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 providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, this issue the authors focus, on Geometry in the Measurement and Geometry strand with strong links for an integrated focus on the Statistics and Probability strand. The small unit of work on the sorting and…

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…

The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the…

Another way to divide a line segment discovered by Nathan Besteman is described along with Euclid's and the GLaD construction. The related projects and problems that teachers of geometry can assign to their students are also presented.

Seven articles present: 1) a solution to a force equilibrium problem, 2) a magic square, 3) a characteristic of right triangles, 4) a family tree of Pythagorean triples, 5) a misunderstanding which may be cleared through modern mathematics, 6) a technique for solving conversion problems, and 7) a special permatation problem. (RS)

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)

Presents six mathematical problems (with answers) which focus on: (1) chess moves; (2) patterned numbers; (3) quadratics with rational roots; (4) number puzzles; (5) Euclidean geometry; and (6) Carrollian word puzzles. (JN)

The five mathematics problems to be solved by high school students participating in the Fifth U.S.A. Mathematical Olympiad are given. (DT)

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)

This book helps teachers define good questions, offers tips on how to create their own good questions, and includes a wide variety of questions for use in the classroom. Each chapter of the book is organized by subject area and age group so that teachers can locate the topic their class is working on, then select probing, thought-provoking…

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

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