### 1: Inferences and Conclusions from Data

1.MCC9-12.S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets

1.MCC9-12.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 procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

1.MCC9-12.S.IC.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

1.MCC9-12.S.IC.2: Decide if a specified model is consistent with results from a given data- generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

1.MCC9-12.S.IC.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

1.MCC9-12.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.

1.MCC9-12.S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

1.MCC9-12.S.IC.6: Evaluate reports based on data.

1.MCC7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that rand om sampling tends to produce representative samples and support valid inferences.

1.MCC7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

1.MCC7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

1.MCC7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations

1.MCC9-12.S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and boxplots).

1.MCC9-12.S.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

### 2: Polynomial Functions

2.MCC9-12.A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

2.MCC9-12.A.SSE.1a: Interpret parts of an expression, such as terms, factors, and coefficients.

2.MCC9-12.A.SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity

2.MCC9-12.A.SSE.2: Use the structure of an expression to identify ways to rewrite it.

2.MCC9-12.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.

2.MCC9-12.A.APR.4: Prove polynomial identities and use them to describe numerical relationships.

2.MCC9-12.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 and polynomial functions.

2.MCC9-12.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).

2.MCC9-12.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.

2.MCC9-12.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.

### 3: Rational and Radical Relationships

3.MCC9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from simple rational functions.

3.MCC9-12.A.CED.: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

3.MCC9-12.A.REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

3.MCC9-12.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 rational.

3.MCC9-12..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. Key features include: intercepts; interval s where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

3.MCC9-12..F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

3.MCC9-12.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.

3.MCC9-12.F.IF.7b: Graph square root, cube root functions.

3.MCC9-12.F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

3.MCC9-12.A.SSE.1a: Interpret parts of an expression by viewing one or more of their parts as a single entity.

3.MCC9-12.A.SSE.2: Use the structure of an expression to identify ways to rewrite it.

### 4: Exponential and Logarithmic Functions

4.MCC9-12.A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

4.MCC9-12.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.

4.MCC9-12.F.IF.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior.

4.MCC9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

4.MCC9-12.F.IF.8b: Use the properties of exponents to interpret expressions for exponential functions.

4.MCC9-12.F.BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

### 5: Trigonometric Functions

5.MCC9‐12.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.

5.MCC9‐12.F.IF.7e: Graph trigonometric functions, showing period, midline, and amplitude.

5.MCC9-12.F.TF.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

5.MCC9-12.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.

5.MCC9-12.F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

5.MCC9-12.F.TF.8: Prove the Pythagorean identity (sin A)² + (cos A)² = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.

### 6: Mathematical Modeling

6.MCC9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

6.MCC9-12.A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

6.MCC9-12.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.

6.MCC9-12.A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

6.MCC9-12.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

6.MCC9-12.F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes

6.MCC9-12.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

6.MCC9-12.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.

6.MCC9-12.F.IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

6.MCC9-12.F.IF.7b: Graph square root, cube root, and piecewise defined functions, including step function s and absolute value functions.

6.MCC9-12.F.IF.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

6.MCC9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

6.MCC9-12.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.

6.MCC9-12.F.IF.8b: Use the properties of exponents to interpret express ions for exponential functions.

6.MCC9-12.F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

6.MCC9-12.F.BF.1: Write a function that describes a relationship between two quantities.

6.MCC9-12.F.BF.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

6.MCC9-12.F.BF.1b: Combine standard function types using arithmetic operations.

6.MCC9-12.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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

6.MCC9-12.F.BF.4: Find inverse functions.

6.MCC9-12.F.BF.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Correlation last revised: 5/10/2018

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