division presented as one activity which should be reintroduced in schools. (MNS)

The mechanisms, images, and language needed for the development of rational-number ideas are briefly discussed. Such ideas are sophisticated and different from natural-numbers ideas. (MNS)

Activities are described which make use of rectangular arrays as a means of illustrating multiplication facts and the distributive property. (DT)

Measurement of distance was used as a basis for teaching first-graders the relation of unit to quantity and the ordinal and transitive nature of natural numbers. These children performed much better on measurement evaluations and almost as well on set theory evaluations as comparison children taught through set theory. (DT)

The goal was to help 7- and 8-year olds develop computational skills in addition and subtraction. Experimental groups received instruction emphasizing mathematical structure while control groups worked on drill activities. Results showed that emphasizing structure facilitated the development of number concepts, place value, and computational…

Thirty-five students from all ability levels in the first and second year of secondary school were interviewed to determine their understanding of appropriate application of number operations. Results of the interviews are classified into five different levels of understanding. (DT)

The rules for seven different games with playing cards are given. Educational uses are discussed briefly for each of the games. (DT)

Shortcuts for multiplying by eleven are presented and explained. (DT)

Whole numbers written in spiral or triangular patterns with spaces occupied by prime numbers blocked in produces interesting visual patterns. Described is a game based on these patterns that may be played at many different levels. (JP)