General Mills and Post: Poor Mathematicians?
This post is a redesign of Kris’s Cereal Box digital fabrication project. Although the tweaks that I describe move Kris’s elementary lesson into the middle school and high school realm, it could be altered to be more of a discovery-type experience for elementary students familiar with digital fabrication and ModelMaker.
I came across a lesson this weekend that very simply stated that companies like General Mills and Post must have some reason for creating cereal boxes in their current dimensions other than “bottom line” economic decisions. The rationale was simple: If companies that make cereal really wanted to maximize their profits, then they would reconsider the way in which cereal was packaged. Cereal companies could sell the same amount of bran flakes and crunchy goodness (volume) by redesigning the packaging (surface area) so that it resembled a cube. Less surface area (packaging materials) and equal volume = lower manufacturing costs. Plus, there would be ecological benefits.
This afternoon I pulled out something that I have not touched for a truly mathematical purpose since high school: a ruler. I wanted to test this lesson’s underlying ideas. I grabbed my box of Total Cinnamon Crunch off the refrigerator, and calculated the following dimensions using my ruler:
- Length: 7 5/8 inches
- Width: 2 inches
- Height:10 1/8 inches
I had to do some fraction-decimal conversions in order to re-create the 3D model below. That was worthwhile as a standalone activity if readers are thinking about mathematical procedures, processes, and algorithms. The following image is a 3D representation of my cereal box (without graphics) in FabLab ModelMaker.
I have to admit that I did not spend the time calculating the cereal box’s surface area and volume. I actually used ModelMaker’s properties to give me the answer for surface area and volume.
- Surface Area: 225.406 inches squared (rounded)
- Volume: 154.406 inches cubed (rounded)
To test the hypothesis, I took the cubic root (I forget the mathematical terms) of the volume, 154.406 inches cubed. The rounded answer was a length, width, and height of 5.365 inches (rounded), the dimensions for my cube. The result? A package that has relatively similar volume (disregarding variations due to rounding) and a much smaller surface area!
If I was going to engineer a cereal box, I would not begin with off-the-shelf examples as a starting point. Greater surface area for a given volume equals higher manufacturing costs and greater waste, a practice that has to have some origin… Why do companies like General Mills and Post continue to produce cereal boxes that are clearly economically and ecologically inferior? The answer to this question is likely an entirely new learning strand that relates to social studies…
Is there truth to the idea that packaging relies more on the Golden Mean then the economic bottom line?
Laura Deisley
Fabulous on many levels. One could take the question a step further, beyond the design implications of the Golden Mean.If you are a product manager, trying to get your product stocked in a grocery store where there is limited shelf space (and you’ve got to pay for shelf space), what is the optimal package that maximizes the number of units you can stock in that space?
What are all of the considerations? Again, fabulous interdisciplinary lesson that is ripe for middle school. (Hmmm…)
Willy
Yes! I like it- another hidden math problem dealing with surface area and volume. How would you design a cereal box that maintains the current volume but maximizes the number of units in a specific shelf space? If you added some fictitious tables that contain information about the size of the forward-facing side of a cereal box and number of sales (because I imagine that plays into the current design), then that would add another dimension.
Katie
I think this is grand. I hope that someone from the cereal companies reads this and makes a change. I would buy cubes just because they were different. They would also make great stacking boxes for the boys. Then again they could be reused for more of an ecological benefit.
Jenn
I figured they made the boxes that way bc it gives them the largest visable surface area on the shelf in which to promote their cereal. Its all about advertising- that’s why they spend so much on developing characters like Tony the Tiger and the Trix rabbit- and they spend the money to print them in color. I think it will be easier to convince some of the Kashi crowd cereal producers to change their box than the sugary cereal crowd.
Great math skills lesson!
Dan on Dan: Storytelling « Willy Kjellstrom: Portfolio & Blog
[...] down point for teachers, including me. I struggled to come up with the proper question for the cereal box challenge which I did not include in the original post: What is the most cost-effective design for cereal [...]
ER
??? Ergonomics… is a 5 inch box too large for the average hand to grip… prior to everything being “supersized”?
Check out Dr. Math’s formula
http://mathforum.org/library/drmath/view/56486.html
And the grip sizes of the tennis players… it also seems like other packages no matter how tall or wide accommodate hand grip size to some level… just a thought! 8)
http://tt.tennis-warehouse.com/archive/index.php/t-100088.html
kjellwr4
Ah… Leave it to a usability expert to think of something that is a wonderful rationale for the current packaging dimensions! Never thought of the need to grip it with one hand. Good point- I rarely (if ever) pour my cereal with two hands.
That being said, is the convenience of the one-handed pour reason enough for the economic/ecological changes of minimizing surface area so that the box is more cube-like? I guess I am working from the assumption that people have two hands which isn’t necessarily the correct perspective. Furthermore, all cereal boxes have an inner, flexible plastic packaging that can be gripped with one hand…
Thanks for the comment.