Secondary school students in Singapore are expected to find an expression for the general or "nth" term of an arithmetic progression (AP) without using the AP formula T[subscript n] = a + (n-1)d, where "a" is the first term, "n" is the number of terms and "d" is the common difference between successive…

Pattern generalisation has become an important feature of mathematics classrooms around the globe. Sometimes these activities focus purely on given numerical terms, but the use of pictorial or figural patterns is now becoming part of the standard repertoire for such generalisation exercises. From a pedagogic point of view, the investigation of…

Presents a divisibility problem and how a class of students discussed the problem and determined a plan to solve it. (ASK)

The author, using a weight machine in an airport lounge, varies the machine's input parameters of height and gender to generate data sets of ideal weight. These data are later used at in-service workshops and in both primary and secondary classrooms to explore patterns and make predictions. (JJK)

Uses colored cube combinations to investigate surface area, volume, and axes of symmetry. (ASK)

An algebraic development of the Fibonnaci sequence, appropriate for use in beginning algebra classes, is presented. (SD)

This paper discusses ways of discussing limits in the secondary classroom. Particular attention is paid to showing that hypothesized answers are not limits to given sequences. (SD)

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)

Pattern recognition is a critical component of success in mathematics. Students at all levels should be provided with opportunities to investigate and uncover patterns throughout their mathematical careers. Further, they should be allowed to explore situations in which pattern recognition plays a vital role in the construction of important…

Some number investigations on the multiplication table are provided by a sequence of four activity sheets. Beginning with examples of triangular and square numbers, the activities lead to the generalization. (MNS)

Discusses the importance of identifying and describing the pattern by students in algebra class. Provides some examples showing the usefulness of the method seeing the pattern from mathematical materials. (YP)

Four activity workshops are suggested which might be used for several different purposes. The reproducible worksheets address clock patterns, patterns with tides, extending Pythagoras, and fractions extended. (PK)

Chess experts remember meaningful knowledge in the form of networks or patterns. Applied to mathematics instruction, effective classroom approaches can use investigation to identify patterns or rules. Described are a class activity and a small-group activity to investigate addition of signed numbers and linear relationships. (MDH)