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### 1 Number and Quantity

- HS.N-RN.A The Real Number System: Extend the properties of exponents to rational exponents.
- HS.N-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
- HS.N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

- HS.N-RN.B The Real Number System: Use properties of rational and irrational numbers.
- HS.N-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
- Checkpoint opportunity

- HS.N-Q.A Quantities: Reason quantitatively and use units to solve problems.
- HS.N-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
- HS.N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.
- HS.N-Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- Checkpoint opportunity

### 2 Algebra and Functions

- HS.A-SSE.A Seeing Structure in Expressions: Interpret the structure of expressions.
- HS.A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
- HS.A-SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
- HS.A-SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

- HS.A-SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
- HS.A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

- HS.A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
- HS.A-SSE.B Seeing Structure in Expressions: Write expressions in equivalent forms to solve problems.
- HS.A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- HS.A-SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
- HS.A-SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- HS.A-SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions.

- HS.A-SSE.B.4 Use the formula for the sum of a finite geometric series (when the common ratio is not 1) to solve problems.
- HS.A-SSE.B.4.a Derive the formula for the sum of a finite geometric series (when the common ratio is not 1).

- Checkpoint opportunity

- HS.A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- HS.A-APR.A Arithmetic with Polynomials & Rational Expressions: Perform arithmetic operations on polynomials.
- HS.A-APR.A.1 Explain 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.
- Checkpoint opportunity

- HS.A-CED.A Creating Equations: Create equations that describe numbers or relationships.
- HS.A-CED.A.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.
- HS.A-CED.A.2 Create equations in two or more variables to represent relationships between quantities and graph equations on coordinate axes with labels and scales.
- HS.A-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
- HS.A-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
- Checkpoint opportunity

- HS.A-CED.A.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.
- HS.A-REI.A Reasoning with Equations & Inequalities: Understand solving equations as a process of reasoning and explain the reasoning.
- HS.A-REI.A.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.

- HS.A-REI.B Reasoning with Equations & Inequalities: Solve equations and inequalities in one variable.
- HS.A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

- HS.A-REI.B.4 Solve quadratic equations in one variable.
- HS.A-REI.B.4.a 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. - HS.A-REI.B.4.b Solve quadratic equations (e.g., for
*x*² = 49) by inspection, 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 and write them as*a*±*bi*for real numbers*a*and*b*.- Checkpoint opportunity

- HS.A-REI.B.4.a Use the method of completing the square to transform any quadratic equation in

- HS.A-REI.C Reasoning with Equations & Inequalities: Solve systems of equations.
- HS.A-REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
- HS.A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- HS.A-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
- HS.A-REI.C.8 Represent a system of linear equations as a single matrix equation in a vector variable.
- HS.A-REI.C.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

- HS.A-REI.D Reasoning with Equations & Inequalities: Represent and solve equations and inequalities graphically.
- HS.A-REI.D.10 Explain 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).
- HS.A-REI.D.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. - HS.A-REI.D.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.
- Checkpoint opportunity

- HS.F-IF.A Interpreting Functions: Understand the concept of a function and use function notation.
- HS.F-IF.A.1 Explain that a function is a correspondence from one set (called the domain) to another set (called the range) that 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*). - HS.F-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

- HS.F-IF.A.3 Demonstrate that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

- HS.F-IF.A.1 Explain that a function is a correspondence from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. If
- HS.F-IF.B Interpreting Functions: Interpret functions that arise in applications in terms of the context.
- HS.F-IF.B.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

- HS.F-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

- HS.F-IF.B.6 Calculate and interpret the average rate of change presented symbolically or as a table, of a function over a specified interval. Estimate the rate of change from a graph.

- Checkpoint opportunity

- HS.F-IF.C Interpreting Functions: Analyze functions using different representations.
- HS.F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
- HS.F-IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
- HS.F-IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- HS.F-IF.C.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

- HS.F-IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
- HS.F-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- HS.F-IF.C.8.a 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.
- HS.F-IF.C.8.b Use the properties of exponents to interpret expressions for exponential functions.

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

- Checkpoint opportunity

- HS.F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
- HS.F-BF.A Building Functions: Build a function that models a relationship between two quantities.
- HS.F-BF.A.1 Write a function that describes a relationship between two quantities.
- HS.F-BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.

- HS.F-BF.A.1.b Combine standard function types using arithmetic operations.
- HS.F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
- Checkpoint opportunity

- HS.F-BF.A.1 Write a function that describes a relationship between two quantities.
- HS.F-BF.B Building Functions: Build new functions from existing functions.
- HS.F-BF.B.3 Identify the effect on the graph of replacing
*f*(*x*) by*f*(*x*) +*k*,*k**f*(*x*),*f*(*k*x), 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. - HS.F-BF.B.4 Find inverse functions.
- HS.F-BF.B.4.a 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.

- HS.F-BF.B.4.a Solve an equation of the form
- Checkpoint opportunity

- HS.F-BF.B.3 Identify the effect on the graph of replacing
- HS.F-LE.A Linear, Quadratic & Exponential Models: Construct and compare linear, quadratic, and exponential models and solve problems.
- HS.F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
- HS.F-LE.A.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
- HS.F-LE.A.1.b Identify situations in which one quantity changes at a constant rate per unit interval relative to another.
- HS.F-LE.A.1.c Identify situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

- HS.F-LE.A.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).

- HS.F-LE.A.3 Use graphs and tables to describe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

- HS.F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
- HS.F-LE.B Linear, Quadratic, & Exponential Models: Interpret expressions for functions in terms of the situation they model.
- HS.F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.
- Checkpoint opportunity

### 3 Data, Statistics, and Probability

- HS.S-ID.A Interpreting Categorical & Quantitative Data: Summarize, represent, and interpret data on a single count or measurement variable.
- HS.S-ID.A.1 Model data in context with plots on the real number line (dot plots, histograms, and box plots).

- HS.S-ID.A.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.

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

- Checkpoint opportunity

- HS.S-ID.B Interpreting Categorical & Quantitative Data: Summarize, represent, and interpret data on two categorical and quantitative variables.
- HS.S-ID.B.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.

- HS.S-ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- HS.S-ID.B.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

- HS.S-ID.B.6.b Informally assess the fit of a function by plotting and analyzing residuals.

- HS.S-ID.B.6.c Fit a linear function for a scatter plot that suggests a linear association.
- Checkpoint opportunity
- HS.S-ID.B.7 Distinguish between correlation and causation.

- HS.S-ID.C Interpreting Categorical & Quantitative Data: Interpret linear models.
- HS.S-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- HS.S-ID.C.8 Using technology, compute and interpret the correlation coefficient of a linear fit.
- Checkpoint opportunity