Common Planner
K–12 Standards

High School — Number and Quantity

Other Illinois Math with Common Core sets

Standards for Mathematical Practice

  • 1.

    Make sense of problems and persevere in solving them.CCSS.Math.Practice.MP1

  • 2.

    Reason abstractly and quantitatively.CCSS.Math.Practice.MP2

  • 3.

    Construct viable arguments and critique the reasoning of others.CCSS.Math.Practice.MP3

  • 4.

    Model with mathematics.CCSS.Math.Practice.MP4

  • 5.

    Use appropriate tools strategically.CCSS.Math.Practice.MP5

  • 6.

    Attend to precision.CCSS.Math.Practice.MP6

  • 7.

    Look for and make use of structure.CCSS.Math.Practice.MP7

  • 8.

    Look for and express regularity in repeated reasoning.CCSS.Math.Practice.MP8

The Real Number System

  • A.

    Extend the properties of exponents to rational exponents.CCSS.Math.Content.HSN-RN.A

    1. 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.CCSS.Math.Content.HSN-RN.A.1

    2. 2.

      Rewrite expressions involving radicals and rational exponents using the properties of exponents.CCSS.Math.Content.HSN-RN.A.2

  • B.

    Use properties of rational and irrational numbers.CCSS.Math.Content.HSN-RN.B

    1. 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.CCSS.Math.Content.HSN-RN.B.3

Quantities

  • A.

    Reason quantitatively and use units to solve problems.CCSS.Math.Content.HSN-Q.A

    1. 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.CCSS.Math.Content.HSN-Q.A.1

    2. 2.

      Define appropriate quantities for the purpose of descriptive modeling.CCSS.Math.Content.HSN-Q.A.2

    3. 3.

      Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.CCSS.Math.Content.HSN-Q.A.3

The Complex Number System

  • A.

    Perform arithmetic operations with complex numbers.CCSS.Math.Content.HSN-CN.A

    1. 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.CCSS.Math.Content.HSN-CN.A.1

    2. 2.

      Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.CCSS.Math.Content.HSN-CN.A.2

    3. 3.

      (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.CCSS.Math.Content.HSN-CN.A.3

  • B.

    Represent complex numbers and their operations on the complex plane.CCSS.Math.Content.HSN-CN.B

    1. 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.CCSS.Math.Content.HSN-CN.B.4

    2. 5.

      (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.CCSS.Math.Content.HSN-CN.B.5

    3. 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.CCSS.Math.Content.HSN-CN.B.6

  • C.

    Use complex numbers in polynomial identities and equations.CCSS.Math.Content.HSN-CN.C

    1. 7.

      Solve quadratic equations with real coefficients that have complex solutions.CCSS.Math.Content.HSN-CN.C.7

    2. 8.

      (+) Extend polynomial identities to the complex numbers.CCSS.Math.Content.HSN-CN.C.8

    3. 9.

      (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.CCSS.Math.Content.HSN-CN.C.9

Vector and Matrix Quantities

  • A.

    Represent and model with vector quantities.CCSS.Math.Content.HSN-VM.A

    1. 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).CCSS.Math.Content.HSN-VM.A.1

    2. 2.

      (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.CCSS.Math.Content.HSN-VM.A.2

    3. 3.

      (+) Solve problems involving velocity and other quantities that can be represented by vectors.CCSS.Math.Content.HSN-VM.A.3

  • B.

    Perform operations on vectors.CCSS.Math.Content.HSN-VM.B

    1. 4.

      (+) Add and subtract vectors.CCSS.Math.Content.HSN-VM.B.4

      1. 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.CCSS.Math.Content.HSN-VM.B.4a

      2. b.

        Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.CCSS.Math.Content.HSN-VM.B.4b

      3. 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.CCSS.Math.Content.HSN-VM.B.4c

    2. 5.

      (+) Multiply a vector by a scalar.CCSS.Math.Content.HSN-VM.B.5

      1. a.

        Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v<sub>x</sub>, v<sub>y</sub>) = (cv<sub>x</sub>, cv<sub>y</sub>).CCSS.Math.Content.HSN-VM.B.5a

      2. 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).CCSS.Math.Content.HSN-VM.B.5b

  • C.

    Perform operations on matrices and use matrices in applications.CCSS.Math.Content.HSN-VM.C

    1. 6.

      (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.CCSS.Math.Content.HSN-VM.C.6

    2. 7.

      (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.CCSS.Math.Content.HSN-VM.C.7

    3. 8.

      (+) Add, subtract, and multiply matrices of appropriate dimensions.CCSS.Math.Content.HSN-VM.C.8

    4. 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.CCSS.Math.Content.HSN-VM.C.9

    5. 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.CCSS.Math.Content.HSN-VM.C.10

    6. 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.CCSS.Math.Content.HSN-VM.C.11

    7. 12.

      (+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.CCSS.Math.Content.HSN-VM.C.12

Frequently asked questions

What grade levels do these standards cover?
Grade 9, Grade 10, Grade 11, and Grade 12
When were these standards adopted?
2010

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