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.