# Quadratic Optimization, Volume, and Boxes Project

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### PRODUCT DESCRIPTION

This project combines two of the NC final exam released questions into one hands on project. Students begin by finding the dimensions need for a box that has a given volume in cubic feet. They must convert to cubic inches to determine what overall size of poster board they will need. Then they must cut out the corners and fold to form an open top box. In the second part, they must calculate how to fit 12 cylinders in the box in a pre-determined arrangement. They then create the 12 cylinders and pack them into the box.
Students are given a variety of dimensions and a specific product to put in their box. This allows for differentiation and all the projects come out with a different appearance, all while covering the same math skill.
Examples of the differentiation: The base of the box has dimensions such that the length is: (Eight less than twice the width,
Three times half of the width, 50% more than the width, Three times half of the width) The products might be: (Body lotion,
Toilet paper,perfume, Canned crescent rolls, Peanut butter)

The design part encourages students to promote their product as though they were a salesman at a stadium or street fair. "Get your popcorn" My students love the creativity portion as much as the math aspect. I assign it and allow them one class day to begin and the remainder is a take home project. This project also requires them to measure, convert units, and use a compass.

A rubric is included for the non-math portion of the project. The file is an editable word document so that you can adjust points/rubric as you see fit.
Total Pages
3
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Teaching Duration
1 hour

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