Module 7 Number Theory

Number Theory explores the patterns and properties of whole numbers. These are concepts many students first encounter in elementary school. In this chapter, you build on some familiar concepts, such as factors, multiples, and prime numbers. You will also introduce engaging divisibility rules, along with a powerful tool: prime factorization. You will then use these to explore the concepts of the greatest common divisor and least common multiple in greater depth.

As future elementary educators, it’s important to you not only understand how numbers work, but also why they work that way. This chapter helps develop a deeper number sense and introduces strategies you can later adapt for your own teaching.

You’ll find that Number Theory is both practical and enriching. It strengthens your problem-solving skills and lays a foundation for helping young learners make sense of math with confidence and curiosity.

Upon completion of this module, you will be able to:

1. Determine the digital root of a number and use it to verify arithmetic operations.
2. Apply divisibility tests for 2, 3, 4, 5,  6,  7,  8,  9, 10,  11, and 12 to check divisibility without full division.
3. Identify and define factors and multiples of whole numbers, and apply this understanding to solve problems.
4. Classify numbers as prime or composite, and find the prime factorization of composite numbers.
5. Determine greatest common factors (GCF) and least common multiple (LCM) using efficient strategies based on context.
6. Be able to connect the current Louisiana Students Standards, and NCTM standards to course content.

To achieve these objectives:

1. Read the sections below and work the embedded exercises within them.
2. Complete MyOpenMath homework for this module.
3. Complete the discussion forum for this module.

Module Pressbooks Resources and Activities