We’ve spent the last few days picking apart The Ritz Cracker Problem, Episode I. I designed this problem about two years ago and this is the first time I have unleashed it onto a group of students. I wasn’t sure what to expect. I set my learning goals and after some individual deliberations, we started big group conversation with the question that you see below.
Translation: If you stack 16 crackers up and then split them into two stacks of eight, can we simply avoid using the volume and surface area formulas by simply dividing the values for the 16-cracker stack in half?
As the discussion continued on this point, it became clear that you could divide the volume in two, but the same wouldn’t be accurate for surface area. The explanation for this became a bit of a sticking point for some.
Then peanut butter and cereal come to the rescue. (I teach in Battle Creek, MI. Cereal is involved in everything we do, after all.) I never even thought of this image. It never crossed my mind.
I asked them why a 16 oz. container of peanut butter or cereal could be, perhaps, $2 but double the amount would almost certainly be less than $4. How is that manageable for the company selling the product?
Now, that is fairly complex answer in reality, but for our purposes in class, the students were able to explain and understand that bigger packages allow the company to push way more product for a minimal increase in packaging. Bigger cereal boxes allow Kellogg’s to sell more of what they make (cereal) while not having to spend time and money messing around with what they don’t make (boxes).
Translation: Combining smaller packages allows can allow for big changes in volume without a correspondingly big change in surface area. The peanut butter and cereal did it!
… and I never saw it coming.