High School Number & Quantity Common Core Standards
39 standards across 4 domains.
The Real Number System
Extending exponents to rational exponents and working with rational and irrational numbers.
HSN-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.
HSN-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
HSN-RN.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.
HSN-RN.A Extend the properties of exponents to rational exponents.
HSN-RN.B Use properties of rational and irrational numbers.
Quantities
Reasoning with units and choosing an appropriate level of accuracy when modeling.
HSN-Q.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.2 Define appropriate quantities for the purpose of descriptive modeling.
HSN-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
HSN-Q.A Reason quantitatively and use units to solve problems.
The Complex Number System
Performing arithmetic with complex numbers and using them in polynomial identities and equations.
HSN-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.
HSN-CN.2 Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
HSN-CN.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
HSN-CN.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.5 (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
HSN-CN.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.
HSN-CN.7 Solve quadratic equations with real coefficients that have complex solutions.
HSN-CN.8 (+) Extend polynomial identities to the complex numbers.
HSN-CN.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
HSN-CN.A Perform arithmetic operations with complex numbers.
HSN-CN.B Represent complex numbers and their operations on the complex plane.
HSN-CN.C Use complex numbers in polynomial identities and equations.
Vector & Matrix Quantities
Representing and operating on vectors and matrices.
HSN-VM.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.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
HSN-VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.
HSN-VM.4 (+) Add and subtract vectors.
HSN-VM.4a 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.4b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
HSN-VM.4c 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.5 (+) Multiply a vector by a scalar.
HSN-VM.5a 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.5b 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).
HSN-VM.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
HSN-VM.7 (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
HSN-VM.8 (+) Add, subtract, and multiply matrices of appropriate dimensions.
HSN-VM.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.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.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.12 (+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
HSN-VM.A Represent and model with vector quantities.
HSN-VM.B Perform operations on vectors.
HSN-VM.C Perform operations on matrices and use matrices in applications.
How many High School Number & Quantity Common Core Standards are there?
There are 39 High School Number & Quantity Common Core Standards on this page, in 4 domains: The Real Number System, Quantities, The Complex Number System and Vector & Matrix Quantities.
How do I write an assessment for a High School Number & Quantity Common Core Math standard?
Pick a standard on this page and choose Make a quiz or Make an exit ticket. AssessmentWiz opens the generator with the standard's code and text filled in, so every question targets that standard.
What does a code like HSN-RN.1 mean?
High school Common Core math codes read category-domain.standard. In HSN-RN.1, "HS" plus the letter names the conceptual category (A is Algebra, F is Functions, G is Geometry, N is Number & Quantity, S is Statistics & Probability), the letters after the hyphen name the domain, and the number is the standard. A trailing letter marks one part of a standard.