Students analyze items from the media to answer mathematical questions related to the article. Exponents and working with large numbers are the underlying mathematical ideas this month.
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Margaret R. Meyer
One of my favorite lessons comes from a problem I first heard posed as an open–ended assessment problem by David Clarke at an NCTM conference years ago:
Readers comment on published articles or offer their own ideas.
Regarding the reflection “On the Area of a Circle” by Cheng, Tay, and Lee (MT April 2012, vol. 105, no. 8, pp. 564-65), it is possible to prove that one can arrange infinitely many sectors of a circle into a rectangle to show that a circle's area is π2. However, the authors' derivation is invalid because they assume their conclusion by using the area of the circle within their proof.
Rina Zazkis, Ilya Sinitsky, and Roza Leikin
A familiar relationship—the derivative of the area of a circle equals its circumference—is extended to other shapes and solids.
Joshua A. Urich and Elizabeth A. Sasse
Students peel oranges to explore the surface area and volume of a sphere.
Martin V. Bonsangue
In the absence of a decimal number system and representations for square roots, Archimedes estimated the value of pi using inscribed and circumscribed polygons to a circle.
Diana Cheng and David Thompson
Labyrinths inspire questions about measuring path lengths and representing patterns.
The term Norman architecture is used to categorize styles of Romanesque architecture developed by the Normans in northwestern Europe, particularly England, in the eleventh and twelfth centuries. The Normans introduced castles, fortifications, monasteries, abbeys, churches, and cathedrals, all with characteristic rounded arches, particularly over windows and doorways, and massive proportions.
