Each course of the series ends with a capstone project. In this course, the third year of a four-year program, topics include linear programming, confidence intervals, congruence, iteration, and recursion. In one of the four capstone investigations, students link soap bubbles and Vergil's famous epic, Aeneid, using geometry, algebra, and optimization. In the epic, a king grants a princess as much land as she can enclose in the hide of an ox. She uses the hide to make a cord to surround a region of land.
Students find maximum area and then extend the process to maximize the surface area of soap bubbles.
This course correlates with the National Council of Teachers of Mathematics Curriculum and Evaluation Standards and Professional Standards for Teaching Mathematics. ENC does NOT distribute this resource.