**A. Number representation**

**1. Compare real numbers.**

a. Classify numbers as natural, whole, integers, rational, irrational, real, imaginary, and/or complex.

b. Use and apply the relative magnitude of real numbers by using inequality symbols to compare them and locate them on a number line.

c. Order real numbers with and without a calculator using relationships involving decimals, rationals, exponents, and radicals.

d. Represent any rational number in scientific notation.

**2. Define and give examples of complex numbers.**

a. State the standard form used to represent complex numbers and describe their real and imaginary parts.

b. Represent i^{n} and square roots of negative numbers as complex numbers.

c. Understand that to solve certain problems and equations, number systems need to be extended from whole numbers to the set of all integers (positive, negative, zero), from integers to rational numbers, from rational numbers to real numbers (rational and irrational numbers), and from real numbers to complex numbers; define and give examples of each of these types of numbers.

**B. Number operations**

**1. Perform computations with real and complex numbers.**

a. Add, subtract, multiply, and divide real numbers accurately, including irrational numbers, numbers with exponents, and absolute value.

b. Transform numerical expressions using field properties (especially the distributive property), order of operations, and properties of exponents.

c. Solve problems involving rational numbers, ratios, percents, and proportions in context of the situation.

d. Calculate the sum, difference, product, and quotient of two complex numbers and express the result in standard form.

**C. Number sense and number concepts**

**1. Use estimation to check for errors and reasonableness of solutions.**

a. Identify the most reasonable solution for a given problem from a list of possible solutions; justify the choice.

b. Use mental estimates to detect potential errors when using a calculator.

c. Justify the need for an exact answer or an estimate in a given problem (e.g., doing taxes vs. determining amount of paint needed for a room).