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Stephan Pelikan, Anna F. DeJarnette, and Stephen Phelps

A monthly set of problems is aimed at a variety of ability levels.

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Finding regular polygons, such as equilateral triangles, squares, hexagons, and even octagons, in art or architecture is not unusual, but seeing a nonagon, or nine-sided regular polygon, such as the Mongolian drum (see photograph 1) is less common. Perhaps 9 is a special number in Mongolia: Shamans have 99 tengri, or spirits, (55 benevolent ones and 44 “dark” ones) on their drums, although the drums are more often circular.

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Jonaki B. Ghosh

Carefully designed tasks enable preservice teachers to explore this puzzle through concrete, pictorial, numerical, symbolic, and graphical representations and engage in explicit and recursive reasoning, deal with counting problems, create Hanoi graphs, and develop mathematical thinking.

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Ahmad M. Alhammouri, Gregory D. Foley, and Kevin Dael

After months of solving real-world problems, high school students enact the full modeling cycle supported by peers, teachers, and technology.