THE REAL NUMBER SYSTEM (N.RN)
EXTEND THE PROPERTIES OF EXPONENTS TO RATIONAL EXPONENTS
MCC9-12.N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5(1/3) to be the cube root of 5 because we want [5(1/3)] 3 = 5[(1/3) x 3] to hold, so [5(1/3)] 3 must equal 5.
USE PROPERTIES OF RATIONAL AND IRRATIONAL NUMBERS
MCC9-12.N.RN.3 Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
MCC9-12.N.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5(1/3) to be the cube root of 5 because we want [5(1/3)] 3 = 5[(1/3) x 3] to hold, so [5(1/3)] 3 must equal 5.
- During 8th grade, students explore integer exponents, including using scientific notation
USE PROPERTIES OF RATIONAL AND IRRATIONAL NUMBERS
MCC9-12.N.RN.3 Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
THE COMPLEX NUMBER SYSTEM (N.CN)
PERFORM ARITHMETIC OPERATIONS WITH COMPLEX NUMBERS
MCC9-12.N.CN.1 Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real.
MCC9-12.N.CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
MCC9-12.N.CN.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
MCC9-12.N.CN.1 Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real.
MCC9-12.N.CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
MCC9-12.N.CN.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
- Determine quotients of complex numbers only. Use complex numbers in polynomial identities and equations.