Introduction • Some packages are shaped like cubes. A cube is a rectangular three-dimensional shape with six identical square faces. 1 unit 1 unit 1 unitAdapted from Connected Mathematics, Filling and Wrapping: Three-Dimensional Measurement, Dale SeymourPublications, 1997
Patterns for a cube• How many different flat patterns you make to fold into a box shaped like a cube? ▫ Sketch the pattern for each one in your notebook ▫ Pattern must be continuous, edges must touch ▫ Cut out the pattern on grid paper to test it• What is the surface of the pattern? Not Allowed Allowed Not Allowed
Making a rectangular box• On grid paper, draw a pattern that will fold into a rectangular box that is not a cube. ▫ Each side length must be a whole number of units ▫ Test the pattern by cutting it out ▫ What is the surface area of the box? ▫ What is the volume of the box? 1 unit 1 unit 3 units
Packaging Blocks• A company wants to package 24 cubes in the shape of a rectangular prism and then package them in a box that exactly fits the prism.• Find all the ways 24 cubes can be arranged into a rectangular prism. Make a sketch of each arrangement you find, and give its dimensions and surface area.• Organize your findings in a table.
Organize your findings in a tableLength Width Height Volume Surface Sketch Area1. Which of your arrangements requires the box made with the least material?2. Which requires the box made with the most material?
Pringles ChallengeGoal• You have been asked to work in groups of three design and test a package to safely ship a single Pringles Potato Chip through the U.S. Postal Service to another school in the U.S. Upon arrival, the chips will be evaluated and scored according to an agreed upon process.
Materials• 1 Pringles Chip• 3” x 5” index cards• 8 ½” x 11” copy paper• Drinking straws• Scissors• Masking tape• Ruler• Utility knife• Cereal boxes
Rules1. No substance may be applied to the chip, or the chip altered in any way.2. You may not use bubble wrap, any type of commercial packaging, foam peanuts or extra chips.3. The chip must be recoverable and edible (but please don’t eat it!) when received by the partner school. It cannot be wet, colored, or varnished.
Constraints4. No pre-made Pringles containers should be used (ex. specially designed Pringles containers for lunch boxes, Pringles cans, etc)5. Also be advised that there is a 3″ x 5″ limit on the size of the package and a fussy postman may reject a smaller package.6. The outer package must be constructed with single-ply cardboard instead of 2-ply.
Constraints7. You may choose a variety of materials for the packing, but you cannot use glass, plastic, wood and you cannot leave grease stains on paper towel. The package should have a mass of 300 grams or less, including the contents.8. Package must be clearly labeled on the outside with the sending school and group. You may not write “Fragile” or “Handle with Care” on the packages.
Testing and Evaluating• Place package on a table and hold a paperback book 12” above the package and drop the book onto the package. If the chip survives, you move on.• Drop a textbook from 12”.• Drop both books from 12”
Scoring• Three measurements must be collected in order to score a package for the Pringles Challenge. ▫ Mass – measured in Kg to at least 3 significant figures ▫ Volume – measured in cubic centimeters to at least 3 significant figures ▫ Intactness score of the chip as determined by the evaluating school, according to the chart below
100 PointsIntactness ScorePerfectly Intact Like it just left the factorySlightly Damaged Cracked, but still in one piece 50 Points Broken along the edges, but 10 PointsChipped Chip less than 5 pieces The chip is broken into two 10 PointsSplit Chip fairly equal piecesSignificantly Chipped and/or cracked into 5 PointsDamaged less than 20 pieces Too many pieces to count 1 PointPringle Dust (more than 20)
Overall Score• The overall score of the package will be used to compare packages. The formula for calculate the overall score will be as follows:Overall Score = Intactness Score (Mass in kg x Volume in cc)Example: a) A perfect chip = Intactness of 100 b) Mass = 256 grams or 0.256 kg c) Volume = 250 cc (2.5 x 10^2)Overall Score = (100/(.256 x 250)) = 100/64 = 1.56 (when rounded to 3 significant figures)