Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

Using modern technology to examine classical mathematics problems at the high school level can reduce difficult computations and encourage generalizations. When teachers combine historical context with access to technology, they challenge advanced students to think deeply, spark interest in students whose primary interest is not mathematics, and…

This article employs the Archimedean method of estimating the value of pi within an inscribed pentagon. We show how to write these approximations in terms of the golden ration.

This article illustrates how the arithmetic series 1 + 2 + 3 + ... + n is pervasive in mathematical contexts as a powerful problem-solving tool.

The heliocentric, or Sun-centered model, one of the most important revolutions in scientific thinking, allowed Nicholas Copernicus to calculate the periods, relative distances, and approximate orbital shapes of all the known planets, thereby paving the way for Kepler's laws and Newton's formation of gravitation. Recreating Copernicus's…

This article describes how the concept of "key idea" can be used in high school geometry to connect students' informal explorations with rigorous mathematical proof. (Contains 6 figures.)

Discoveries of Charles Babbage in the 1800s are described. Origins of the difference engine, his calculating machine, the principles of computation applied to tables, and the design and construction of his engine are included. (MNS)

Binomial coefficients are used to prove two conjectures concerning the partitioning of an N-dimensional space. (MP)

This article shows how an inexpensive calculator can be used advantageously to determine repeating decimals. Even the decimal representations of numbers, such as one-seventeenth and one-nineteenth, can be easily computed. Many examples are given, and some theoretical discussion is included. (Author/MP)

Shortcuts to use when performing operations with the calculator are given. Algorithms discussed include reciprocals, powers, parentheses, infinite series, and synthetic division. (MP)

The concept of prime factorization is discussed and two rules are developed: one for finding the number of divisors of a number and the other for finding the sum of the divisors. (MP)

Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)

Discusses a calculation method to approximate pi. Describes how to get an approximation to the circumscribed and inscribed perimeters of regular polygons of n sides. Presents the computer program and result of the approximation. (YP)