Precalculus/Calculus

In this course, students complete a unique 12-part year-long project ranging from algebra through calculus. This original project begins with students choosing three locations on the Earth and involves using linear equations, creating piece-wise functions to match data, using limits to test for continuity, finding and using first and second derivatives, using integrals to solve problems, and other topics such as average value, arc length, trapezoidal approximations, and even partial derivatives.

Students also complete supplemental projects that explore data of their choice from their native countries. Students use this data to create functions and use those functions to calculate predictions about the future of their data. In addition, throughout the year, students complete their own textbook problems, understanding how they're created, and exchange their problems with other students to further enhance their knowledge of mathematics. Students also create their own exams and answer sheets.

A major theme of the course involves student-centered hands-on work (performance-based assessments) that cannot be copied from such that each project, exam and homework assignment is unique to the individual student.

Readings: 
"A Short History of Nearly Everything"
"Functions in the Real World"
Media Used: 
TI-83 Graphing Calculator
Google Earth
Significant Assignments: 

Create your own homework assignments: Throughout the year, students create their own homework problems to complete and then exchange those problems with other students in the class. Students keep their problems in a safe place so that the final product is like a student-created math textbook they can bring to college.

Create your own exams: Students consistently create exams to assess their knowledge about the particular subject we are studying. Students exchange exams and work together to find and correct mistakes. On exam day, students each have their own unique exam.

Significant Activities or Projects: 

The Map Project is a year-long 12-part project ranging from algebra through calculus. This is the main performance-based assessment students complete.

The Native Country Project, wherein students collect data from some aspect of their native countries (population, car accidents, disease, etc) and use the data to explore applications in math.

The Products Project, in which students try to save companies money by repackaging their products to use less surface area (keeping the volume constant) or hold more volume (keeping the surface area constant)

Sample PBATs: 
The Map Project Part One
The Native Country Project