It's minutes until lunch, but students in Liz Ogren's fifth-grade classroom are far too engrossed to notice.

A few join their teacher on the floor as they tackle mathematical principles by designing cityscapes. "I'm adding historian landmarks," one says, and Mrs. Ogren doesn't miss a beat. "Historical," she says gently. "Beautiful."

For 26 years, Liz has given hundreds of students at Glen Lake Elementary School in Minnetonka an unforgettably fresh approach to learning.

No one is more grateful than a former student named Hannah Swaden, who struggled with math until Liz explained it in a way that finally made sense. It made so much sense that Hannah later earned a degree in elementary education and, if you look closely at this photo of happy, engaged students, you'll see one happy, engaged, former student, too: Hannah, who now team-teaches with her mentor.

"I love watching her teach," Liz says. "I love watching you teach," Hannah says.

Their mutual admiration is genuine, and bittersweet. In 2007, at age 44, Liz learned that she had Parkinson's disease. Medications help her manage it, but her energy level wanes. She's cut back on her hours and uses her illness to teach students about living robustly no matter what. "I'm hoping I can be a role model for the fact that we all have hurdles in life," she says.

Liz helped Hannah over a huge hurdle in fifth grade, when the teacher found a math tutor for her smart but struggling student. "She let me learn on my own time," says Hannah, 26.

Hannah graduated from Hopkins High School in 2004, then earned a teaching degree from the University of Wisconsin-Madison in 2009. When she heard about Liz's health challenges, she volunteered in her classroom in 2009, then worked as a short-term sub in 2010 when Liz had surgery.

"If I'm off, she can tell," Liz says of Hannah, who jumps in wordlessly to flip pages or pick up a worksheet Liz has dropped.

They laugh at their contrasting styles. Hannah is organized, Liz spontaneous. "I'm crazy, and she colors inside the lines," Liz jokes. "We balance each other out."

Liz plans to teach part-time in the fall but, whatever happens come September, she's gratified that her protégé will walk these halls. "Hannah," Liz says, "teaches with the depth and the breadth of a seasoned educator."

"Duets" is an occasional feature that celebrates unique relationships between two people. Gail Rosenblum writes the words, and Jim Gehrz takes the pictures. Send ideas to gail.rosenblum@startribune.com, or call 612-673-7350. Please put "Duets" in the subject field.