VMI Course Registration: Spring 2026

This course introduces teachers to the branch of mathematics known as number theory, in which one studies properties of positive integers with respect to the operations of multiplication and division. Topics include properties of prime and composite numbers, the sieve of Eratosthenes and distributions of primes and composites, the fundamental theorem of arithmetic, properties of greatest common factors and methods of computing greatest common factors, properties of least common multiples, use of base ten and expanded notation, writing numbers and computing in different bases, basic ideas of modular arithmetic, the Division Algorithm, the Euclidean Algorithm, letter arrangements and lottery problems, counting problems, and problem solving in various contexts.

This course builds teacher knowledge about the ways in which students construct essential mathematical understanding of multiplicative and fractional reasoning. Participants will explore the learning progressions associated with these critical mathematical ideas and understand the models and strategies that students use to build a deep understanding of the associated concepts. Participants will examine the mathematical concepts that precede the multiplication and fraction topics as well as the concepts that build from these critical understandings. Participants will review research based practices for high quality mathematics instruction and assessment to address the Common Core State Standards for Mathematics for students in grades 3 – 5.

While a deep understanding of multiplicative and fractional reasoning is critically important for grades 3 – 5 classroom teachers, the material in this course is essential content knowledge for all PreK-8 teachers and is equally helpful to interventionists, special educators, math specialists and administrators.