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As a new employee of the Raider Kola Company's
marketing team, you have been waiting for an opportunity to demonstrate
your abilities. Several
teams have been selected to design a new packaging unit for the
distribution of the various soft drinks produced by the company.
You are expected to present, in writing, to the company's executives a
convincing (and professional) argument that your design is the best in
terms of efficiency. You
know that the company's executives are most impressed when new ideas are
supported by mathematical analysis rather than by approximate
measurements.
It is rumored that a rival company, Popzi, has
plans to unveil a different package in an upcoming advertising campaign.
You have overheard some of the vice-presidents whispering,
"Why would two rows of three cans be the best packaging arrangement
for the six soft-drink cans? Should we consider a different number of cans as well as a
new arrangement of cans?" Because
the pressure is on from Popzi, your team has only a short time to
complete your design and prepare a written presentation.
(Due date: ____________)
You have been given twelve soft-drink cans to use.
You can use any other tools your team has available.
Be sure to submit all of your drawings (a minimum of 4 designs
for a 3-pack, 4-pack, 5-pack,…, 12-pack very neatly presented and
including the competed worksheets p. 1-3) for all of your
attempts as part of the investigation.
Be sure to include:
1.
measurements
2.
efficiencies (with all calculations), and
3.
tessellation of the plane, if possible.
(Trace each shape and make a model that you can use to show how
well the shape fills the plane.) If it will not tessellate the plane, clearly mark this
instead.
Any or all of these could possibly be used in
future explorations. (Your choice should be done on Geometer's
Sketchpad and copied into your word-processed report.)
YOUR
GOAL: Create a
portfolio of designs. Find
the most efficient package possible for sets of three cans or more.
Remember that we define efficiency as the ratio of the area of
the bottoms of the cans to the area of the bottom of the box.
Also address the package's shelf efficiency by exploring
tessellation of the package.
Efficiency Templates
Evaluation |
