Examines the gear system of a mountain bike to discover any redundancy in the many gear settings available to the cyclist. Suggests a best strategy for changing up through the gears on a typical 21-gear system and an adjustment to the available gears that would result in a smoother change. (Author/ASK)

Presents a variety of problems for elementary and secondary school students that focus on probability. Activities involving coins, M & M candies, and the game show "Let's Make a Deal," are described, and Web sites for the activities are listed as well as sites for lesson plans. (LRW)

Presents an activity in which attribute blocks help middle school students understand the fundamental counting principle and the multiplication rule. Demonstrates how these materials can aid students in building a conceptual understanding of multiplication and the counting principle. (ASK)

Suggests that teachers could write problems to suit student populations in their schools and in the process of doing so encourage discussion, reflection, and writing by their students on mathematical language. Presents a series of games for the creation of equations for Year 7 students. (Contains 13 references.) (ASK)

Presents an activity in which students use computer-based spreadsheets to find out how much grain should be added to a chess board when a grain of rice is put on the first square, the amount is doubled for the next square, and the chess board is covered. (ASK)

Pupils progress through a relatively small number of key stages called growth points in numeracy learning. Identifies growth points in developing numeracy and suggests that better support can be offered to children when teachers are aware of the growth points. (ASK)

Begins with some context setting on new views of statistics and statistical education reflected in the introduction of exploratory data analysis (EDA) into the statistics curriculum. Introduces a detailed example of an EDA learning activity in the middle school that makes use of the power of the spreadsheet to mediate students' construction of…

Demonstrates how play can be the catalyst to undertake mathematics. Presents 15 activities on different mathematical subjects such as geometry. (ASK)

Two studies examined the impact of mathematical games, some involving parents playing games with children in class, on 5- to 7-year-olds' number knowledge. Results showed that games appeared to be most effective as a way of enhancing children's learning when a sensitive adult was available to support and extend the children's learning as they…

Presents a problem and its solution on generating the complete set of triples of given sides of a triangle. Determines that students who work through the problem stand to learn a great deal more than just which particular triangles fit the given requirements. (ASK)

Details a lesson that utilizes trigonometric identities to determine the optimal angle between the atoms of covalent bonds. Generates a proof of the optimal angle for a molecule with four identical atoms bonded to a central atom that has a complete valence shell. (DDR)

Discusses the rationale behind the technique of rationalizing the denominator in algebra. Argues that the importance of this technique is greatly exaggerated and is usually unnecessary. Examines an appropriate application of rationalizing the denominator. (ASK)

Presents an activity to investigate physico-mathematical concepts and provide mathematics arguments that are very close to a proof with the advent and availability of powerful technology. Demonstrates without using calculus how the law of reflection for parabolas is derived from Fermat's principle of least time. (ASK)

Explains how to code and decode messages using Hill ciphers which combine matrix multiplication and modular arithmetic. Discusses how a graphing calculator can facilitate the matrix and modular arithmetic used in the coding and decoding procedures. (ASK)

Argues that mathematics is, to a large extent, the study of patterns. Presents an activity in which students search for patterns in the Fibonacci sequence and Pascal's Triangle. (ASK)