# The City of Numbers: Unique Prime Factorization, Manipulative Development and the Big Apple

## Document Type

Presentation Abstract

11-2-2020

## Abstract

The Fundamental Theorem of Arithmetic (FTA) states that every positive integer greater than 1 can be represented in exactly one way apart from rearrangement as a product of one or more primes (Hardy and Wright, 1979, pp. 2-3). Unique prime factorization is the basis for the multiplicative structure of the integers and, as such, is important for students of arithmetic. Nevertheless, research has shown that many students and their teachers fail to appreciate the uniqueness statement of the FTA. For more than five years I have pursued a quest to help young learners better understand the importance of prime numbers. This quest led me to develop a manipulative and an accompanying lesson which was studied in classrooms of 4th grade students. I will share the manipulative and what we learned when it was put to use, and, then, tell the story of how its use has led to new questions and even a trip to New York City.