11th & 12th Grade Algebra II – Modeling with Polynomials

Amy Burke is a Teacher on Special Assignment (TSA) in the San Lorenzo Unified School District (San Lorenzo, California). She supports high school math teacher development in the district. At the time that the video was shot, she had been a TSA for three years, and previously was a high school mathematics teacher for 10 years. In her current role, she supports and coaches new teachers and provides program and professional development for her district. This lesson was recorded in Arroyo High School, where many students participate in a free and reduced-price lunch program; as of the 2016/17 academic year, the student population was 21% Asian, 44% Latino, 13% Filipino, 12% White, 8% Black, and 2% other.

In this lesson, Burke works with 11th- and 12th-grade students on learning to find the maximum volume of an open-top box. They constructed the boxes by cutting out squares from the corners of a rectangular sheet of paper printed with a grid of 1 cm squares. The students develop initial conjectures, then work in pairs to use their initial conjectures to build a model for calculating the volume of their box.  

On the whiteboard, pairs share the dimensions and volume of their boxes and the cut size, and everyone works with this whole-class data set. To do so, they use laptops with the Desmos website to create a regression curve that models the behavior of the data set. Students return to their original conjecture to revise and improve it as they move forward. During partner talk and table talk, they serve in specific group roles to facilitate sharing of their ideas, critique the reasoning of others, and make use of the Desmos applications as a mathematical tool to deepen their thinking. 

Amy also engages in a substantive pre- and post-lesson coaching conversation with colleague Deidre Grevious, in whose Arroyo High School classroom this lesson was recorded.  The work represented in this set of video clips is based on the lesson “Multiplying and Factoring Polynomial Expressions,” developed by Engage NY and modified by the Charles A. Dana Center at The University of Texas at Austin.