### A: Algebra

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

2.1.1: Interpret the structure of expressions

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

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

2.2.1: Understand the relationship between zeros and factors of polynomials

A-APR.2: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

A-APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial (limit to 1st- and 2nd-degree polynomials).

2.2.2: Use polynomial identities to solve problems

A-APR.4: Prove polynomial identities and use them to describe numerical relationships.

#### 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-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.

A-REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

2.4.2: Represent and solve equations and inequalities graphically

A-REI.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

### 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.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.7c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

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

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 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.

#### F-LE: Linear, Quadratic, and Exponential Models

3.3.1: Construct and compare linear, quadratic, and exponential models and solve problems

F-LE.4: For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

#### F-TF: Trigonometric Functions

3.4.1: Extend the domain of trigonometric functions using the unit circle

F-TF.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-TF.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

3.4.2: Model periodic phenomena with trigonometric functions

F-TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

3.4.3: Prove and apply trigonometric identities

F-TF.8: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

### G: Geometry

#### G-CO: Congruence

4.1.1: Make geometric constructions

G-CO.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

G-CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

#### G-C: Circles

4.2.1: Understand and apply theorems about circles

G-C.2: Identify and describe relationships among inscribed angles, radii, and chords.

G-C.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

4.2.2: Find arc lengths and areas of sectors of circles

G-C.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

#### G-GPE: Expressing Geometric Properties with Equations

4.3.1: Translate between the geometric description and the equation for a conic section

G-GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

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

4.3.2: Use coordinates to prove simple geometric theorems algebraically

G-GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

### S: Statistics and Probability

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

5.1.1: Summarize, represent, and interpret data on a single count or measurement variable

S-ID.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

5.1.2: 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-IC: Making Inferences and Justifying Conclusions

5.2.1: Understand and evaluate random processes underlying statistical experiments

S-IC.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

S-IC.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

5.2.2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

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

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

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

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

Correlation last revised: 9/15/2020

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