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January 2005, Volume 98, Issue 5


Making Mathematical Connections by Constructing Tetrahedra
Jennifer Bergner, Randall Groth
A polyhedra construction project that illustrates how one activity can address several of the mathematics content standards. Directions are given for a multiple day lesson on building a large tetrahedron in groups.

Visualizing the Domain and Range of the Composition of Functions
Nial Neger, Michael Frame
A graphical method for visualizing compositions of functions; this method is used to find domains and ranges of compositions. Authors use examples of graphical iterations from Chaos Theory. Directions are given for teachers/students to use their graphing calculators in similar examples.

Placing a Deck of Cards in Order
Mark Yates
Finding the minimum number of moves to order a deck of cards by placing them in suits, but not necessarily in order. Students gather data and create equations to model their patterns in algebra or statistics.

That Ubiquitous Sum: 1 + 2 + 3 + • • • + n
Stanley Bezuszka, Margaret Kenney
How the arithmetic series 1 + 2 + 3 + . . . + n is pervasive in mathematical contexts as a powerful problem-solving tool. Algebra students solve the problem with multiple approaches including geometric and creating general equations. Authors discuss the work of Cantor and Gauss in relation to the series.