You may want to keep the following periodicals and books in the classroom for students to browse through.
Aha! Insight (Book, 6-10)
Martin Gardner; W. H. Freeman (for Scientific American), 1978; $15 (paper). This book contains short, fun problems that Gardner has collected, that can all be solved easily--if one chooses a good approach. Many of the problems involve combinatorics (counting), algorithms, or logic. Illustrated with cartoons.
Math EQUALS (Book, 6-10)
Teri Perl, Addison-Wesley, 1978; $20. Each chapter contains a biography of a woman mathematician, followed by mathematics activities related to her work. There are a few discrete mathematics activities, including those in a chapter on Lady Ada Byron Lovelace (1815-1852), who wrote about Charles Babbage's design for a machine that anticipated the modern computer.
QUANTUM: The student magazine of math and science
(Magazine, 10-College) Springer-Verlag, 6/yr.; $20/yr.
This is a new magazine on mathematics and physics for sophisticated high school students. It has well-written, challenging articles about current math and science topics and also has a problem section. It is a collaborative effort of the NCTM and the American Association of Physics Teachers, along with their counterparts in Russia. (Quantum was inspired by the Russian journal Kvant, which in turn may have been inspired by an older Hungarian mathematics newsletter for students.)
Math Horizons (Magazine, 11-College)
MAA, 4/yr; $35/yr ($20/yr, MAA members).
Written for undergraduates, this also makes interesting reading for high-school students, and teachers at all levels. Articles include profiles of famous contemporary mathematicians, including John Conway (tiling, knots, and game theory), Fan Chung (graph theory), Persi Diaconis (probability and magic), and Jean Taylor (soap-film surfaces). There are articles giving information on careers in mathematics, as well as a problem section.