CCSS.Math.Content.HSN-RN: The Real Number System

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

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

Operations with Radical Expressions
Simplifying Radical Expressions

CCSS.Math.Content.HSN-Q: Quantities

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

CCSS.Math.Content.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.

Distance-Time Graphs
Distance-Time Graphs - Metric
Distance-Time and Velocity-Time Graphs
Distance-Time and Velocity-Time Graphs - Metric
Household Energy Usage

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

Unit Conversions 2 - Scientific Notation and Significant Digits

CCSS.Math.Content.HSN-CN: The Complex Number System

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

CCSS.Math.Content.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.

Points in the Complex Plane
Roots of a Quadratic

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

Points in the Complex Plane

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

Points in the Complex Plane
Roots of a Quadratic

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

CCSS.Math.Content.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.

Points in the Complex Plane

CCSS.Math.Content.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.

Points in the Complex Plane

CCSS.Math.Content.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.

Points in the Complex Plane

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

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

Roots of a Quadratic

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

Points in the Complex Plane

CCSS.Math.Content.HSN-VM: Vector and Matrix Quantities

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

CCSS.Math.Content.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).

Adding Vectors
Vectors

CCSS.Math.Content.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.

Adding Vectors

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

2D Collisions
Adding Vectors
Golf Range
Vectors

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

CCSS.Math.Content.HSN-VM.B.4: Add and subtract vectors.

CCSS.Math.Content.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.

Adding Vectors
Vectors

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

CCSS.Math.Content.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.

Dilations

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

Translations

CCSS.Math.Content.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.

Solving Linear Systems (Matrices and Special Solutions)

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

Translations