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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 1 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. 2 You could use the following review as a guide to students: 3