Goal: Collect data regarding weight versus volume for shipping of products. You will create/select an ideal box to ship an egg with foam packing peanuts. A contest will be conducted.
Procedure:
1. Label each of your boxes with A, B, C, etc.
2. Find the volume of each of your boxes. Measure to the nearest ¼ inch. Record the volume in the table below.
3. Fill each box with your shipping item, and foam packing peanuts. Be sure the box can close easily but the item does not shift. Weigh each box (ounces) and record below.
Box Label ( Weight , Volume ) Ratio of weight to volume
A
B
C
D
E
4. Graph the data (weight, volume) on a piece of graph paper.
5. Draw a line of best fit.
6. Calculate the slope.
7. Using y = mx + b , calculate the y-intercept.
8. Write the equation of the line of best fit.
9. Explain the real life meaning of slope.
10. Explain the real life meaning of the y-intercept.
11. Using your equation from #8 above, predict the weight of a package that is 1 feet tall, 2 feet wide, and 3 feet tall.
12. Calculate the ratio weight to volume for each of your boxes and record the decimal value in the last column of the table in #3 above.
13. As a manufacturer responsible for shipping, which of your ratios would be the best assuming your product will arrive safely.
Teacher Notes:
In the manufacturing process, many of the items once completed will need to be shipped to other companies (for additional assembly), shipped to warehouses for distribution, or directly to the customer. During the shipping process, it is critical that the item arrive in perfect condition. If damaged during the shipping process, companies must repair or replace the item. In addition, if products are damaged often, customers will search out other companies to fulfill the order request.
One method of providing cushion for shipped items is with packing peanuts. These foam-packing fragments are made of a variety of materials and in different shapes.
Shipping costs have historically been calculated on the basis of gross weight in kilograms or pounds. By charging only by weight, lightweight, low-density packages become unprofitable for freight carriers due to the amount of space they take up in the truck/aircraft/ship in proportion to their actual weight. The concept of Dimensional Weight has been adopted by the transportation industry worldwide as a uniform means of establishing a minimum charge for the cubic space a package occupies.
Dimensional weight favors shippers of dense objects and penalizes those who ship lightweight boxes. A box of unpopped corn kernels will likely be charged by gross weight; a box of popcorn will probably be charged by its dimensional weight. This is because the large box of popcorn takes up a lot of space but does not fill up a vehicle's capacity in terms of weight, making it an inefficient use of space.
Shippers avoid dimensional weight charges by using smaller boxes, by compressing their goods, and by reducing the use of packing materials.
CTE Goal: Students will understand the packaging needs of manufacturing companies.
Math Goal: Students will collect data and use the line of best fit to create an equation to predict weight of packing materials.
Materials Needed: Each group needs 4-5 small boxes, packing peanuts (enough to fill the largest box), access to a digital scale, small item for shipping (does not have to be the same for all groups), and a raw egg per group if you do the contest. Ideally, the small item for shipping can be a plastic Easter egg with a little weight inside. Packing peanuts can be recycled at your school by reclaiming them in the packages received by your school if you let staff know that you need them
CTE Situation: Teachers need to summarize/demonstrate the information found under Teacher Notes. Then continue with this. Students are to find the “best” foam packing peanuts package for an egg to be shipped. The box is to be dropped (to simulate shipping) from 12 feet. To win the contest between students (groups), the egg must survive unbroken and the ratio of weight in ounces to volume in inches should be the largest decimal value. This is designed for students to find the optimum volume for shipping without damaging the product. The egg contest can be skipped but is a fun extension.
Similar CTE Situation: Discuss other packaging methods such as bubble wrap, shrink wrap, cardboard, etc. Why do companies choose what they do?
Egg Drop Contest: A fun extension is to have each group create/find the ideal box, fill with foam packing peanuts and an egg. The winner will be the group that drops their box without breaking the egg, and has the largest ratio (#12 & 13). To keep the packing peanuts clean, place the egg in a zip lock bag.
