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by Dave Youngs
This month the Puzzle Corner presents a math
activity that can be used by itself, or in conjunction with a unit on
apples. September is the month in which Johnny Appleseed's birthday
is celebrated. It is also when the apple harvest begins in our area
making apples fresh and readily available. (Did you ever wonder when
that apple you had for lunch was picked?) Because of this, I usually
did a mini-unit on apples at the end of the month that used various
AIMS activities along with language, art, music, and cooking
activities.
The AIMS apple activities were always a hit with my elementary
students and provided a great way to introduce the class to some of
the important science process skills early in the school year. For a
listing of AIMS activities dealing with apples, search the AIMS
Activity Database on our web site.
This month's activity is a modification of a popular puzzle in
recreational mathematics. The original version of this puzzle
challenges you to divide an object, usually a cake, into eight pieces
using only three straight cuts. While this seems impossible at first,
the solution is found by those who persist. Instead of challenging
students right away with this version of the puzzle, I have chosen to
make it more open-ended, and hopefully less frustrating.
Apple Pie Slicing shows a pie sliced into six pieces
with three straight cuts going through the center. It challenges
students to see how many different numbers of pieces (2-8 are all
possible) they can "slice" a pie into using three straight cuts. (The
cuts do NOT have to go through the center of the
pie.) Students are then asked to determine the minimum and maximum
number of pieces possible and to justify their answers. With a little
work, students should be able to slice the pie into two, three, four,
five, and seven pieces. After some creative thinking they may even
come up with the solution for eight pieces. (It IS
possible).
As with all Puzzle Corner actvities, I recommend
that you try the puzzle yourself before assigning it to your
students. This way you will experience first-hand the kinds of things
your students will encounter when working on the problem--just be
careful no to underestimate their problem-solving abilities. Trying
the problem yourself will help you build your PSPQ (problem solving
persistence quotient). Hopefully, it also will allow you to
experience the "joy of discovery."
I hope that you and your students find this puzzle interesting and
worthwhile.
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