# [N] Number and Quantity

Studentsâ€™ prior knowledge includes:

• Students know that there are numbers that are not rational, and approximate them by rational numbers (grade 8)
• Students apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers (grade 7)
##### The Real Number System
• Extend the properties of exponents to rational exponents.
• Use properties of rational and irrational numbers.
##### Quantities
• Reason quantitatively and use units to solve problems
##### The Complex Number System
• Perform arithmetic operations with complex numbers.
• Represent complex numbers and their operations on the complex plane.
• Use complex numbers in polynomial identities and equations
##### Vector and Matrix Quantities
• Represent and model with vector quantities.
• Perform operations on vectors.
• Perform operations on matrices and use matrices in applications.

## MAT-HS.N Overview: [N] Number and Quantity

### MAT-HS.N-RN Domain: [N-RN] The Real Number System

• MAT-HS.N-RN.01 Explain how rational exponents are like integer exponents with radical notation
• MAT-HS.N-RN.02 Apply properties of exponents to expressions with radicals/rational exponents
• MAT-HS.N-RN.03 Explain which sums or products of two numbers are rational or irrational, why
• MAT-HS.N-RN.04 Perform basic operations on radicals and simplify radicals to write equivalent expressions

### MAT-HS.N-Q Domain: [N-Q] Quantities*

• MAT-HS.N-Q.01 Use units to understand and guide the solution of multi-step problems
• MAT-HS.N-Q.02 Define appropriate quantities for the purpose of modeling
• MAT-HS.N-Q.03 Report quantities at a level of accuracy reflecting limitations on measurement

### MAT-HS.N-CN Domain: [N-CN] The Complex Number System

• MAT-HS.N-CN.01 Know that every complex number has the form a + bi with a and b real
• MAT-HS.N-CN.02 Use the relation i^2 1 and commutative/associative/distributive properties
• MAT-HS.N-CN.03 Find the conjugate of a complex number
• MAT-HS.N-CN.04 Represent complex numbers on complex plane in rectangular and polar form
• MAT-HS.N-CN.05 Represent +, , x, and conjugation of complex numbers geometrically
• MAT-HS.N-CN.06 Calculate the distance between numbers in the complex plane
• MAT-HS.N-CN.07 Solve quadratic equations with real coefficients that have complex solutions
• MAT-HS.N-CN.08 Extend polynomial identities to the complex numbers
• MAT-HS.N-CN.09 Show the Fundamental Theorem of Algebra is true for quadratic polynomials

### MAT-HS.N-VM Domain: [N-VM] Vector and Matrix Quantities

• MAT-HS.N-VM.01 Recognize vector quantities as having both magnitude and direction
• MAT-HS.N-VM.02 Find the components of a vector by subtracting the coordinates
• MAT-HS.N-VM.03 Solve problems involving velocity that can be represented by vectors
• MAT-HS.N-VM.04 Add and subtract vectors
• N-VM.04.a Add vectors end-to-end, componentwise, and by the parallelogram rule
• N-VM.04.b Given two vectors, determine the magnitude and direction of their sum
• N-VM.04.c Understand vector subtraction
• MAT-HS.N-VM.05 Multiply a vector by a scalar
• N-VM.05.a Represent and perform scalar multiplication graphically by scaling vectors
• N-VM.05.b Compute the magnitude of a scalar multiple
• MAT-HS.N-VM.06 Use matrices to represent and manipulate data
• MAT-HS.N-VM.07 Multiply matrices by scalars to produce new matrices
• MAT-HS.N-VM.08 Add, subtract, and multiply matrices of appropriate dimensions
• MAT-HS.N-VM.09 Understand matrix multiplication for square matrices is not commutative
• MAT-HS.N-VM.10 Understand that the 0 and identity matrices play a role in matrix + and x
• MAT-HS.N-VM.11 Multiply a vector by a matrix to produce another vector
• MAT-HS.N-VM.12 Work with 2 x 2 matrices as transformations of the plane

### A Sample of HS Math Concept Number and Quantity to Become Ready for College and Career

#### The Real Number System

• Extend the properties of exponents to rational exponents.
• Use properties of rational and irrational numbers.

#### Quantities

• Reason quantitatively and use units to solve problems.

#### The Complex Number System

• Perform arithmetic operations with complex numbers.
• Represent complex numbers and their operations on the complex plane.
• Use complex numbers in polynomial identities and equations.

#### Vector and Matrix Quantities

• Represent and model with vector quantities.
• Perform operations on vectors.
• Perform operations on matrices and use matrices in applications.