Lauren Olmstead's first reaction was apprehension.
Her precalculus teacher, Donna Johnson, tasked her class with constructing geometric "roller coasters" - a series of equation-based lines and arcs that would carry a marble from the top of a board to a bottom.
If a line was too steep, the marble could gather too much speed and fly off the course. If a slope was too soft, the marble could stop halfway.
A collection of the roller coasters was on display Thursday night in the Juneau-Douglas High School commons as part of "An Evening at JDHS," a monthly exhibit of academic projects. Five math and five foreign-language classes participated this month.
"Everyone did it in different ways," said Olmstead, a junior, of her shamrock-decorated, craft-foam course. "I typed out all the equations on my calculator, and once I knew what they looked like, I wrote them on graph paper five or six times to get it right. Eventually, I got it to where it worked."
About 250 students, parents and teachers attended Thursday's showcase, the fifth so far. Brett Dillingham, known in town for his storytelling, was invited by JDHS principal Bernie Sorenson to coordinate the monthly events. They are sponsored by a National Science Foundation grant received by the Tlingit and Haida Central Council.
"Most students don't get a venue to showcase their academics to their parents when they're in high school," Dillingham said. "Parents usually don't see these things. Kids do it, they show it to their teachers and that's the end of it. That's not how it is here."
Parents received an invitation to Thursday's gathering. Food was served and Steve Nelson played piano. Many of the JDHS music students are at the Sitka Music Festival.
Students in advanced algebra 2-trigonometry created a series of designs on a y-axis using equations for hyperbolas, parabolas, ellipses, circles and absolute value lines. One plotted the head of Mario, star of many Nintendo games.
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Sophomore Bobbie Jo Koerperich's 20-equation illustration of a Spanish sun won an award for "most complicated."
"We learned how to use equations in a more practical manner," Koerperich said. "It showed us different ways we could use and arrange these equations, rather than just drawing them for no purpose."
A group of math students compared the national medal counts at the last two Olympics to each country's population and gross domestic product.
Wilson, Mircea Brown, Brian Howard and Jane Hartle examined the 2006 Winter Olympics in Turin. They divided each country's total medals by its gross domestic product per capita, and discovered that Russia (5.238 quotient), China (3.179) and Germany (1.620) ranked first, second and third. The United States was a distant eighth (.828).
"The bigger the country is, the more talent they should have and the better chance they should have of winning in the Olympics," Wilson said.
"I didn't even know some of these countries existed," he said. "Getting to learn about each country and how many medals they won was pretty interesting."
Korry Keeker can be firstname.lastname@example.org.