Park City Mathematics Institute Math Topics/Physics Project Abstracts Drafts of Project Files (password required)
Physics Lab with Graphing Calculators
Holly Farnsworth and Nicole Benevento
This is a 3-5 day lab where students will analyze data that they collect using different probes and a graphing calculator. Students will use basic knowledge to understand what is happening in their graph. They will extend their knowledge to conjecture about what they think will happen if their graph was to continue. Homework worksheet and extension worksheet are provided. Further extension ideas are also suggested.
How Many Ways Can You Write an Equation?
Kyle Barriger, Rani Fischer, Brian Hopkins
This unit introduces students to the differences between recursive equations and closed-form equations. First, students are taught how to write recursive equations. Second, students are taught how to find closed-form equations from first- and second-order, homogeneous, recursive equations. The unit builds on students' knowledge of quadratic equations, systems of equations, and permutations. The unit includes a series of problems that build on one another culminating in finding a closed-form equation for the Fibonacci sequence. The final problem is designed to be used as an assessment of the student's learning during this unit.
Measuring Heights (Right Triangle Trigonometry) Using Made-In-Class Clinometers
Tom Meyer
Bring paper-and-pencil right triangle trigonometry problems alive (geometry: right triangle trigonometry). Students construct a basic “clinometer” (instrument to measure angles of elevation or angles of depression). From the clinometer-measured angle and the measured horizontal distance from the observer to the base of the object (e.g., tree, flagpole), students use trigonometry to find the vertical side of the right triangle. After adjusting for the height of the eyes of the viewer, students have the height (depth) of the object. Related object height determination projects can be done by classes as early as 3rd grade.

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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.
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