|Matthew Peeples, Naval Academy Preparatory School
The following is an online extra from the June/July 2011 issue of MAA FOCUS. Read the entire issue here. Read more MAA Sample Articles and Features
Every summer, students at the United States Naval Academy Preparatory School (NAPS) in Newport, Rhode Island, hold NITRO games, an all-day event capping for NAPS Indoctrination Training & Readiness Operation.
The day pits platoon against platoon in physically and mentally demanding events to determine the top platoon and company. Additionally, the academic departments (English, physics, chemistry and mathematics) contribute by creating their own competitions, which take place between the physical challenges.
The NAPS Mathematics Department contributed a new challenge this year: giant tangram puzzles. In such a puzzle, a person arranges geometric pieces, cut from a square, to match an image. Tangrams are given as interesting geometric perception puzzles to teach such concepts as symmetry and reflection—common ideas later presented in graphing functions. The shapes are used to create silhouette forms, and the goal of the puzzle solver is to arrange the shapes in that form.
To make the challenge appropriate for students participating in the NITRO competition, however, a physical and team-building aspect was added by creating tangram puzzles that measured 8 feet by 8 feet when assembled into a square. The large, heavy pieces required students to work together to create the (appropriately nautically themed) shapes given in silhouette form. The pieces were designed and built by the math department members, Matthew Peeples, Jake Bray, Vincent Lynch, Craig Bratter, Joseph Kunicki, and Thor Aakre, and required several days to assemble.
The result was a very challenging intellectual activity that required a high degree of cooperation and reasoning ability by each squad. Out of eight puzzles given, most teams completed only one or two puzzles, although a few solved as many as six.
Although some of the puzzles were very easy for individuals to solve on a small scale, the activity illustrated that it is much more difficult to get a team of 10 to 12 students to work cooperatively while reasoning geometrically. However, when they move on to the Naval Academy, these students will need such basic geometric reasoning skills to be successful in calculus. Furthermore, when these students become officers in the United States Navy, they will be expected to maneuver ships or groups of ships cooperatively.
The tangram is a combination of plane polygonal pieces such that the edges of the polygons are coincident. There are 13 convex tangrams (where a "convex tangram" is a set of tangram pieces arranged into a convex polygon) (Eric W. Weisstein,"Tangram," MathWorld)
Members of the Naval Academy Preparatory School (NAPS) Math Department hold up a well-used tangram puzzle arranged as a square: from left to right are math instructors Jake Bray, Vincent Lynch, Joseph Kunicki, and Matthew Peeples.
Instructors Craig Bratter and Vincent Lynch. Dr. K does some cutting.
Left to right, Vincent Lynch, Jake Bray, Craig Vincent Lynch and Matthew Peeples show off the
Bratter, Joseph Kunicki, and Thor Aakre. final product.
A platoon argues over assembling a puzzle. One completed puzzle: the anchor shape.