Ch 16: MTEL Math: Number Theory

About This Chapter

Use the video lessons and self-assessment quizzes in our Number Theory chapter to help you prepare for the MTEL Mathematics examination. Expert instructors go through engaging lessons to help you make certain you're ready for the MTEL exam.

MTEL Math: Number Theory - Chapter Summary

Our instructors will show you everything you need to know about number theory for the MTEL: Mathematics examination. We'll cover the concepts you need to understand, such as prime factorization and modular arithmetic. In this chapter you'll learn about:

  • Prime, composite, odd and even numbers
  • Finding the prime factorization of a number
  • Finding the least common multiple
  • Word problems involving greatest common factor and least common factor
  • Euclid and his discoveries
  • Mersenne prime
  • Perfect numbers
  • Fermat's last theorem

Thanks to our short video lessons and self-assessment quizzes, you'll learn the basic concepts surrounding number theory. We'll also teach you techniques for solving all types of number theory questions so you're well prepared for your MTEL Mathematics examination.

MTEL Math: Number Theory Chapter Objectives

The Massachusetts Tests for Educator Licensure (MTEL) exams test the preparedness for future educators to teach in pre-kindergarten through 12th grade classrooms. The MTEL Mathematics test is designed to test a future educator's readiness to teach mathematics or related courses.

This chapter, Number Theory, will be most applicable to the exam's Number Sense and Operations subarea and will be especially useful for questions dealing with principles of number theory. The Number Sense and Operations subarea accounts for 12% of the exam's score weight and is one of the six testing areas found on the MTEL Mathematics test.

The test consists of multiple-choice questions and open-response assignments and takes roughly 4 hours and 15 minutes to complete.

11 Lessons in Chapter 16: MTEL Math: Number Theory
Test your knowledge with a 30-question chapter practice test
What Are Prime Numbers? - Definition & Examples

1. What Are Prime Numbers? - Definition & Examples

In this lesson, we'll do a brief review of factors, and then learn how factors make prime numbers unique. You can also test your knowledge with a brief quiz.

What Are Composite Numbers? - Definition & Examples

2. What Are Composite Numbers? - Definition & Examples

In this lesson, you'll learn what composite numbers are and briefly touch on prime numbers. You'll also learn a couple of rules about composite numbers. Then, you can test your new knowledge with a brief quiz.

What Are Odd & Even Numbers? - Definition & Examples

3. What Are Odd & Even Numbers? - Definition & Examples

In this lesson, you'll learn what odd and even numbers are with the help of some visual aids. You'll also learn some interesting properties of odd and even numbers. Then, you can test your new knowledge with a brief quiz.

How to Find the Prime Factorization of a Number

4. How to Find the Prime Factorization of a Number

The prime factorization of a number involves breaking that number down to its smallest parts. This lesson will show you two different ways to discover the prime factorization of any number.

How to Find the Greatest Common Factor

5. How to Find the Greatest Common Factor

If the factors of a number are the different numbers that you can multiply together to get that original number, then the greatest common factor of two numbers is just the biggest one that both have in common. See some examples of what I'm talking about here!

How to Find the Least Common Multiple

6. How to Find the Least Common Multiple

The least common multiple of two numbers is the smallest number that can be divided evenly by your two original numbers. See some examples of what I'm talking about here!

Word Problems: Greatest Common Factor & Least Common Multiple

7. Word Problems: Greatest Common Factor & Least Common Multiple

In this video lesson, you will learn what kinds of word problems you can expect to see that involve the greatest common factor or the least common multiple. Learn what you need to do to understand these problems and then to solve them.

Who is Euclid? - Biography, Contribution & Theorems

8. Who is Euclid? - Biography, Contribution & Theorems

In this lesson, you'll explore the life and achievements of the Greek mathematician Euclid, and test your understanding about Ancient Greece, early math, and the principles of Euclidean geometry.

Modular Arithmetic & Congruence Classes

9. Modular Arithmetic & Congruence Classes

Modular arithmetic revolves around remainders; we'll explore what this means in greater detail and learn how to recognize congruence classes. We'll also learn how to add, subtract, and multiply in modular arithmetic.

Perfect Numbers & Mersenne Primes

10. Perfect Numbers & Mersenne Primes

Although computers facilitate searches for prime numbers and perfect numbers, fundamental number theory is still very relevant. In this lesson we explore how a particular type of prime number, the Mersenne prime, relates to perfect numbers.

Fermat's Last Theorem: Definition & Example

11. Fermat's Last Theorem: Definition & Example

Considered a mathematical mystery for hundreds of years, watch this video lesson to learn what Fermat's Last Theorem tells us and why mathematicians struggled for years to prove it true.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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Other Chapters

Other chapters within the MTEL Mathematics (09): Practice & Study Guide course

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