### N: Number and Quantity

#### N-RN: The Real Number System

1.1.1: Extend the properties of exponents to rational exponents

N-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.

#### N-CN: The Complex Number System

1.3.1: Perform arithmetic operations with complex numbers

N-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.

N-CN.2: Use the relation ??² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

1.3.2: Use complex numbers in polynomial identities and equations

N-CN.7: Solve quadratic equations with real coefficients that have complex solutions.

### A: Algebra

#### A-SSE: Seeing Structure in Expressions

2.1.1: Interpret the structure of expressions

A-SSE.1: Interpret expressions that represent a quantity in terms of its context.

A-SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

A-SSE.2: Use the structure of an expression to identify ways to rewrite it.

2.1.2: Write expressions in equivalent forms to solve problems

A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A-SSE.3a: Factor a quadratic expression to reveal the zeros of the function it defines.

A-SSE.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

#### A-APR: Arithmetic with Polynomials and Rational Expressions

2.2.1: Perform arithmetic operations on polynomials

A-APR.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

#### A-CED: Creating Equations

2.3.1: Create equations that describe numbers or relationships

A-CED.1: Create equations and inequalities in one variable and use them to solve problems.

A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A-CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

#### A-REI: Reasoning with Equations and Inequalities

2.4.1: Understand solving equations as a process of reasoning and explain the reasoning

A-REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

2.4.2: Solve equations and inequalities in one variable

A-REI.4: Solve quadratic equations in one variable.

A-REI.4a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

A-REI.4b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions.

2.4.3: Solve systems of equations

A-REI.6: Solve systems of linear equations algebraically, exactly, approximately, and graphically while focusing on pairs of linear equations in two variables.

### F: Functions

#### F-IF: Interpreting Functions

3.1.1: Interpret functions that arise in applications in terms of the context

F-IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F-IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

3.1.2: Analyze functions using different representations

F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

F-IF.7b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F-IF.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F-IF.8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F-IF.8b: Use the properties of exponents to interpret expressions for exponential functions.

F-IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

#### F-BF: Building Functions

3.2.1: Build a function that models a relationship between two quantities

F-BF.1: Write a function that describes a relationship between two quantities.

F-BF.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

F-BF.1b: Combine standard function types using arithmetic operations.

3.2.2: Build new functions from existing functions

F-BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

### G: Geometry

#### G-SRT: Similarity, Right Triangles, and Trigonometry

4.1.1: Understand similarity in terms of similarity transformations

G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:

G-SRT.1a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

G-SRT.1b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G-SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G-SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

4.1.2: Prove theorems using similarity

G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

4.1.3: Define trigonometric ratios and solve problems involving right triangles

G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

#### G-GMD: Geometric Measurement and Dimension

4.2.1: Explain volume formulas and use them to solve problems

G-GMD.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

G-GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

### S: Statistics and Probability

#### S-ID: Interpreting Categorical and Quantitative Data

5.1.1: Summarize, represent, and interpret data on two categorical and quantitative variables

S-ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S-ID.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

S-ID.6b: Informally assess the fit of a function by plotting and analyzing residuals.

#### S-CP: Conditional Probability and the Rules of Probability

5.2.1: Understand independence and conditional probability and use them to interpret data

S-CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S-CP.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

S-CP.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

S-CP.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

S-CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

5.2.2: Use the rules of probability to compute probabilities of compound events in a uniform probability model

S-CP.6: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

Correlation last revised: 9/15/2020

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