Model a contextual situation graphically using appropriate scales and features.

Define functions and evaluate points in tables, graphs, and contextual situations using function notation.

Identify features of functions, including x-intercept and y-intercept, in context. Evaluate function notation in context.

Identify the domain and range through contextual situations, and explore domain and range on a graph. Represent domain and range with inequalities.

Calculate and interpret the rate of change from two points on a graph, in a situation, or in function notation.

Describe and sketch functions using the features of domain and range, intercepts, function behavior, and the value of the function.

Analyze the key features of a contextual situation and model these graphically.

Draw quadratic functions represented contextually. Identify key features of the graph and relate to context.

Sketch an exponential function that represents a situation. Identify key features of the graph and relate to context.

Draw a graph to represent a system of functions. Identify the solution to a system represented graphically and in context.

Analyze functions and identify parent functions of graphs. Identify variables of a situation and the scale of the associated graph. Represent a situation in a graph, table, and description.

Describe statistics. Represent data in frequency graphs and identify the center of a data set.

Describe center and spread. Represent data in a box plot (box-and-whisker plot) and calculate the center and spread.

Represent data in a histogram and calculate the center. Identify when the median and mean are not the same value.

Describe the shape of the data in box plots and histograms. Choose an appropriate measure of center (or an appropriate shape) based on the shape and the relationship between the mean and the median. 

Calculate and interpret the spread (variance) of a data set.

Calculate the standard deviation and compare two symmetrical distributions based on the mean and standard deviation.

Interpret the standard deviation and interquartile range.

Calculate population percentages using the standard deviation.

Given summary statistics, describe the best measures of center and spread. Describe reasoning.

Define categorical and numerical data. Create two-way tables to organize bivariate categorical data.

Describe relative and relative conditional frequencies of two-way tables.

Create scatterplots and identify function shapes in scatterplots.

Calculate, with technology, the correlation coefficient for a data set. Explain why correlation does not determine causation.

Determine the function of best fit and create a linear equation from least squares regression using technology.

Use residuals to assess the strength of the model for a data set.

Describe the relationship between two quantitative variables in a contextual situation represented in a scatterplot using the correlation coefficient, least squares regression, and residuals as evidence.

Identify properties of operations that result in equivalent linear expressions.

Use properties of equations to analyze and write equivalent equations.

Solve single-variable linear equations using properties of equality.

Solve equations with a variable in the denominator.

Solve for a variable in an equation or formula.

Write equations using defined variables to represent a contextual situation.

Define variables; write and solve equations to represent a contextual situation.

Write and solve equations to represent contextual situations where estimations and unit conversions are required.

Solve unbounded single-variable inequalities in contextual and non-contextual situations.

Write and graph compound single-variable inequalities to describe the solution to contextual and non-contextual situations.

Solve and graph compound inequalities where algebraic manipulation is necessary in contextual and non-contextual situations.

Identify the solutions and features of a linear equation and when two linear equations have the same solutions.

Write linear equations given features, points, or graph in standard form, point-slope form, and slope-intercept form.

Determine if a function is linear based on the rate of change of points in the function presented graphically and in a table of values.

Identify inverse functions graphically and from a table of values in contextual and non-contextual situations.

Find inverse functions algebraically, and model inverse functions from contextual situations.

Describe the solutions and features of a linear inequality. Graph linear inequalities.

Write linear inequalities from graphs.

Write linear inequalities from contextual situations.

Solve a system of linear equations graphically.

Identify solutions to systems of inequalities graphically. Write systems of inequalities from graphs and word problems.

Solve linear systems of equations of two variables by substitution.

Identify solutions to systems of equations algebraically using elimination. Write systems of equations.

Identify solutions to systems of equations using any method. Write systems of equations.

Identify solutions to systems of equations with three variables.

Write equations and graph linear relationships with different domains.

Graph piecewise functions presented algebraically and write piecewise functions from graphs.

Evaluate a piecewise function written algebraically, with and without context.

Write and graph piecewise functions from contextual situations.

Graph, evaluate, and write step functions, with and without context.

Graph absolute value functions in the coordinate plane and identify domain and range. 

Identify the solutions to an absolute value equation.

Solve absolute value equations algebraically and identify extraneous solutions.

Identify the solution(s) to an absolute value inequality. 

Solve absolute value inequalities algebraically and verify graphically.

Identify solutions to a system of absolute value and linear functions graphically and algebraically.

Identify and describe vertical translations of functions.

Identify and describe horizontal translations of functions.

 Identify and describe vertical scaling of functions, including reflections over the $$x$$-axis.  

Identify and describe horizontal scaling of functions, including reflections over the $$y$$-axis.

Apply transformations to functions.

Use exponent rules to analyze and rewrite expressions with non-negative exponents.

Add and subtract polynomial expressions using properties of operations.

Multiply polynomials using properties of exponents and properties of operations. 

Solve mathematical applications of exponential expressions.

Use negative exponent rules to analyze and rewrite exponential expressions.

Define rational exponents and convert between rational exponents and roots. 

Write equivalent radical and rational exponent expressions. Identify quantities as rational or irrational.

Simplify radical expressions.

Multiply and divide rational exponent expressions and radical expressions.

Add and subtract rational exponent expressions and radical expressions.

Describe and analyze sequences given their recursive formulas.

Write recursive formulas for sequences, including the Fibonacci sequence.

Define arithmetic and geometric sequences, and identify common ratios and common differences in sequences.

Write explicit rules for arithmetic sequences and translate between explicit and recursive formulas.

Write explicit rules for geometric sequences and translate between explicit and recursive formulas.

Compare rates of change in linear and exponential functions shown as equations, graphs, and situations.

Write linear and exponential models for real-world and mathematical problems.

Graph exponential growth functions and write exponential growth functions from graphs.

Write exponential growth functions to model financial applications, including compound interest.

Write, graph, and evaluate exponential decay functions.

 Identify features of exponential decay in real-world problems.

Solve exponential growth and exponential decay application problems.

Compare quadratic, exponential, and linear functions represented as graphs, tables, and equations.

Identify key features of a quadratic function represented graphically. Graph a quadratic function from a table of values.

Calculate and compare the average rate of change for linear, exponential, and quadratic functions.

Factor quadratic expressions using the greatest common factor. Demonstrate equivalence between expressions by multiplying polynomials.

 Identify solutions to quadratic equations using the zero product property (equations written in intercept form).

Factor quadratic equations and identify solutions (when leading coefficient is equal to 1).

Factor quadratic equations and identify solutions (when leading coefficient does not equal 1).

Factor special cases of quadratic equations—difference of two squares.

Factor special cases of quadratic equations—perfect square trinomials.

Solve quadratic equations by factoring. Compare solutions in different representations (graph, equation, and table).

Solve quadratic equations by taking square roots. 

Graph quadratic functions using $${x-}$$intercepts and vertex.

Interpret quadratic solutions in context.

Describe features of the vertex form of a quadratic function and write quadratic equations in vertex form from graphs.

Complete the square.

Complete the square to identify the vertex and solve for the roots of a quadratic function.

Solve and interpret quadratic applications using the vertex form of the equation.

Convert and compare quadratic functions in standard form, vertex form, and intercept form.

Derive the quadratic formula. Use the quadratic formula to find the roots of a quadratic function. 

Determine the number of real roots of a quadratic function using the discriminant of the quadratic formula. 

Graph quadratic functions from all three forms of a quadratic equation.

Describe transformations to quadratic functions. Write equations for transformed quadratic functions.

Graph and describe transformations to quadratic functions in mathematical and real-world situations.

Write and analyze quadratic functions for projectile motion and falling bodies applications.

Write and analyze quadratic functions for geometric area applications.

Write and analyze quadratic functions for revenue applications.

Solve and identify solutions to systems of quadratic and linear equations when two solutions are present.

Solve and identify solutions to systems of quadratic and linear equations when two, one, or no solutions are present.