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This lab is meant to launch your Polynomials unit in an Algebra 2 class or an Honors Algebra 1 class. This is a perfect addition to any PrBL/PBL run class. Before teaching students anything, let them explore an application for a polynomial (cubic) function and derive a function themselves. The pre-lab directs students to build an open-face-box out of a single piece of paper with the largest volume possible in any way they choose (do not give them any further directions!). At the end of the pre-lab one day one, have a discussion with students about what works and what doesn't, what was difficult, etc. You will begin the lab procedure on day 2. The lab directs every lab group to create a box using a specific algorithm. Every group should create a different size box and then calculate the volume. Students then create an aggregated data table. The lab also reinforces graphing skills such as plotting coordinate points and calculating a maximum value on a graphing calculator. The post lab asks them to look at features which will move them toward intervals of increasing/decreasing, intervals where the function is positive/negative, and end behavior. Finally, the post lab asks, how would you do this all over again, with a different size paper? Materials Needed for Pre-Lab: card stock printed and cut to fit 26 x 20 cm squares (available here for free), rulers, pencils, scissors, tape, calculators, a timer & a display table for finished products Lab Set Up: Assign lab partners, assign " side length of square" numbers from 1 - 9 to each group Materials Needed for Lab: card stock printed and cut to fit 26 x 20 cm squares (available here for free), scissors, tape, ruler, a display table for finished products. Adaptations: You can adjust the lab so that each lab pair creates 3 open face boxes and they have more of their own creation to use for the basis of What If? Questions and Post Lab.

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