Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

The objectives, content, and intent of an undergraduate mathematics course at the University of Northern California. The course focuses on gambling and bets, with the focus of ideas on probability, expected value, computers, and the mathematics of finance. (MP)

An attempt to combine the advantages of group instruction with the advantages of individualized instruction is described. The rationale, procedure, and method are discussed in turn. Test results indicated that students learn at least as well by this combined method. Student opinion was generally favorable. (LS)

The nature of an investigation into numbers termed Nearly Isosceles Pythagorean Triples (NIPTs) is detailed. The exploration, even though it is stated to have no practical value, is defended as helping pupils see the beauty of patterns in mathematics. Two questions regarding the pattern of generating NIPTs are noted. (MP)

Described is a two-week summer residential program designed for students who have been identified through one of several middle school talent searches. Discussed are the assumptions and goals, course content and pedagogy, evaluation, and materials of the program. (CW)