Grade 7 Unit Project: Filling & Wrapping
The Worldwide Sporting Company (WSC) wants a new set of package designs for their
table-tennis balls. The table-tennis balls are about 3.8cm in diameter. WSC has decided
to offer a scholarship to the student who convinces the company to use their design. The
criteria WSC have established are:
1. The board of directors wants a small package (containing 2 balls), a medium
package (containing 4 balls) and a large package (containing 8 balls)
2. The president of the company wants the costs of the package to be considered
3. The marketing division wants the packages to be appealing to the customers, to
stack easily and to look good on store shelves.
Part 1: The Design
You are to prepare an entry for the package design contest. Your task is to design three
different size packages including the following:
 A description of the shape or shapes of the packages you have designed and an
explanation for why you selected these shapes
 Nets for each of your packages that, when they are cut out, folded and taped
together, will make models of your packages. Use centimeter grid paper or,
preferably card, to make your patterns
 Calculations of how much each of your package designs will cost to construct.
The packaging material costs $0.005 per square centimeter
Part 2: Write a report
You will submit your designs and written proposal to WSC. Your written proposal
should try to convince WSC that your designs are the ones they should use. Showing
how you have addressed the WSC’s three criteria.
This report is to be written to company officials and you need to think about the
presentation of your written proposal. It should be neat, well organized and easy to read
so that company officials can follow your work and ideas easily
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Skills
 Conceptualize area as a measure of wrapping an object
 Conceptualize volume as a measure of filling
 Explore the relationship of the surface area of rectangular prisms and cylinders to the total area
of a flat pattern needed to wrap the solid
 Understand the relationship between a cubic centimeter and a millimeter
 Calculate the area, surface area and volume of 3-D figures
 Develop strategies for finding the dimensions, surface area & volume of cylinders
 Be aware that changing the dimensions of an object changes its volume and changing the
volume of an object will alter its dimensions
 Investigate methods of finding the volume of irregular objects
Standards
 7.N.19 Justify the reasonableness of answers using estimation
 7.A.6 Evaluate formulas for given input values (surface area, rate, and density problems)
 7.G.1 Calculate the radius or diameter, given the circumference or area of a circle
 7.G.2 Calculate the volume of prisms and cylinders, using a given formula and a calculator
 7.G.3 Identify the two-dimensional shapes that make up the faces and bases of threedimensional shapes (prisms, cylinders, cones and pyramids)
 7.G.4 Determine the surface area of prisms and cylinders, using a calculator and a variety of
methods
 7.M.2 Convert capacities and volumes within a given system
 7.M.11 Estimate surface area
Sample Packages:
The following sample packages will help review the packages your students design.
Table tennis balls are 3.8 cm in diameter. The sample packages below assume a
diameter of 4 cm for ease of calculations.
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You could use the following review as a guide to students:
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