Paper Moon: Simulating a Total Solar Eclipse
Sean Madden, James Downing, Jocelyne Comstock
This article describes a classroom activity in which a solar eclipse is simulated and a mathematical model is developed to explain the data. Students use manipulative devices and graphing calculators to carry out the experiment and then compare their results to those collected in Koolymilka, Australia, during the 2002 eclipse. Includes a description of how to set up the simulation and examples of student work.
Read how you can use this article as part of a Professional Development Experience.
Understanding Conic Sections Using Alternate Graph Paper
Elizabeth Brown, Elizabeth Jones
A description of two alternative coordinate systems and their use in graphing conic sections. This alternative graph paper helps students explore the idea of eccentricity using the definitions of the conic sections. Includes multiple examples of the uses of these alternative graphing sections, along with focus - directrix definitions of conic sections to be used with the new coordinate systems.
The Matrix Connection: Fibonacci and Inductive Proof
Tamara Veenstra, Catherine Miller
This article presents several activities (some involving
graphing calculators) designed to guide students to discover several
interesting properties of Fibonacci numbers. Then, we explore interesting
connections between Fibonacci numbers and matrices; using this connection and
induction we prove divisibility properties of Fibonacci numbers. Includes
problems and samples of tasks used to help student discover patterns within the
Fibonacci Sequence and connections to matrix algebra.
Using the Dynamic Power of Microsoft Excel to Stand on the Shoulders of Giants
John Donovan II
article shows how Microsoft Excel's ability to vary parameters with sliders
allows students to "stand on the shoulders of giants" and discover
characteristics of polynomial functions. The article presents several problems
and shows how they can be better understood from a graphical approach using
Excel. Includes problems with possible solutions and follow up questions that
lead students to an in-depth understanding of polynomials.
Finding Complex Roots: Can You Trust Your Calculator?
Barbara Ciesla, John Watson
This article investigates a specific instance when the
textbook answer for finding a root of a complex number differed with the answer
given by the TI-83. After explaining the reason for the difference the article
then expands the definition of the integral root of a complex number to an
arbitrary complex power of a complex number. Read now to see where false
assumptions might be made based on the results of a calculator and see
explanations of how to overcome those assumptions with logic and proof.