The author and his first-year algebra students explored the quadratic behavior behind the parabolic shape of fountains at the local family splash park. This hands-on discovery project has three main parts: (1) gathering data by experimenting with and photographing the fountains; (2) analyzing the photographs to obtain numerical data; and (3)…

Illustrates exploration of composition of functions, translations, and inverse functions on a graphing calculator. Includes reproducible student worksheets. (MKR)

Worksheets designed to help students explore factoring integers are presented. (MP)

Using De Moivre's theorem and a parametric graphing utility, examines powers and roots of complex numbers and allows students to establish connections between the visual and numerical representations of complex numbers. Provides a program to numerically verify the roots of complex numbers. (MDH)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

The calculator is used to help students discover the Rule of 72 which is, in turn, used to investigate problems involving population, inflation, and energy reserves. (MP)

Three examples are given illustrating the use of the calculator in problems where determining patterns and making conjectures are stressed. (MP)

These exercises are designed to expose students to the nature and effects of inflation and consumption rates. Pupils are expected to see how long it takes for costs to increase to certain levels, and how quickly various growth rates can deplete a finite resource. Worksheets suitable for duplication are provided. (MP)

The construction of tables of numbers is discussed as a learning activity that involves work in such things as reciprocals, calculators, formulas, patterns, discovery, prime numbers, and other types of numbers. (MP)

This discussion of cyclic patterns that appear in repeating decimals includes the use of the calculator in discovering the patterns. (MP)

Consideration of a definite integral in an advanced calculus class led to a great deal of mathematical thinking and to the joy of discovery. Graphing calculators allowed students to investigate quick solutions which should be regarded as stepping stones to additional investigation and rigorous proof. With slight modifications to their proofs,…

Uses a discovery lesson for determining the area of an equilateral triangle given a side length as an illustration of how to introduce features of the TI-92 graphing calculator geometry package within a mathematical context. (KHR)

Demonstrates how the uniqueness and anonymity of a student's Social Security number can be utilized to create individualized polynomial equations that students can investigate using computers or graphing calculators. Students write reports of their efforts to find and classify all real roots of their equation. (MDH)

Activities to extend the core curriculum through the study of the periodicity of rational numbers to help students develop calculator and research skills are presented. Four worksheets are included, to be used as discovery activities. A computer program is listed, as well as examples of periodic pictures. (MNS)

Examples of composite functions present students with intriguing questions that they can explore using calculators and computers, geometric and algebraic methods, and approximation techniques. Student-centered activities allow students to make discoveries about functions. (MLN)