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### AI-N Number and Quantity

- AI-N.RN The Real Number System
- Use properties of rational and irrational numbers.
- AI-N.RN.3 Use properties and operations to understand the different forms of rational and irrational numbers.
- AI-N.RN.3a Perform all four arithmetic operations and apply properties to generate equivalent forms of rational numbers and square roots.
- AI-N.RN.3b Categorize the sum or product of rational or irrational numbers.

- Checkpoint opportunity

- AI-N.RN.3 Use properties and operations to understand the different forms of rational and irrational numbers.

- Use properties of rational and irrational numbers.
- AI-N.Q Quantities
- Reason quantitatively and use units to solve problems.
- AI-N.Q.1 Select quantities and use units as a way to:
- AI-N.Q.1.i interpret and guide the solution of multi-step problems;
- AI-N.Q.1.ii choose and interpret units consistently in formulas; and
- AI-N.Q.1.iii choose and interpret the scale and the origin in graphs and data displays.

- AI-N.Q.3 Choose a level of accuracy appropriate to limitations on measurement and context when reporting quantities.
- Checkpoint opportunity

- AI-N.Q.1 Select quantities and use units as a way to:

- Reason quantitatively and use units to solve problems.

### AI-A Algebra

- AI-A.SSE Seeing Structure in Expressions
- Interpret the structure of expressions.
- AI-A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
- AI-A.SSE.1a Write the standard form of a given polynomial and identify the terms, coefficients, degree, leading coefficient, and constant term.
- AI-A.SSE.1b Interpret expressions by viewing one or more of their parts as a single entity.

- AI-A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.

- AI-A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
- Write expressions in equivalent forms to reveal their characteristics.
- AI-A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
- AI-A.SSE.3c Use the properties of exponents to rewrite exponential expressions.

- Checkpoint opportunity

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

- Interpret the structure of expressions.
- AI-A.APR Arithmetic with Polynomials and Rational Expressions
- Perform arithmetic operations on polynomials.
- AI-A.APR.1 Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.
- Checkpoint opportunity

- Understand the relationship between zeros and factors of polynomials.
- AI-A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.

- Perform arithmetic operations on polynomials.
- AI-A.CED Creating Equations
- Create equations that describe numbers or relationships.
- AI-A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
- AI-A.CED.2 Create equations and linear inequalities in two variables to represent a real-world context.
- AI-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.
- AI-A.CED.4 Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
- Checkpoint opportunity

- Create equations that describe numbers or relationships.
- AI-A.REI Reasoning with Equations and Inequalities
- Understand solving equations as a process of reasoning and explain the reasoning.
- AI-A.REI.1a Explain each step when solving a linear or quadratic 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.

- Solve equations and inequalities in one variable.
- AI-A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
- AI-A.REI.4 Solve quadratic equations in one variable.
- AI-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. Understand that the quadratic formula is a derivative of this process. - AI-A.REI.4b Solve quadratic equations by: inspection, taking square roots, factoring, completing the square, the quadratic formula, and graphing. Write complex solutions in
*a + bi*form.

- AI-A.REI.4a Use the method of completing the square to transform any quadratic equation in
- Checkpoint opportunity

- Solve systems of equations.
- AI-A.REI.6a Solve systems of linear equations in two variables both algebraically and graphically.
- AI-A.REI.7a Solve a system, with rational solutions, consisting of a linear equation and a quadratic equation (parabolas only) in two variables algebraically and graphically.

- Represent and solve equations and inequalities graphically.
- AI-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.
- AI-A.REI.11 Given the equations
*y*=*f*(*x*) and*y*=*g*(*x*):- AI-A.REI.11.i recognize that each x-coordinate of the intersection(s) is the solution to the equation
*f*(*x*) =*g*(*x*); - AI-A.REI.11.ii find the solutions approximately using technology to graph the functions or make tables of values; and
- AI-A.REI.11.iii interpret the solution in context.

- AI-A.REI.11.i recognize that each x-coordinate of the intersection(s) is the solution to the equation
- AI-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.
- Checkpoint opportunity

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

### AI-F Functions

- AI-F.IF Interpreting Functions
- Understand the concept of a function and use function notation.
- AI-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*). - AI-F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- AI-F.IF.3 Recognize that a sequence is a function whose domain is a subset of the integers.

- AI-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
- Interpret functions that arise in applications in terms of the context.
- AI-F.IF.4 For a function that models a relationship between two quantities:
- AI-F.IF.4.i interpret key features of graphs and tables in terms of the quantities; and
- AI-F.IF.4.ii sketch graphs showing key features given a verbal description of the relationship.

- AI-F.IF.5 Determine the domain of a function from its graph and, where applicable, identify the appropriate domain for a function in context.
- AI-F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.
- Checkpoint opportunity

- AI-F.IF.4 For a function that models a relationship between two quantities:
- Analyze functions using different representations.
- AI-F.IF.7 Graph functions and show key features of the graph by hand and by using technology where appropriate.
- AI-F.IF.7a Graph linear, quadratic, and exponential functions and show key features.
- AI-F.IF.7b Graph square root and piecewise-defined functions, including step functions and absolute value functions, and show key features.

- AI-F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.
- AI-F.IF.8a For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.

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

- AI-F.IF.7 Graph functions and show key features of the graph by hand and by using technology where appropriate.

- Understand the concept of a function and use function notation.
- AI-F.BF Building Functions
- Build a function that models a relationship between two quantities.
- AI-F.BF.1 Write a function that describes a relationship between two quantities.
- AI-F.BF.1a Determine a function from context. Define a sequence explicitly or steps for calculation from a context.

- AI-F.BF.1 Write a function that describes a relationship between two quantities.
- Build new functions from existing functions.
- AI-F.BF.3a Using
*f*(*x*) +*k*,*k**f*(*x*), and*f*(*x*+*k*):- AI-F.BF.3a.i identify the effect on the graph when replacing
*f*(*x*) by*f*(*x*) +*k*,*k**f*(*x*), and*f*(*x*+*k*) for specific values of*k*(both positive and negative); - AI-F.BF.3a.ii find the value of
*k*given the graphs; - AI-F.BF.3a.iii write a new function using the value of
*k*; and - AI-F.BF.3a.iv use technology to experiment with cases and explore the effects on the graph.

- AI-F.BF.3a.i identify the effect on the graph when replacing
- Checkpoint opportunity

- AI-F.BF.3a Using

- Build a function that models a relationship between two quantities.
- AI-F.LE Linear, Quadratic, and Exponential Models
- Construct and compare linear, quadratic, and exponential models and solve problems.
- AI-F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
- AI-F.LE.1a Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal factors over equal intervals.
- AI-F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.
- AI-F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another, and therefore can be modeled exponentially.

- AI-F.LE.2 Construct a linear or exponential function symbolically given:
- AI-F.LE.2.i a graph;
- AI-F.LE.2.ii a description of the relationship;
- AI-F.LE.2.iii two input-output pairs (include reading these from a table).

- AI-F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

- AI-F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
- Interpret expressions for functions in terms of the situation they model.
- AI-F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
- Checkpoint opportunity

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

### AI-S Statistics and Probability

- AI-S.ID Interpreting Categorical and Quantitative Data
- Summarize, represent, and interpret data on a single count or measurement variable.
- AI-S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
- AI-S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, sample standard deviation) of two or more different data sets.
- AI-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).
- Checkpoint opportunity

- Summarize, represent, and interpret data on two categorical and quantitative variables.
- AI-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.
- AI-S.ID.6 Represent bivariate data on a scatter plot, and describe how the variables’ values are related.
- AI-S.ID.6a Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.

- Checkpoint opportunity

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

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