College- and Career-Readiness Standards
2.1.1: Interpret the structure of expressions
A-SSE.1: Interpret expressions that represent a quantity in terms of its context.
A-SSE.1a: Interpret parts of an expression, such as terms, factors, and coefficients.
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.
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.
2.2.2: Understand the relationship between zeros and factors of polynomials
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).
2.3.1: 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 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.
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.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
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.5: Given a system of two equations in two variables, show and explain why the sum of equivalent forms of the equations produces the same solution as the original system.
A-REI.6: Solve systems of linear equations algebraically, exactly, and graphically while focusing on pairs of linear equations in two variables.
2.4.4: Represent and solve equations and inequalities graphically
A-REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
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, quadratic, absolute value, and exponential functions.
A-REI.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
3.1.1: Understand the concept of a function and use function notation
F-IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F-IF.3: Recognize that sequences are functions whose domain is a subset of the integers.
3.1.2: 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.
3.1.3: 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 functions (linear and quadratic) and show intercepts, maxima, and minima.
F-IF.7b: Graph square root and piecewise-defined functions, including absolute value functions.
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.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
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 or steps for calculation from a context.
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.
3.3.1: Construct and compare linear, quadratic, and exponential models and solve problems
F-LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.
F-LE.1a: Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
F-LE.1b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F-LE.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F-LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
3.3.2: Interpret expressions for functions in terms of the situation they model
F-LE.5: Interpret the parameters in a linear or exponential function in terms of a context.
4.1.1: Summarize, represent, and interpret data on a single count or measurement variable
S-ID.1: Represent and analyze data with plots on the real number line (dot plots, histograms, and box plots).
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.
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).
4.1.2: Summarize, represent, and interpret data on two categorical and quantitative variables
S-ID.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
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-ID.6c: Fit a linear function for a scatter plot that suggests a linear association.
4.1.3: Interpret linear models
S-ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
S-ID.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.
S-ID.9: Distinguish between correlation and causation.
Correlation last revised: 9/24/2019