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<title>High School Number and Quantity Common Core Standards</title>
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<h1 align="center">High School Number and Quantity Common Core Standards</h1><p align="center">Here are the <a href="core-index.html">Common Core Standards</a> for High School Number and Quantity, with links to resources that support them. We also encourage plenty of exercises and book work.</p><div class="corYrSubj">High School Number and Quantity | The Real Number System</div>
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<div class="corTitle">Extend the properties of exponents to rational exponents.</div>
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<div class="corCore"><span class="corCode">HSN.RN.A.1</span><span class="corDescr">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.</span></div><div class="corPages">
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<div class="corPage"><a href="../exponent.html">Exponents</a></div>
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<div class="corPage"><a href="../numbers/nth-root.html">nth Roots</a></div>
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<div class="corPage"><a href="../algebra/exponent-laws.html">Laws of Exponents</a></div>
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<div class="corPage"><a href="../algebra/negative-exponents.html">Negative Exponents</a></div>
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<div class="corPage"><a href="../algebra/exponent-fractional.html">Fractional Exponents</a></div></div>
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<div class="corCore"><span class="corCode">HSN.RN.A.2</span><span class="corDescr">Rewrite expressions involving radicals and rational exponents using the properties of exponents.</span></div><div class="corPages">
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<div class="corPage"><a href="../exponent.html">Exponents</a></div>
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<div class="corPage"><a href="../numbers/nth-root.html">nth Roots</a></div>
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<div class="corPage"><a href="../algebra/exponent-laws.html">Laws of Exponents</a></div>
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<div class="corPage"><a href="../algebra/negative-exponents.html">Negative Exponents</a></div>
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<div class="corPage"><a href="../algebra/exponent-fractional.html">Fractional Exponents</a></div>
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<div class="corPage"><a href="../algebra/exponents-using.html">Using Exponents in Algebra</a></div>
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<div class="corPage"><a href="../algebra/exponents-squaring-negative.html">Exponents of Negative Numbers</a></div>
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<div class="corPage"><a href="../algebra/square-root.html">Squares and Square Roots in Algebra</a></div>
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<div class="corPage"><a href="../algebra/variables-exponents-multiply.html">Variables with Exponents - How to Multiply and Divide them</a></div></div>
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<div class="corTitle">Use properties of rational and irrational numbers.</div>
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<div class="corCore"><span class="corCode">HSN.RN.B.3</span><span class="corDescr">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.</span></div><div class="corPages">
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<div class="corPage"><a href="../numbers/irrational-finding.html">Is It Irrational?</a></div>
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<div class="corPage"><a href="../irrational-numbers.html">Irrational Numbers</a></div>
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<div class="corPage"><a href="../square-root.html">Squares and Square Roots</a></div></div><div class="corYrSubj">High School Number and Quantity | Quantities</div>
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<div class="corTitle">Reason quantitatively and use units to solve problems.</div>
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<div class="corCore"><span class="corCode">HSN.Q.A.1</span><span class="corDescr">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.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/equation-formula.html">Equations and Formulas</a></div></div>
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<div class="corCore"><span class="corCode">HSN.Q.A.2</span><span class="corDescr">Define appropriate quantities for the purpose of descriptive modeling.</span></div><div class="corPages">
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<div class="corPage"><a href="../activity/soup-can.html">Activity: Soup Can</a></div>
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<div class="corPage"><a href="../algebra/mathematical-models.html">Mathematical Models</a></div>
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<div class="corPage"><a href="../algebra/introduction.html">Introduction to Algebra</a></div>
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<div class="corPage"><a href="../algebra/introduction-multiply.html">Algebra Introduction: Multiplication</a></div></div>
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<div class="corCore"><span class="corCode">HSN.Q.A.3</span><span class="corDescr">Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.</span></div><div class="corPages">
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<div class="corPage"><a href="../rounding-numbers.html">Rounding Numbers</a></div>
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<div class="corPage"><a href="../algebra/approximate-solutions.html">Approximate Solutions</a></div></div><div class="corYrSubj">High School Number and Quantity | The Complex Number System</div>
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<div class="corTitle">Perform arithmetic operations with complex numbers.</div>
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<div class="corCore"><span class="corCode">HSN.CN.A.1</span><span class="corDescr">Know there is a complex number i such that i^2 = -1, and every complex number has the form a + bi with a and b real. </span></div><div class="corPages">
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<div class="corPage"><a href="../numbers/complex-numbers.html">Complex Numbers</a></div>
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<div class="corPage"><a href="../numbers/imaginary-numbers.html">Imaginary Numbers</a></div>
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<div class="corPage"><a href="../numbers/evolution-of-numbers.html">The Evolution of Numbers</a></div></div>
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<div class="corCore"><span class="corCode">HSN.CN.A.2</span><span class="corDescr">Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.</span></div><div class="corPages">
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<div class="corPage"><a href="../numbers/complex-numbers.html">Complex Numbers</a></div>
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<div class="corPage"><a href="../numbers/imaginary-numbers.html">Imaginary Numbers</a></div>
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<div class="corPage"><a href="../numbers/complex-number-calculator.html">Complex Number Calculator</a></div>
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<div class="corPage"><a href="../associative-commutative-distributive.html">Commutative Associative and Distributive Laws</a></div></div>
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<div class="corCore"><span class="corCode">HSN.CN.A.3</span><span class="corDescr">Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/conjugate.html">Conjugate</a></div>
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<div class="corPage"><a href="../numbers/complex-numbers.html">Complex Numbers</a></div>
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<div class="corPage"><a href="../numbers/imaginary-numbers.html">Imaginary Numbers</a></div>
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<div class="corPage"><a href="../numbers/complex-number-calculator.html">Complex Number Calculator</a></div></div>
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<div class="corTitle">Represent complex numbers and their operations on the complex plane.</div>
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<div class="corCore"><span class="corCode">HSN.CN.B.4</span><span class="corDescr">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.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/complex-plane.html">Complex Plane</a></div>
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<div class="corPage"><a href="../numbers/complex-numbers.html">Complex Numbers</a></div>
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<div class="corPage"><a href="../polar-cartesian-coordinates.html">Polar and Cartesian Coordinates</a></div>
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<div class="corPage"><a href="../algebra/trig-four-quadrants.html">Sine Cosine and Tangent in Four Quadrants</a></div></div>
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<div class="corCore"><span class="corCode">HSN.CN.B.5</span><span class="corDescr">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^(1/2)]i)^3 = 8 because (-1 + [3^(1/2)]i) has modulus 2 and argument 120 degrees.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/complex-plane.html">Complex Plane</a></div>
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<div class="corPage"><a href="../numbers/complex-numbers.html">Complex Numbers</a></div>
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<div class="corPage"><a href="../numbers/imaginary-numbers.html">Imaginary Numbers</a></div>
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<div class="corPage"><a href="../numbers/complex-number-calculator.html">Complex Number Calculator</a></div></div>
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<div class="corCore"><span class="corCode">HSN.CN.B.6</span><span class="corDescr">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.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/complex-plane.html">Complex Plane</a></div></div>
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<div class="corTitle">Use complex numbers in polynomial identities and equations.</div>
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<div class="corCore"><span class="corCode">HSN.CN.C.7</span><span class="corDescr">Solve quadratic equations with real coefficients that have complex solutions.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/quadratic-equation.html">Quadratic Equations</a></div>
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<div class="corPage"><a href="../algebra/factoring-quadratics.html">Factoring Quadratics</a></div>
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<div class="corPage"><a href="../quadratic-equation-solver.html">Quadratic Equation Solver</a></div>
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<div class="corPage"><a href="../algebra/fundamental-theorem-algebra.html">Fundamental Theorem of Algebra</a></div>
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<div class="corPage"><a href="../algebra/quadratic-equation-derivation.html">Derivation of Quadratic Formula</a></div></div>
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<div class="corCore"><span class="corCode">HSN.CN.C.8</span><span class="corDescr">Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x - 2i).</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/special-binomial-products.html">Special Binomial Products</a></div></div>
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<div class="corCore"><span class="corCode">HSN.CN.C.9</span><span class="corDescr">Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/polynomials-solving.html">Solving Polynomials</a></div>
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<div class="corPage"><a href="../algebra/fundamental-theorem-algebra.html">Fundamental Theorem of Algebra</a></div></div><div class="corYrSubj">High School Number and Quantity | Vector & Matrix Quantities</div>
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<div class="corTitle">Represent and model with vector quantities.</div>
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<div class="corCore"><span class="corCode">HSN.VM.A.1</span><span class="corDescr">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(bold), |v|, ||v||, v(not bold)).</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/vectors.html">Vectors</a></div></div>
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<div class="corCore"><span class="corCode">HSN.VM.A.2</span><span class="corDescr">Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/vectors.html">Vectors</a></div></div>
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<div class="corCore"><span class="corCode">HSN.VM.A.3</span><span class="corDescr">Solve problems involving velocity and other quantities that can be represented by vectors.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/vectors.html">Vectors</a></div></div>
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<div class="corTitle">Perform operations on vectors.</div>
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<div class="corCore"><span class="corCode">HSN.VM.B.4</span><span class="corDescr">Add and subtract vectors.<br />
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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.<br />
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b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.<br />
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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.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/vectors.html">Vectors</a></div>
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<div class="corPage"><a href="../algebra/vector-calculator.html">Vector Calculator</a></div></div>
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<div class="corCore"><span class="corCode">HSN.VM.B.5</span><span class="corDescr">Multiply a vector by a scalar.<br />
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a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).<br />
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b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v is not equal to 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/vectors.html">Vectors</a></div></div>
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<div class="corTitle">Perform operations on matrices and use matrices in applications.</div>
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<div class="corCore"><span class="corCode">HSN.VM.C.6</span><span class="corDescr">Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. </span></div><div class="corPages"></div>
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<div class="corCore"><span class="corCode">HSN.VM.C.7</span><span class="corDescr">Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. </span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/matrix-introduction.html">Matrices</a></div></div>
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<div class="corCore"><span class="corCode">HSN.VM.C.8</span><span class="corDescr">Add, subtract, and multiply matrices of appropriate dimensions.</span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/matrix-introduction.html">Matrices</a></div>
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<div class="corPage"><a href="../algebra/matrix-multiplying.html">How to Multiply Matrices</a></div></div>
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<div class="corCore"><span class="corCode">HSN.VM.C.9</span><span class="corDescr">Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. </span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/matrix-multiplying.html">How to Multiply Matrices</a></div>
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<div class="corPage"><a href="../associative-commutative-distributive.html">Commutative Associative and Distributive Laws</a></div></div>
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<div class="corCore"><span class="corCode">HSN.VM.C.10</span><span class="corDescr">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. </span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/matrix-introduction.html">Matrices</a></div>
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<div class="corPage"><a href="../algebra/matrix-inverse.html">Inverse of a Matrix</a></div>
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<div class="corPage"><a href="../algebra/matrix-determinant.html">Determinant of a Matrix</a></div>
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<div class="corPage"><a href="../algebra/matrix-multiplying.html">How to Multiply Matrices</a></div></div>
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<div class="corCore"><span class="corCode">HSN.VM.C.11</span><span class="corDescr">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.</span></div><div class="corPages"></div>
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<div class="corCore"><span class="corCode">HSN.VM.C.12</span><span class="corDescr">Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. </span></div><div class="corPages">
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<div class="corPage"><a href="../algebra/matrix-determinant.html">Determinant of a Matrix</a></div></div><p> </p><!-- #EndEditable -->
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