High School Number and Quantity: Common Core Standards

Your Teacher Information Pack for High School Number and Quantity: every Common Core standard with its official code, notes on which states use them, and trusted links. Tick what you're teaching and send it straight into the lesson plan maker.

Does my state use these standards?

Your state may use its own standards. Common Core is not federal law: each state decides. For math (compiled 2026-10-20, check your state's site before relying on it):

• Use their own standards, not Common Core (14): Alabama, Alaska, Florida, Georgia, Indiana, Kentucky, Minnesota, Missouri, Nebraska, Oklahoma, South Carolina, Tennessee, Texas, Virginia. Codes on this page won't match your state's paperwork.
• Adapted and renamed (24): Arizona, Arkansas, Colorado, Idaho, Kansas, Louisiana, Maine, Maryland, Massachusetts, Mississippi, Montana, New Hampshire, New Jersey, New York, North Carolina, North Dakota, Ohio, Oregon, Pennsylvania, South Dakota, Utah, West Virginia, Wisconsin, Wyoming. Mostly similar, but check wording and codes.
• Common Core as written (13): California, Connecticut, Delaware, District of Columbia, Hawaii, Illinois, Iowa, Michigan, Nevada, New Mexico, Rhode Island, Vermont, Washington.

Full state list with links to each state's standards

The standards

Standards are grouped into domains (big areas such as Operations & Algebraic Thinking) and clusters (the bold lines). Each code links to the official page. ★ marks a modeling standard and (+) additional mathematics for advanced courses.

The Real Number System (RN) 3 standards

• Extend the properties of exponents to rational exponents.
  • HSN.RN.A.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)3 to hold, so (5^1/3)³ must equal 5.
  • HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
• Use properties of rational and irrational numbers.
  • HSN.RN.B.3 Explain why the sum or product of two 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.

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Quantities (Q) 3 standards

• Reason quantitatively and use units to solve problems.
  • HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.★
  • HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.★
  • HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.★

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The Complex Number System (CN) 9 standards

• Perform arithmetic operations with complex numbers.
  • HSN.CN.A.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.
  • HSN.CN.A.2 Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
  • HSN.CN.A.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.(+)
• Represent complex numbers and their operations on the complex plane.
  • HSN.CN.B.4 (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.(+)
  • HSN.CN.B.5 (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)³ = 8 because (-1 + √3 i) has modulus 2 and argument 120°.(+)
  • HSN.CN.B.6 (+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.(+)
• Use complex numbers in polynomial identities and equations.
  • HSN.CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.
  • HSN.CN.C.8 (+) Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x - 2i).(+)
  • HSN.CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.(+)

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Vector & Matrix Quantities (VM) 12 standards

• Represent and model with vector quantities.
  • HSN.VM.A.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).(+)
  • HSN.VM.A.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.(+)
  • HSN.VM.A.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.(+)
• Perform operations on vectors.
  • HSN.VM.B.4 (+) Add and subtract vectors.(+)
    • HSN.VM.B.4.a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
    • HSN.VM.B.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
    • HSN.VM.B.4.c Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
  • HSN.VM.B.5 (+) Multiply a vector by a scalar.(+)
    • HSN.VM.B.5.a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v_x, v_y) = (cv_x, cv_y).
    • HSN.VM.B.5.b Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
• Perform operations on matrices and use matrices in applications.
  • HSN.VM.C.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.(+)
  • HSN.VM.C.7 (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.(+)
  • HSN.VM.C.8 (+) Add, subtract, and multiply matrices of appropriate dimensions.(+)
  • HSN.VM.C.9 (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.(+)
  • HSN.VM.C.10 (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.(+)
  • HSN.VM.C.11 (+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.(+)
  • HSN.VM.C.12 (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.(+)

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Standards for Mathematical Practice apply to every grade and course

• MP1 Make sense of problems and persevere in solving them.
• MP2 Reason abstractly and quantitatively.
• MP3 Construct viable arguments and critique the reasoning of others.
• MP4 Model with mathematics.
• MP5 Use appropriate tools strategically.
• MP6 Attend to precision.
• MP7 Look for and make use of structure.
• MP8 Look for and express regularity in repeated reasoning.

Read what each practice means

Tests and key dates

Each state sets its own tests and testing windows. Check your state education department (links on our state list) and your district calendar.

Official documents

• Official standards page: Math › Content › HSN

Trusted free resources

• Khan Academy – Free practice, videos and teacher tools (US grades and courses).

Links only: we don't copy their content and we aren't connected to these organisations.

More packs

Related: Kindergarten Math, Grade 1 Math, Grade 2 Math, Grade 3 Math, Grade 4 Math, Grade 5 Math, Grade 6 Math, Grade 7 Math.

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