By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

Today, the Common Core State Standards for Mathematics (CCSSI 2010) expect students in as early as eighth grade to be knowledgeable about irrational numbers. Yet a common tendency in classrooms and on standardized tests is to avoid rational and irrational solutions to problems in favor of integer solutions, which are easier for students to…

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

A study is conducted to prove Kaprekar's conjecture with the help of mathematical concepts such as iteration, fixed points, limit cycles, equivalence cases and basic number theory. The experimental approaches, the different ways in which they reduced the problem to a simpler form and the use of tables and graphs to visualize the problem are…

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

Using license plates and telephone numbers for teaching probability ideas involving counting rules is suggested. How each is useful is illustrated in some detail. (MNS)

Explores trapezoidal numbers, which are the result of subtracting two triangular numbers. Includes classroom activities involving trapezoidal numbers to help students develop their problem-solving skills. Includes reproducible student worksheets. (MKR)

In a series of exercises students develop designs in which nodes are labelled according to the isolation rules defined. Strategies for creating new designs from known ones, finding the maximum number of isolation designs on a given configuration, and developing larger isolation designs are encouraged. Sample worksheets are included. (SD)

Solution of, and commentary on, a problem suitable for use in the secondary school mathematics classroom. Topics from arithmetic, algebra, and number theory appear in a unified way. (FL)

Problems which can be solved or partially solved by the Gregory Interpolation Formula are presented. The formula is explained and applied to three problems. (MNS)

A history of perfect numbers is presented, which briefly covers the 27 values known at this time. (MP)

Shares some explorations of Fibonacci sequences with a special focus on problem-solving and posing processes. (ASK)

A classic problem involving the "misuse" of mathematical induction is presented. The error in the "proof" is then exposed. The generalization of this problem is presented as a false theorem which should serve to highlight the error. (LS)

Elucidated is the relationship among three threads of mathematical investigations: Kirkman's schoolgirl problems, finite geometries, and Euler's n-square officer problems. (JP)