Polynomial Optimization Problem

Polynomial Optimization Problems... Okay, its just the box problem that we've been trying to get the kids to understand every year of every math class EVER!!! I've always done a hands on approach and a project. I feel like I'm finally connecting all the dots to what can happen with the optimization problems. I've had obvious influences from Fawn Nguyen's blog and really buy into the process of constructing the boxes. But my kiddos struggled visualizing the formula from the box so I wanted to introduce tables, graphs, sketches and expressions into my process.

The Exploration- I designed a Desmos Activity . First part of the Desmos activity explores the common problem of maximizing area given a restriction on perimeter. The second question is the open box with the four corners cut. Students are still participating in hands on construction with the influence of recording their data in many different ways.

The Project- Students design and market a popcorn container for Rohan Oza in the Shark Tank. Students explore and/or come up with viable nets that work to create a box with a lid. They write expressions for volume, length, width, and height. Once they've explored at least two possibilities, they decide on a box construction and come up with a reason why. Hopefully, it has something to do with volume. (fingers crossed). There are some other 21st century skills embedded through designing the actual product, marketing it, and coming up with a pitch for Rohan Oza in "The Tank".

Here is my project planning document. Maximizing Volume Package Design Project Above are a couple of screenshots of the detailed project info and rubric.