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by Dave Youngs.
This month's Puzzle Corner activity can be done with nothing more than
a few quarters. In Quarter Quandary students are asked what will happen
if two quarters are placed side by side and then one is rotated around the circumference
of the other. (The quarters should be fairly new so that the edge ridges are
not wornÑthis keeps them from slipping during the rotation.) If the portraits
on the two coins are facing in the same direction at the start, how will they
be aligned at the end of one rotation? How many times will the portrait on the
rotated coin go around in one rotation? Please answer these questions for yourself
and then get two new quarters and try the activity.
Were you surprised? If so, you are like most people who do this activity. Logic
seems to indicate that the portrait on the rotated quarter should go around
once and end up in its original position after the rotation. After actually
doing the activity, most people are quite surprised that this logical answer
is not correct since the rotated quarter actually makes two complete rotations
around the stationary one. This element of surprise makes Quarter Quandary
similar to discrepant events in science. These scientific discrepant events,
with their unexpected outcomes, provide students with an excellent opportunity
to examine scientific phenomena in detail and thus learn something new as a
result. As a mathematical discrepant event, Quarter Quandary provides
a similar opportunity for students to learn some interesting mathematics.
Worksheet
The challenge in this activity, then, is not to discover that the quarter makes
two rotations around the other quarter. Rather, it is to come up with a valid
reason for why this happens. This is what your students will be asked to do
in Quarter Quandary. As is the practice in this column, the solutionÑin
this case an explanation for the puzzling resultsÑwill appear next month in
our solutions archive. Puzzle Corner |
