This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by…

In this article we discuss an open-ended problem involving quadrilaterals that we continually offer each semester. The task has been posed to undergraduate and graduate students in methods and problem solving classes. The task involves drawing all possible four sided figures with corners at the dots. A four by four array of dots is included in the…

Investigated here are some of the results which can be obtained using the double-sided straight edge. Seventeen possible constructions are presented with solutions or partial solutions given to most. (MP)

A problem is posed concerning the area of certain parts of a plane geometric figure. The problem was used in a student contest with 71 of 270 mathletes answering correctly. An outline of the general proof is given. (LS)

Comments on student responses to the three dimensional items produced by first investigating flat paper cutouts of the items. (KHR)

This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

The overall results of the fourth U.S.A. Mathematical Olympiad are discussed. The names of the eight finalists are listed, as are the problems in the test. (SD)

An elementary knowledge of geometry is shown to be helpful in problem solving, especially in that the shortest distance between two points is a straight line. (MN)

The technique of organizing data in tables to solve counting problems in geometry is illustrated in the solution of five problems. (MN)

The author has selected a number of episodes that illustrate some of the successes and failures of humanity's attempt to find the area of the circle and presents them as problem studies. (MN)

The author organizes some of the information known about the problem of dividing space by five planes in general position along with its extensions, and consolidates it to highlight some interesting patterns in both methods of solving analogous problems and their results. (MN)

Provides domino geometry problems, problems with arithmetic progressions, and magic pentagram sums. (JM)

The last 13 of 32 exercises of a course designed to give a wide range of skills in deductive, inductive, and indirect methods of proof in geometry are presented. (MP)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)