The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…

Relationships between the linear dimensions, surface area, and volume of parallelepipeds are examined. (SD)

Simple patterns both in mathematics and music are discussed. Several activities using standard instruments and handmade devices are described. (MNS)

Four categories of abuses are discussed: calculations, games and puzzles; mystical button pushing; and checking answers. Useful activities are illustrated for the categories of calculations, patterns, exploration, applications, and new content. (MP)

Activities suitable for use with primary school students are described. The author offers advice concerning expectations of the students, use of the vocabulary of probability, integration of activities with other classroom work, and related topics. (SD)

A problem concerning the generation of an array of numbers is posed. The author examines the use of this problem in several secondary-school and college classes. (SD)

Advocated is developing intuitive ideas of limits whenever the opportunity arises in elementary mathematics. Examples are given for geometry, fractions, sequences and series, areas, probability, graphing, and the golden section. (MNS)

Activities involving estimation of the number of objects in a configuration can motivate students to consider parametric models. (SD)

Having students find and cut out of graph paper the 12 pentominoes can provide an enjoyable exercise in perception, discovery, and double checking. The pentominoes can then be used to illustrate informally several geometric concepts. (SD)

Three worksheets for use in studying triangular, square, and pentagonal numbers are presented. (SD)

Activity questions based on the prime factorization of numbers can be answered by reference to the lattice structure of factors. (SD)

This pamphlet introduces the student to the basic ideas and procedures of transformational geometry through a series of worksheets. After developing intuitively the idea of rigid motion, vector diagrams are introduced, and translations are discussed in some detail. (SD)

Worksheets to be used for practice on addition and multiplication are provided. (SD)

Described are a discrete group of isometries that fix a line but do not stabilize a point. Each type is accompanied by an example of their representation in concrete form which served as material on which young children could operate. Pupil responses to each situation are provided. (CW)

When a simple game was presented as a challenge to a primary-school girl, she solved the problem, and went on to generalize her solution. (SD)