An understanding of geologic time is comprised of 2 facets. Events in Earth's history can be placed in relative and absolute temporal succession on a vast timescale. Rates of geologic processes vary widely, and some occur over time periods well outside human experience. Several factors likely contribute to an understanding of geologic time, one of…

Explores trapezoidal numbers, which are the result of subtracting two triangular numbers. Includes classroom activities involving trapezoidal numbers to help students develop their problem-solving skills. Includes reproducible student worksheets. (MKR)

Problems which can be solved or partially solved by the Gregory Interpolation Formula are presented. The formula is explained and applied to three problems. (MNS)

Shares some explorations of Fibonacci sequences with a special focus on problem-solving and posing processes. (ASK)

The author gives a method for involving students in developing and verifying elementary number theory hypotheses by studying areas and perimeters of primitive pythagorean triangles. (MN)

Problems are discussed in which addition facts are presented using words instead of numbers. The letters are then replaced by numbers that will make the addition problems correct. (MP)

A class's struggle with the computer solution of a nontrivial problem is related. The use of algorithms allowed a trial-and-error approach.

Conjectures about triangular arrangements of nine digits are stated and proved. (DT)

How can a chain with 63 links be cut in 3 places so that you could hand a person any number of links from 1 to 63? Considers variations on the problem and derives a general formula. (TO)

Problems set in the real world help students see the relevance of mathematics. Topics that provide sources of real problems are discussed, with examples: mazes, packing, and networks. (MNS)

This section contains brief articles on triangular differences, when one is not equal to one, using calculators to check solutions of quadratic equations, and a county agents' problem. (MNS)

Sometimes the immediate use of an algebraic approach to solve a problem can obscure what is actually happening. The solution to one problem is described both algebraically and through a numerical approach. (MNS)

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

The converse of a familiar construction problem is explored, and a partial solution presented. The general problem is "Given a segment with length whose square is x, construct a segment with length 1." (SD)

Topics covered include alternate methods for finding LCM and GCF, imaginative word problems, and a primes-breakdown method of factoring quadratics. (MP)