**MISSOULA **– A University of Montana mathematics professor has discovered a way to make prime factorization fun for elementary school students – earning him a national Rosenthal Prize for Innovation and Inspiration in Math Teaching.

The name of his lesson is “City of Numbers,” and it involves building blocks and a grid system.

UM Mathematics Associate Professor Matt Roscoe created the lesson for fourth through eighth grade students. The project helps students understand multiplicative structures of whole numbers and their prime factorizations in a visual way.

“Students collectively build the prime factorizations of each whole number 1-100 as a tower of blocks, each block representing a prime,” he said. “These towers are then placed on a 10-by-10 grid numbered from 1 to 100. The lesson ends with students discovering and communicating patterns they find in the representation.”

Many students first learn about prime numbers in fourth grade. Stacking up blocks on a gridded system allows them to visualize a number’s multiplicative structure at an age when they do not yet understand exponents.

“I hope that my contributions to the field will be characterized by moving mathematics instruction toward a future where students experience mathematics as a venue for the expression of creativity, exploration and discovery,” Roscoe said.

Roscoe has brought his “City of Numbers” lesson to different elementary school classrooms and said students are always excited about using the building blocks. Teachers have built at least five sets in Montana and one in California.

“It’s exciting for me too,” Roscoe said. “Students often see patterns that I have never considered. For example, one student found that all sevens move like ‘a knight on the chess board.’ That’s a pretty cool observation but even more interesting is the question that follows: ‘I wonder why?’”

Roscoe said he has always been passionate about teaching mathematics and thinking about patterns.

The Rosenthal Prize for Innovation and Inspiration in Math Teaching promotes hands-on math teaching in upper elementary school classrooms. Roscoe won $15,000 with the prize.

Roscoe joins the University of Saskatchewan’s Nat Banting – the first Canadian to earn the prize – in earning recognition for his math teaching methods. Both received awards at the Museum of Mathematics in New York City Jan. 7.