Park City Mathematics Institute
Lesson Study
Project Abstract

The purpose of our lesson study was to collaboratively create, teach, reflect on and revise a lesson for high school students in an Algebra (Math II) classroom and a Calculus classroom. We met eight hours per week for two and a half weeks. The lesson was piloted to the High School Math Camp in the Park City Mathematics Institute which followed with a feedback session for revisions. After the pilot, teams reflected and revised their lessons for the final lesson. The final lesson was taught by the Algebra Team to 28 high school students and by the Calculus team to 16 high school students attending the Winter Sports School in Park City, Utah.

Grade Level: 9th and 10th
Subject: Algebra 1 (Math II)
Topic: Factoring Quadratic Expressions
Authors: Renu Budhraja, Stephen Cimaglia, Nancy Cummings, Jasper DeAntonio, Jaime Ross
Group Facilitators: Kristen LaPlante and Jake Leibold
The overarching goal of the lesson was for students to factor quadratic expressions from standard form (ax2 + bx + c) to factored form when a = 1, with some students able to factor when a>1. Students began the lesson with a "Which Does Not Belong" activity to be exposed to different forms of quadratic expressions. They then completed a card sort to find matching expressions in standard form, factored form and an area model. Based on their card sort, students created a team strategy to factor quadratic expressions and created a poster to share their strategy and examples with the class. After a quick check for understanding, students chose the station activity that best suited their needs on practicing factoring or pushing their understanding to expressions with a > 1. Finally, students completed an exit slip to verify their conceptual understanding of factoring. The lesson also included extension opportunities to further their thinking throughout the lesson. The lesson ended with Kit-Kats©, a very important feature to our lesson, so students could take a break after a long 80 minute lesson.
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Grade Level: 11th and 12th
Subject: Calculus
Topic: Trigonometry graphs and identities through transformations
Authors: Alissa Abad, Melanie Battles, Gary Cruz, Pete Horsch, Julia Shube
Group Facilitators: Jake Leibold and Kristen LaPlante
The overarching goal of this lesson was to use transformations to explore and verify trigonometric identities. The explicit content of this lesson included matching graphs and identities to form groups of equivalences, and asking groups to justify their decisions as many ways as possible. Using a variety of strategies, students identified similarities between the functions and their graphs. They then recorded and presented their findings, and critiqued each other’s work.
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IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540.
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