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by Dave Youngs.
Puzzle Corner | Student
Worksheet
This month's Puzzle Corner activity is based on a thought problem from
recreational mathematics that most people find difficult. (I remember puzzling
over it for quite some time before coming up with the solution.) In this problem,
people are challenged to think of a way to support a pot over a fire using only
four metal strips and four rocks evenly spaced around the fire. This seems
like a simple thing to do, but there is a hitch - the rocks can't be moved and
they are too far apart for the metal strips to span the gaps between them. If
you've not encountered this brainteaser, think of how you might solve it.
Although the original thought problem is quite difficult, even for adults,
it can be adapted for use in upper elementary and middle school classrooms if
two things are done:
- materials are provided so that students can actually build the structure
necessary to solve the thought problem, and
- students are allowed to build a number of other supporting structures before
being given the challenge of the original brainteaser.
While a variety of materials can be used to model this brainteaser, the ones
chosen here are paper cups and craft sticks. Each student or group working on
the problem will need four craft sticks and five paper cups. The craft sticks
represent the metal strips of the original problem. The rocks are represented
by four of the cups placed upside down on a flat surface. The fifth cup, placed
right side up, represents the pot.
To get students used to building with these materials, they are given a warm-up
assignment in which they are asked to construct various structures using only
the craft sticks and four cups to support a fifth cup. Since there are no restrictions
in this warm-up activity, students should be able to quickly build several workable
supporting structures. Placing the four cups close to each other and placing
the craft sticks in a tic-tac-toe-like arrangement on the cups can make one
such structure. This provides a sturdy platform for support the fifth cup. There
are a number of other similar structures that can be built quite easily. Students
should be given enough time to build several structures and sketch them in the
space provide on the student sheet before moving on to the challenge.
After this initial construction experience, students are ready to tackle the
harder problem posted by the original brainteaser. In this challenge students
are told that they must now try to build a structure in which each craft stick
only touches one supporting cup. In other words, the craft sticks can't
be used to bridge the gaps between the cups. After some failed attempts, students
may claim this is impossible without using some additional materials, like tape
or glue, to connect the craft sticks to each other. If this happens, you will
need to assure students that this task is possible.
If you sense that this puzzle may be too frustrating for you students, you
may want to do it as a group, rather than individual activity. Another option
is to let individual students work on the puzzle for a set period of time in
class, and then encourage them to take the cups and craft sticks home so that
they can work on the puzzle over a longer period of time. Many veteran puzzle-solvers
know that it is sometimes helpful to put a puzzle away for awhile and then pick
it up again at a later time. These puzzlers often find that the solution comes
easily on subsequent attempt.
Student Worksheet I have that you and your students enjoy this puzzle. |
