Place value understanding requires the same activity that students use when developing fractional and algebraic reasoning, making this understanding foundational to mathematics learning. However, many students engage successfully in mathematics classrooms without having a conceptual understanding of place value, preventing them from accessing…

Illustrations are provided which show how some algebraic manipulations done prior to doing calculations can eliminate unnecessary storage of data, reduce the total number of needed steps, and avoid overflow. (MN)

Two methods are considered for finding the logarithm of a number using elementary arithmetic. (DT)

An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

Discusses terminology used by teachers for the symbol "-x" which cause students to become confused. Suggested methods of avoiding this confusion are presented. (JP)

Presents a mathematical puzzle that asks about "missing" area and leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. Discusses the inquiry, the concepts, the solution, and an extension that deepens all students' understanding of the connections between algebra and…

Enrichment topics dealing with solutions of polynomials over modular systems are described. (SD)

Explores abundant numbers and presents a proof that abundant numbers of every order exist. Readers are encouraged to use the included computer program to explore abundant numbers for themselves, look for patterns in the output, and consider further questions. (Author/MKR)

Describes an activity in which students, grades 7-12, explore patterns and properties of repunits, an integer written as a string of ones. Includes extensions for exploring algebraic justifications. (MKR)