A collection of boxes from local shops led to some curiosity.
I was trying to use an example with pizza box design in our polynomials unit, but needed to cater to (yes, pun intended) the visual learners in the room. So, off I went to play the teacher card and ask for an unused medium box from several places to see if one store held an advantage over another size-wise.

Of course, the shops obliged, so I should give a shout-out here to Pizza Hut, Gambino's Pizza, and Wheat State Pizza. I hope to time this to influence a bit of Super Bowl ordering hysteria, but a math teacher's endorsement is probably not big on their respective radars, let's face it.

Focus your attention, though, on the center box in my photo. It seems to have a chunk missing out of that front edge, no? That box belongs to Pizza Hut, called their new Eco Box, and had previously included some text on the box boasting it would "keep tons of cardboard out of landfills annually." Of course, the math teacher in me wanted to quantify just how many tons of cardboard they were talking about.

Old Pizza Hut box. Click image for source link.
I also must disclose, a significant amount of my information and some graphics came from a blog post on Chainalytics' website written by Rich Lindgren as well as a post of the same article on Packaging Matters' blog.

They begin by taking note of Pizza Hut's previous box design. Nothing out-of-the-ordinary. Just a standard, rigid, corrugated cardboard pizza box. As a math teacher, if you have not unfolded one of these boxes to show how the volume of the box can be shown from its flat template, I highly recommend it for the sake of the visual learners in your class. 

Label the height of the box as "x )" and the subsequent size of the width could be described as (16 - 2x) with respect to the overall width of 16 inches for the template less x inches for the left and right edges, and the length as (32 - 3x) / 2 to account for the front edge folding over itself and the back edge of the box. Showing students that the volume of the box, V = x (16 - 2x) ((32 - 3x)/2) , has many values has led to interesting conversation for me but mainly drives at the inquiry as to why the maximum volume is NOT utilized, which lends to the idea of perhaps rephrasing the function so that we can more easily state that the base must remain a square. If you have suggestions on this, please include them in the comments below.

The Pizza Hut Eco Box. Click for image source link.
Anyhow, enter the Pizza Hut Eco Box. Again, nothing out-of-the-ordinary at first glance. But that front edge is different than your average pizza box, actually it is half the height of the front edge but does not hamper the box's performance at all. 

Earlier versions of this box claimed they would "keep tons of cardboard out of landfills annually." My skepticism got the better of me, so here I am writing a blog post about it.

Box flat comparison. Click image for source link.
Turns out, that little missing strip of cardboard really has a big impact when extended upon Pizza Hut's annual sales projections. Packaging Matters' blog post saved me some time in calculating, and visualizing, those figures.

Okay, I'm buying into the "tons of cardboard" savings claim now, because I realize Pizza Hut is a pretty big player in the world of pizza.

Plus, this visualization also gives me yet another example in calculating percent change, which are fun to accumulate.

Visual of annual cardboard conserved. Click for image source.
Quoted straight from the Packaging Matters blog post:

Now 4% does not seem like a huge number, but at Pizza Hut USA volumes (estimated 675,000 boxes per day), that is an annual reduction of over 46 million square feet of corrugated board.  To put that in perspective, that would be an NFL Football Field w/o end zones over 128 feet high.

With an estimated half-cent savings per box, it is not likely to come with a price drop on their menu, but the cost savings the company will incur is likely to be in the millions of dollars.

And while only shaving off about two inches of space these flat boxes will occupy on a stockroom shelf is not a substantial victory in clearing kitchen space, it is indeed a case of "less is more."

Again, I want to thank local pizza shops Pizza HutGambino's Pizza, and Wheat State Pizza, for allowing me to play the teacher card and get a "free" box from them. I'm sure they are going to get some business out of me in the future. And while I'm at it, I'd be remiss if I didn't tell you that their stuff is worth a try, if you are in the are.

Also, I tried to time this post on Super Bowl Sunday, the capstone of the week with the most pizza purchasing power annually (an anticipated 4 million pizzas purchased in 2012, not including homemade pies or frozen pies). I'm not trying to soak up any spotlight, but figured it was appropriate timing for this topic. 

And just like the rest of you, I'm rooting for Coach Harbaugh's team.