P.N: Number and Quantity

P.N-CN: The Complex Number System

P.N-CN.A: Perform arithmetic operations with complex numbers.

P.N-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

P.N-CN.B: Represent complex numbers and their operations on the complex plane.

P.N-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

P.N-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

P.N-VM: Vector and Matrix Quantities

P.N-VM.A: Represent and model with vector quantities.

P.N-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.

Adding Vectors
Vectors

P.N-VN.B: Perform operations on vectors.

P.N-VM.B.4: Add and subtract vectors.

P.N-VM.B.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.

Adding Vectors
Vectors

P.N-VM.B.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

Vectors

P.N-VM.B.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.

Adding Vectors
Vectors

P.N-VM.C: Perform operations on matrices and use matrices in applications.

P.N-VM.C.8: Add, subtract, and multiply matrices of appropriate dimensions.

Translations

P.N-VM.C.12: Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Dilations
Translations

P.A: Algebra

P.A-APR: Arithmetic with Polynomials and Rational Expressions

P.A-APR.C: Use polynomial identities to solve problems.

P.A-APR.C.5: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.

Binomial Probabilities

P.A-REI: Reasoning with Equations and Inequalities

P.A-REI.C: Solve systems of equations.

P.A-REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

P.A-REI.C.9: Find the inverse of a matrix if it exists, and use it to solve systems of linear equations (using technology for matrices of dimension 3 x 3 or greater).

Solving Linear Systems (Matrices and Special Solutions)

P.F: Functions

P.F-IF: Interpreting Functions

P.F-IF.C: Analyze functions using different representations.

P.F-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

Absolute Value with Linear Functions
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions

P.F-BF: Building Functions

P.F-BF.B: Build new functions from existing functions.

P.F-BF.B.4: Find inverse functions.

P.F-BF.B.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

P.F-BF.B.4d: Produce an invertible function from a non-invertible function by restricting the domain.

Logarithmic Functions

P.F-BF.B.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

P.F-TF: Trigonometric Functions

P.F-TF.A: Extend the domain of trigonometric functions using the unit circle.

P.F-TF.A.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi - x, pi + x, and 2pi - x in terms of their values for x, where x is any real number.

Cosine Function
Sine Function
Sum and Difference Identities for Sine and Cosine
Tangent Function
Translating and Scaling Sine and Cosine Functions

P.F-TF.A.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

P.F-TF.C: Apply trigonometric identities.

P.F-TF.C.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Sum and Difference Identities for Sine and Cosine

P.G: Geometry

P.G-GPE: Expressing Geometric Properties with Equations

P.G-GPE.A: Translate between the geometric description and the equation for a conic section.

P.G-GPE.A.2: Derive the equation of a parabola given a focus and directrix.

Parabolas

P.G-GPE.A.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

Ellipses
Hyperbolas

P.G-GMD: Geometric Measurement and Dimension

P.G-GMD.A: Explain volume formulas and use them to solve problems.

P.G-GMD.A.2: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Prisms and Cylinders
Pyramids and Cones

P.S: Statistics and Probability

P.S-IC: Making Inferences and Justifying Conclusions

P.S-IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

P.S-IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Polling: City
Polling: Neighborhood

P.S-IC.B.4: Use data from a random sample to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Polling: City

P.S-IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Polling: City
Polling: Neighborhood

P.S-IC.B.6: Evaluate reports based on data.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Real-Time Histogram

P.S-CP: Conditional Probability and the Rules of Probability

P.S-CP.B: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

P.S-CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

Binomial Probabilities
Permutations and Combinations

P.S-MD: Using Probability to Make Decisions

P.S-MD.A: Calculate expected values and use them to solve problems.

P.S-MD.A.1: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

Polling: City

P.S-MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Polling: City

P.S-MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated. Find the expected value.

Binomial Probabilities
Geometric Probability
Probability Simulations
Theoretical and Experimental Probability

P.S-MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically. Find the expected value.

Geometric Probability
Probability Simulations
Theoretical and Experimental Probability

P.S-MD.B: Use probability to evaluate outcomes of decisions.

P.S-MD.B.7: Analyze decisions and strategies using probability concepts.

Estimating Population Size
Probability Simulations
Theoretical and Experimental Probability

P.MP: Standards for Mathematical Practice

P.MP.1: Make sense of problems and persevere in solving them.

Biconditional Statements
Conditional Statements
Estimating Population Size

P.MP.2: Reason abstractly and quantitatively.

Conditional Statements
Estimating Population Size

P.MP.3: Construct viable arguments and critique the reasoning of others.

Biconditional Statements

P.MP.6: Attend to precision.

Biconditional Statements
Using Algebraic Expressions

P.MP.8: Look for and express regularity in repeated reasoning.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

Correlation last revised: 5/20/2019

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.