The students huddled around their tables, scribbling and erasing their notes, nodding and shaking their heads and rearranging the blocks in front of them.

“There has to be a hole in the middle.” “We need to create a base first.” “How many windows?”

These students, gathered in Drexel’s James E. Marks Intercultural Center last week, were from Philadelphia high schools and middle schools. And they’d just been given an engineering challenge that was enough to stump the PhD students who were there to serve as judges.

They were at Drexel last week for the second edition of the Philadelphia Engineering/Math Challenge presented by Drexel’s Math Forum. They came from nine different neighborhood and charter schools in the city to take part in problem-solving competitions designed to bring math to life.

In this case, they were given 50 connectible blocks and told to assemble a “hotel” that would produce the highest possible profit. They would be charged money based on the amount of space the structure took up and how high it rose, and they would reap revenues for rooms based on their windows and roof access.

For the doctoral students there to judge the competition, the problem sounded simple at first, but they quickly realized it would involve untold numbers of trials and errors to understand all the possible configurations.

“We were all talking over there: ‘How would you solve it?’” said electrical engineering PhD student Brandon Morton.

But that was the point for the young students there: to act like engineers, trying and calculating and trying again, learning the whole time.

“It gives students a chance to bring their creativity into math class,” said Max Ray, a professional collaboration facilitator for the Math Forum, of the problem-solving techniques that the Forum favors. Most teams went through two or three different designs in the roughly 40 minutes they were allotted. And that was a good thing in the eyes of the judges, who were awarding points for the students’ process as well as their results.

The Engineering/Math Challenge is in the pilot stage this year. It came about when Trey Smith, a science teacher and sponsor of the National Society of Black Engineers chapter at Boys’ Latin of Philadelphia Charter School, wanted to give his school’s math team a chance to take part in a competition that went behind “Jeopardy!”-style quizzing.

Events at the challenge include the presentation of a video of students presenting a visual, real-world math problem, filmed and edited ahead of time; slideshow presentations of Math Forum Problems of the Week the students have worked on for weeks; a high-speed quiz bowl; and the engineering challenge for which the students constructed their “hotels” last week.

It’s a way to make math, science and engineering come alive for the students, Smith said.

“For our math team, we had 25 students show up on a Saturday morning to take a math test,” he said.

Teachers join the students at the competition, and they can take the activities back to their classrooms when they return.

In last week’s competition, every school placed in at least one competition. In the engineering contest, two groups managed to reap more than $15,000 in “profits” for their hotels, and two more earned special commendations for their communication and design process.

“They seemed to have some really thoughtful conversations,” Ray said, and came up with solutions that rivaled what math teachers have been able to do with the same activity. At the end of the day, he said, the students left Drexel with excitement on their faces, ready to come back for the next challenge in March.