# NUMBER THEORY AND THE FUNDAMENTALS

• How can the patterns and relationships around us be expressed mathematically?

• How can these mathematical generalizations be used to derive new relationships or be evaluated in specific situations?

• How can the operations and relations among numbers be characterized symbolically and then built into a theoretical system of study?

*VOCABULARY AND DEFINITIONS

*SET NOTATION AND VENN DIAGRAMS: the basics of set theory

*NUMBER THEORY-REAL NUMBERS AND THEIR SUBSETS: the concept of prime and divisibility, factors and multiples, Fundamental Theorem of Arithmetic, decimal, base-5, and binary, the real number line, absolute value, negative values, counting numbers, zero, integers, rational and irrational numbers, exponents and roots, zero as an exponent, simple logarithms, properties of real numbers, examination of properties using matrices

*COMPUTATION WITH REAL NUMBERS: order of operations, grouping symbols: ( ), [ ], { }, | |, ______; computation with negative integers, computation with exponents, the many ways to express multiplication, absolute value, evaluating arithmetic expressions, matrix addition and subtraction, scientific notation, exponential growth and decay

Factorization

Prime factorization

Use of Venn diagrams to observe the relationship between two numbers in terms of their prime factors, to determine the GCF, to see how other factors are created, and to determine the LCM (least common multiple)

Placement of numbers onto the number line to gain an appreciation for their relative magnitude.

Conversion of numbers from one place-value system to another.

Items in this concept area are embedded throughout the course and assessed in part throughout the year.