Park City Mathematics Institute
Drafts of Project Files (password required)
- HANDS-ON LESSONS
- Sassy Similarity
- Rebecca Alleva, Evelyn Baracaldo, Anna Prusch, Joyce Rhee
- This hands-on classroom activity allows students to explore the concept of similarity through the use of origami paper. Students will identify corresponding parts of similar figures and calculate ratios of corresponding sides to prove similarity. Prompts for class discourse are included as well as supplementary problems to check for understanding.
- Pythagoras in the Folds
- Anna Fox, Zack Bassman
- Haga's theorem states that one carefully chosen fold creates three similar 3-4-5 right triangles on a piece of origami paper. Students use angle relationships, similarity, proportions, and the Pythagorean theorem to derive the lengths of the sides of these right triangles to verify Haga's theorem. Hands on activities provide a powerful tool for students to explore geometric concepts in a tactile, concrete fashion. This activity gives students the opportunity to identify, describe, and verify geometric relationships in the folded paper and generates collaborative learning and discussion. By physically creating a geometric object, students become personally invested in the outcome of the activity. At the end of the lesson, the students will have something that they can literally take home with them, and refer back to for further review. Folding instructions with teacher notes, and a student worksheet are included.
- Bisecting Paralellograms
- Assegid Derseh, Eric Flam
- This hands-on classroom activity allows students to explore the concept of congruence through the use of folding paper in the shapes of squares, rectangles, rhombi, and parallelogram. Students will identify corresponding parts of congruent triangles and use them show that any segment, through the point of intersection of the diagonals of a parallelogram, bisects it. Prompts for class discourse are included as well as supplementary problems to check for understanding.
- DYNAMIC SOFTWARE
- Introduction to the Geometer's Sketchpad®: A Series of Challenges for Students
- Seth Leavitt, Kaitlyn Peterson Spong, Felipe Rico, Todd Smallcanyon
- Through a series of challenges, students learn to use Geometer's Sketchpad as a vehicle to explore in geometry. In each challenge, students are given a specific task and a restriction on the tools they are able to use. By engaging in the challenge, students will learn the function of the given tools and develop a need to learn and use more of the features of Sketchpad. The challenges are meant for students with no or limited prior exposure to the program.
- CONNECTING ALGEBRA & GEOMETRY
- Problem Solving within the Context of High School Geometry, Algebra I, and Algebra II
- Sara Rezvi, Jessica Barker, Cameron Cassidy, Mary Gruber
- Problem solving and communication are central elements of the NCTM Principles and Standards of School Mathematics. This project presents three different rich problems with multiple entry points and extensions that cross the typical Algebra 1, Geometry and Algebra 2 curricula and promote connections between the courses. The problems include the stair-step problem, clock problems and investigating r-gonal numbers. Students at all levels will be expected to look for patterns, problem solve, justify their solutions and clearly communicate their thinking to others. The problems are designed to give students multiple entry points, so that students of all levels will be engaged in mathematical thinking. Classroom discourse is emphasized and each problem includes questions to push student thinking and promote high level discourse among students.
Back to Investigating Geometry Index
PCMI@MathForum Home || IAS/PCMI Home
© 2001 - 2018 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King
With program support provided by Math for America
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.