Math teachers Amy Hogan, of Brooklyn Technical High School, and Ellie Terry, of the High School of Telecommunication Arts and Technology, present an election modeling project their students worked on last fall.

How much voting power does a New Yorker really wield? How can statistics presented by the media manipulate readers? How do you raise sweatshop wages without sacrificing profit?

These are a few of the questions that math teachers in New York City are asking their students as they try to bring complex and abstract concepts to life. To answer them, students must supplement the equations and formulas found in textbooks by grappling with real-world applications.

The lessons cover a mathematical practice known as modeling that has been around for decades but is now getting a closer look in schools around the city as teachers try to align their math lessons to Common Core standards that require real-world applicability.

Using modeling to present lessons is one of two instructional focuses that the Department of Education has laid out this year for math teachers.

“It’s the practice of solving real-world problems,” said Brooklyn Technical High School’s Patrick Honner, a teacher at Brooklyn Technical High School who in December won a $10,000 award for an innovative math lesson he developed.

In the prize-winning lesson, Honner had students design hats out of paper materials. At the beginning of the unit, Honner’s students measured the dimensions of one half of a sphere, then had to create hats that contained the exact same area. At the end of class, the students presented their hats in a fashion show.

Honner was one of several teachers who showed off their modeling lessons to colleagues late last year in 10-minute TED talk–style presentations at the headquarters of Math for America, an organization that offers fellowships to math teachers. The group is preparing to open the fellowships up to science teachers as well and has even caught the attention of Gov. Andrew Cuomo, who wants to replicate its stipend model to reward top-performing teachers.

While the city is encouraging math teachers to tackle modeling, in some ways the practice is at odds with the way that the city and state assess students. In a presentation called “g=4, and Other Lies the Test Told Me,” Honner showed slides of test questions that showed what he said were flawed approaches to solving math problems.

Elisabeth Jaffe of Baruch College Campus High School turned to an unusual source for a two-and-a-half-week algebra unit: newspapers.

“I felt like our students are not aware enough of current events,” said Jaffe, one of 97 teachers from around the country to win the prestigious Presidential Award for Excellence in Mathematics and Science Teaching in 2012. “You’ll ask them, ‘Who’s the vice president?’ and they won’t know, which is sad and depressing.”

Jaffe said she asked herself, “How can I relate it back to math in a really clear way?”

Jaffe created a website and assigned her students to read articles in the New York Times, focusing on the economics stories that packed many numbers into the stories. Then they had to compare them with the raw data to determine if the stories fairly represented the statistics. On the website, students wrote their critiques.

In another presentation, Amy Hogan, from Brooklyn Tech, and Ellie Terry, from High School of Telecommunication Arts and Technology, shared a unit they had recently wrapped up in time for the 2012 presidential election. The students studied the country’s electoral college and examined and mapped on a graph how many votes each state received compared with its total population. They found that California, Texas, and New York had many electoral votes but had less power per voter compared to the voters who contribute to Wyoming’s four electoral votes.

“There was a lot of Nate Silver adoration,” said Hogan, referring to the statistician whose model accurately predicted the election results.

While many of the teachers taught in selective high schools, Mohammed Aminyar, a teacher at East Side Community High School, which has more students eligible free and reduced lunch, said modeling worked in his classroom as well. He said his students responded to data that addressed social issues and inequities. His class has looked at the housing market in post-Katrina New Orleans, Iraq War casualties, and prices of MTA subway cards.

One project assigned students to look at the earning sheets of a fictitious shoe company that used sweatshop labor in South America and asked them to come up with a way to raise the workers’ wages without giving up too much profit.

“When it comes to justice, the students are really kind of, like, up in arms about what’s fair and what’s not fair,” said Aminyar.