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### HSN Number and Quantity

- HSN.RN The Real Number System
- HSN.RN.1 Use properties of rational and irrational numbers
- HSN.RN.B.3 Explain why the sum/difference or product/quotient (where defined) of two rational numbers is rational; the sum/difference of a rational number and an irrational number is irrational; the product/quotient of a nonzero rational number and an irrational number is irrational; and the product/quotient of two nonzero rationals is a nonzero rational.
- HSN.RN.B.4 Simplify radical expressions. Perform operations (add, subtract, multiply, and divide) with radical expressions. Rationalize denominators and/or numerators.
- Checkpoint opportunity

- HSN.RN.1 Use properties of rational and irrational numbers
- HSN.Q Quantities
- HSN.Q.2 Reason quantitatively and use units to solve problems
- HSN.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.
- HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. (I.E., Use units appropriate to the problem being solved.)
- HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- Checkpoint opportunity

- HSN.Q.2 Reason quantitatively and use units to solve problems

### HSA Algebra

- HSA.SSE Seeing Structure in Expressions
- HSA.SSE.3 Interpret the structure of expressions
- HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression using appropriate vocabulary, such as terms, factors, and coefficients. Interpret complicated expressions by viewing one or more of their parts as a single entity.
- HSA.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

- HSA.SSE.4 Write expressions in equivalent forms to solve problems
- HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- Checkpoint opportunity

- HSA.SSE.3 Interpret the structure of expressions
- HSA.APR Arithmetic with Polynomials and Rational Expressions
- HSA.APR.5 Perform arithmetic operations on polynomials
- HSA.APR.A.1 Add, subtract, and multiply polynomials. Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication.
- Checkpoint opportunity

- HSA.APR.6 Understand the relationship between zeros and factors of polynomials
- HSA.APR.B.3 Identify zeros of polynomials (linear, quadratic only) when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.

- HSA.APR.7 Use polynomial identities to solve problems
- HSA.APR.C.4 Prove polynomial identities and use them to describe numerical relationships.

- HSA.APR.8 Rewrite rational expressions
- HSA.APR.D.7 Add, subtract, multiply, and divide by nonzero rational expressions. Understand that rational expressions, like the integers, are closed under addition, subtraction, and multiplication.

- HSA.APR.5 Perform arithmetic operations on polynomials
- HSA.CED Creating Equations
- HSA.CED.9 Create equations that describe numbers or relationships
- HSA.CED.A.1 Create equations and inequalities in one variable and use them to solve problems.
- HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities. Graph equations, in two variables, on a coordinate plane.
- HSA.CED.A.3 Represent and interpret constraints by equations or inequalities, and by systems of equations and/or inequalities. Interpret solutions as viable or nonviable options in a modeling and/or real-world context.
- HSA.CED.A.4 Rearrange literal equations using the properties of equality.
- Checkpoint opportunity

- HSA.CED.9 Create equations that describe numbers or relationships
- HSA.REI Reasoning with Equations and Inequalities
- HSA.REI.10 Understand solving equations as a process of reasoning and explain the reasoning
- HSA.REI.A.1 Assuming that equations have a solution, construct a solution and justify the reasoning used.
- HSA.REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

- HSA.REI.11 Solve equations and inequalities in one variable
- HSA.REI.B.3 Solve linear equations, inequalities and absolute value equations in one variable, including equations with coefficients represented by letters.
- HSA.REI.B.4 Solve quadratic equations in one variable. 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. Solve quadratic equations (as appropriate to the initial form of the equation) by: inspection of a graph, taking square roots, completing the square, using the quadratic formula, factoring. Recognize complex solutions and write them as*a*±*b**i*for real numbers*a*and*b*. (Algebra 2 only) - Checkpoint opportunity

- HSA.REI.12 Solve systems of equations and inequalities graphically
- HSA.REI.C.5 Solve systems of equations in two variables using substitution and elimination. Understand that the solution to a system of equations will be the same when using substitution and elimination.
- HSA.REI.C.6 Solve systems of equations algebraically and graphically.
- HSA.REI.C.7 Solve systems of equations consisting of linear equations and nonlinear equations in two variables algebraically and graphically.

- HSA.REI.13 Solve systems of equations
- HSA.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
- HSA.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 by using technology to graph the functions, making tables of values, finding successive approximations. Include cases (but not limited to) where*f*(*x*) and/or*g*(*x*) are linear, polynomial, absolute value, exponential. (Introduction in Algebra 1, Mastery in Algebra 2) - HSA.REI.D.12 Solve linear inequalities and systems of linear inequalities in two variables by graphing.
- Checkpoint opportunity

- HSA.REI.10 Understand solving equations as a process of reasoning and explain the reasoning

### HSF Functions

- HSF.IF Interpreting Functions
- HSF.IF.14 Understand the concept of a function and use function notation
- HSF.IF.A.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. Understand that 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*. Understand that the graph of*f*is the graph of the equation*y*=*f*(*x*). - HSF.IF.A.2 In terms of a real-world context: use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation.
- HSF.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

- HSF.IF.A.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. Understand that if
- HSF.IF.15 Interpret functions that arise in applications in terms of the context
- HSF.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 given a verbal description of the relationship.
- HSF.IF.B.5 Relate the domain of a function to its graph. Relate the domain of a function to the quantitative relationship it describes.
- HSF.IF.B.6 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.
- Checkpoint opportunity

- HSF.IF.16 Analyze functions using different representations
- HSF.IF.C.7 Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph exponential functions, showing intercepts and end behavior.
- HSF.IF.C.8 Write expressions for functions in different but equivalent forms to reveal key features of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values (vertex), and symmetry of the graph, and interpret these in terms of a context.
- HSF.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

- HSF.IF.14 Understand the concept of a function and use function notation
- HSF.BF Building Functions
- HSF.BF.17 Build a function that models a relationship between two quantities
- HSF.BF.A.1 Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation.

- HSF.BF.18 Build new functions from existing functions
- HSF.BF.B.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 (k, a constant both positive and negative); Find the value of k given the graphs of the transformed functions. Experiment with multiple transformations and illustrate an explanation of the effects on the graph with or without technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. - Checkpoint opportunity

- HSF.BF.B.3 Identify the effect on the graph of replacing

- HSF.BF.17 Build a function that models a relationship between two quantities
- HSF.LE Linear, Quadratic, and Exponential Models
- HSF.LE.19 Construct and compare linear, quadratic, and exponential models and solve problems
- HSF.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. Show that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
- HSF.LE.A.2 Construct linear and exponential equations, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
- HSF.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or any polynomial function.

- HSF.LE.20 Interpret expressions for functions in terms of the situation they model
- HSF.LE.B.5 In terms of a context, interpret the parameters (rates of growth or decay, domain and range restrictions where applicable, etc.) in a function.
- Checkpoint opportunity

- HSF.LE.19 Construct and compare linear, quadratic, and exponential models and solve problems

### HSS Statistics and Probability

- HSS.ID Interpreting Categorical and Quantitative Data
- HSS.ID.21 Summarize, represent, and interpret data on a single count or measurement variable
- HSS.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
- HSS.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.
- HSS.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

- HSS.ID.22 Summarize, represent, and interpret data on two categorical and quantitative variables
- HSS.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.
- HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
- Checkpoint opportunity

- HSS.ID.23 Interpret linear models
- HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- HSS.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
- HSS.ID.C.9 Distinguish between correlation and causation.
- Checkpoint opportunity

- HSS.ID.21 Summarize, represent, and interpret data on a single count or measurement variable