The proof that the area of a quadrilateral is one-ninth the area of another quadrilateral is presented. The proof is designed to give geometry students insight into techniques that can be used in other problems. (FL)

A method for introducing ideas of probability theory is presented. The method is illustrated by solving a coin tossing" problem. (FL)

Two problems related to the mean-value theorem lead into a problem requiring the use of the universal chord theorem. This latter theorem is discussed and a proof given. (MP)

This article examines the classroom value of assigning good mathematical problems and especially of encouraging many different approaches to their solutions. (Contains 6 figures.)

Different representations of rational numbers are considered and students are lead through activities that explore patterns in base ten and other bases. With this students are encouraged to solve problems and investigate situations designed to foster flexible thinking about rational numbers.

While waiting for his meal to arrive, a truck driver was using his straw to move water from one glass to another when he was struck by this question: If I keep doing this, will the two glasses ever have exactly the same amount of water? This article looks at various problems related to that question.

It is proved that if the differential equations "y[(n)] = f(x,y,y[prime],...,y[(n-1)])" and "y[(m)] = g(x,y,y[prime],...,y[(m-1)])" have the same particular solutions in a suitable region where "f" and "g" are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical…

A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

The matrix diagonalization method is used to solve a limit problem.

Teachers face many challenges when attempting to teach problem solving to young children. This article examines these challenges from a classroom teacher's perspective and suggests ways to facilitate reform in mathematics instruction.

The extreme interval values and statistics (expected value, median, mode, standard deviation, and coefficient of variation) for the smallest (min) and largest (max) values of exponentially distributed variables with parameter ? = 1 are examined for different observation (sample) sizes. An extreme interval value g[subscript a] is defined as a…