Module 5 - Introduction

OC0111113_Nutshell_Intro_Module5.jpg

 

Teacher candidates must demonstrate an understanding of the number theory and a command of the number sense contained in the Mathematics Content Standards for California Public Schools (1997) as outlined in the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve (1999) from an advanced standpoint. To ensure a rigorous view of number theory and its underlying structures, candidates have a deep conceptual knowledge. They prove and use properties of natural numbers. They formulate conjectures about the natural numbers using inductive reasoning, and verify conjectures with proofs.

Please read carefully the following summary description of this topic. Don't worry if you don't yet understand it completely, or, if you have already studied this material, check your understanding with the practice problems at the end and move on to the next topic.

 
  • Prove and use basic properties of natural numbers (e.g., properties of divisibility)
  • Use the Principle of Mathematical Induction to prove results in number theory
  • Know and apply the Euclidean Algorithm
  • Apply the Fundamental Theorem of Arithmetic (e.g., find the greatest common factor and the least common multiple, show that every fraction is equivalent to a unique fraction where the numerator and denominator are relatively prime, prove that the square root of any number, not a perfect square number, is irrational)