### N: Number and Quantity

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

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.4: Extend polynomial identities to the complex numbers.

### A: Algebra

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

A.SSE.6: Interpret expressions that represent a quantity in terms of its context.

A.SSE.6.a: Interpret parts of an expression, such as terms, factors, and coefficients.

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

A.APR.9: 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.APR.10: 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.11: 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.

#### A.CED: Creating Equations

A.CED.16: Create equations and inequalities in one variable and use them to solve problems.

A.CED.17: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.18: 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.19: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

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

A.REI.21: 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

F.IF.22: 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.23: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.24: 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.

F.IF.25: 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.25.a: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.25.b: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F.IF.25.c: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.IF.27: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

#### F.BF: Building Functions

F.BF.28: Combine standard function types using arithmetic operations.

F.BF.29: 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.BF.30: Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

### S: Statistics and Probability

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

S.ID.32: 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.

#### S.IC: Making Inferences and Justifying Conclusions

S.IC.33: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

S.IC.35: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

S.IC.36: 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.37: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

S.IC.38: Evaluate reports based on data.

#### S.MD: Using Probability to Make Decisions

S.MD.39: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

S.MD.40: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Correlation last revised: 3/17/2015

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