Park City Mathematics Institute
Lesson Study
Project Abstract
Properties of Isosceles Triangles
Grade Level: High School
Subject: Geometry
Authors: Gail Burrill*, Teri Hulbert, Chris Bolognese, Nancy Buck, Brian Hsu, Dan Kang, Kristen LaPlante, Nicholas Molnar
 
The lesson study group worked collaboratively over the course of three weeks (approximately 8 hours a week) to design, implement, and revise a high school geometry lesson. The first draft of the lesson was taught to 16 high school students who attended the Park City Mathematics Institute Summer Math Camp. After reflecting on and revising the lesson from this experience, the lesson was then taught to 17 high school students attending Mountain View High School in Orem, Utah. These 10th through 12th grade students attended the summer course to recover high school credit and had previously taken a course on geometry at least once.
 
The overarching goal of the lesson was for students to recognize and utilize symmetry in geometric figures, specifically in the context of isosceles triangles. The explicit content in the lesson includes identifying properties of isosceles triangles, determining sufficient information to define an isosceles triangle, and applying these properties to find missing information in a given figure. The opening activity engages students in using a cutout right triangle to construct an isosceles triangle, promoting the language of symmetry and observing congruent corresponding parts. In the second act, students first mark a triangle with enough information to be isosceles, then consider sample responses first individually then as a whole group. Here, students critique the reasoning of others and can use dynamic geometry to test or affirm their conjectures. The final part includes a quick check, application problems, and a reflection on what students took away from the lesson.
 
download zipped folder LessonStudy2015.zip [generic login required]

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.