Fifteen ancient world powers gathered Wednesday in a Salt Lake City classroom to discuss their civilizations' progress.
"We've just started metallurgy," said one leader.
"I'm working on the wheel," said another.
"I need some help with irrigation," said a third.
Nevermind that all the leaders were actually fourth through eighth-graders at the private school Realms of Inquiry. The students face hundreds of complex decisions in running their own virtual societies as part of a math game called Empire created by their teacher, Scott Laidlaw. They've spent nearly six months learning basic and advanced math by playing the game, which Laidlaw hopes to eventually be used in other schools.
It's a way to teach math, Laidlaw said, that keeps students interested by showing them real world applications. As with Singapore math, Laidlaw encourages students to focus on solving problems using mental strategies rather than paper and pencil. Through Empire, they learn both math and about the rise and fall of ancient civilizations.
"By engaging them in a story, you've engaged the imagination," Laidlaw said. "If you can imagine math in one context, that gives you the power to imagine math in a different context."
In the game, students start their empires around 5,000 B.C. -- near the dawn of civilization -- with populations of 100 people each. The goal is to build their empires' strength and populations as much as possible by the Bronze Era. Each empire has its own military, religion, tax system, infrastructure, scientific advances and resources. Empires can exist peacefully or conquer their neighbors.
Students control their empires largely through an online system called The Ethos created by Laidlaw and a friend. They also build rough models of their empires on a huge 3D map that sits in a corner of Laidlaw's classroom.
It's up to each student how an empire grows, but each step up the civilization ladder requires math.
Students must calculate their latest tax revenue figures by multiplying population numbers against tax rates, which rise as they build more religious monuments and make such advancements as the creation of written language. They also must figure out how much food to distribute, when to build infrastructure and how much to invest in their militaries.
Sixth-grader Jay Cawthon decided Wednesday to give the people of his empire, Peace World, 2,136 of 2,236 possible baskets of barley.
"The more food you distribute, the more population you're going to get," Cawthon said.
Seventh-grader Michaela Webb had the opposite challenge Wednesday -- keeping her population limited in hopes of avoiding a plague. In the game, the number of deaths in any empire equals the number of citizens squared, divided by 6,000, multiplied by the food diversity index, plus 1 percent of the population.
As long as plague doesn't strike, Webb's Ketquoibo empire stands poised to soon start conquering others. As a testament to her empire's strength, Webb recently built the pinnacle of all religious structures in the game: a ziggurat or giant, pyramid-like structure. Using Pythagorean theorem, multiplication, division and formulas for calculating the volumes of various shapes, Webb figured out that using 1,000 workers, it would take her 2,460 days to build the structure.
"It was a ton of work," Webb said. "I want to win."
Laidlaw said the game, which he's spent five years developing, has captured his class' attention. The teacher, who holds a doctorate in education, said he hopes to roll out a more sophisticated version of the game to sell to other schools next year. He's already secured a $5,000 matching grant from the Willard L. Eccles Charitable Foundation to improve the online part of the game.
Fourth-grader Carson Luke said Empire makes math interesting. He said he hopes to one day build his empire, Constitution, to the point where he can start conquering his enemies.
"At my old school, we just did worksheets and tests," Luke said. "In this game, it's much more hands-on."
Realms of Inquiry, 1140 S. 900 East, Salt Lake City, is a private school for gifted and talented students. Most classes have fewer than 14 students. Learning is intended to be a collaborative effort, the school's Web site says, but exploration and independent study is encouraged. Students also participate in an outdoor program that includes rock climbing, caving, biking and winter skills and are offered overseas trips.