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### A1.NQ Number and Quantity

- A1.NQ.A Extend and use properties of rational exponents.
- A1.NQ.A.1 Explain how the meaning of rational exponents extends from the properties of integer exponents.
- A1.NQ.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1.
- Checkpoint opportunity

- A1.NQ.B Use units to solve problems.
- A1.NQ.B.3 Use units of measure as a way to understand and solve problems involving quantities.
- A1.NQ.B.3.a Identify, label and use appropriate units of measure within a problem.
- A1.NQ.B.3.b Convert units and rates.
- A1.NQ.B.3.c Use units within problems.
- A1.NQ.B.3.d Choose and interpret the scale and the origin in graphs and data displays.

- A1.NQ.B.4 Define and use appropriate quantities for representing a given context or problem.
- A1.NQ.B.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- Checkpoint opportunity

- A1.NQ.B.3 Use units of measure as a way to understand and solve problems involving quantities.

### A1.SSE Seeing Structure in Expressions

- A1.SSE.A Interpret and use structure.
- A1.SSE.A.1 Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions.
- A1.SSE.A.2 Analyze the structure of polynomials to create equivalent expressions or equations.
- A1.SSE.A.3 Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.
- A1.SSE.A.3.a Find the zeros of a quadratic function by rewriting it in factored form.
- A1.SSE.A.3.b Find the maximum or minimum value of a quadratic function by completing the square.

- Checkpoint opportunity

### A1.CED Creating Equations

- A1.CED.A Create equations that describe linear, quadratic and exponential relationships.
- A1.CED.A.1 Create equations and inequalities in one variable and use them to model and/or solve problems.
- A1.CED.A.2 Create and graph linear, quadratic and exponential equations in two variables.
- A1.CED.A.3 Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context.
- A1.CED.A.4 Solve literal equations and formulas for a specified variable that highlights a quantity of interest.
- Checkpoint opportunity

### A1.REI Reasoning with Equations and Inequalities

- A1.REI.A Understand solving equations as a process, and solve equations and inequalities in one variable.
- A1.REI.A.1 Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(s) as the original.
- A1.REI.A.2 Solve problems involving quadratic equations.
- A1.REI.A.2.a Use the method of completing the square to create an equivalent quadratic equation.
- A1.REI.A.2.b Derive the quadratic formula.
- A1.REI.A.2.c Analyze different methods of solving quadratic equations.

- Checkpoint opportunity

- A1.REI.B Solve systems of equations.
- A1.REI.B.3 Solve a system of linear equations algebraically and/or graphically.
- A1.REI.B.4 Solve a system consisting of a linear equation and a quadratic equation algebraically and/or graphically.
- A1.REI.B.5 Justify that the technique of linear combination produces an equivalent system of equations.

- A1.REI.C Represent and solve linear and exponential equations and inequalities graphically.
- A1.REI.C.6 Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane.
- A1.REI.C.7 Graph the solution to a linear inequality in two variables.
- A1.REI.C.8 Solve problems involving a system of linear inequalities.
- Checkpoint opportunity

### A1.APR Arithmetic with Polynomials and Rational Expressions

- A1.APR.A Perform operations on polynomials.
- A1.APR.A.1 Add, subtract and multiply polynomials, and understand that polynomials follow the same general rules of arithmetic and are closed under these operations.
- A1.APR.A.2 Divide polynomials by monomials.
- Checkpoint opportunity

### A1.IF Interpreting Functions

- A1.IF.A Understand the concept of a function and use function notation.
- A1.IF.A.1 Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range.
- A1.IF.A.1.a Represent a function using function notation.
- A1.IF.A.1.b Understand that the graph of a function labeled ∫ is the set of all ordered pairs (x, y) that satisfy the equation y=f(x).

- A1.IF.A.2 Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

- A1.IF.A.1 Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range.
- A1.IF.B Interpret linear, quadratic and exponential functions in terms of the context.
- A1.IF.B.3 Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.
- A1.IF.B.4 Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.
- A1.IF.B.5 Determine the average rate of change of a function over a specified interval and interpret the meaning.
- A1.IF.B.6 Interpret the parameters of a linear or exponential function in terms of the context.
- Checkpoint opportunity

- A1.IF.C Analyze linear, quadratic and exponential functions using different representations.
- A1.IF.C.7 Graph functions expressed symbolically and identify and interpret key features of the graph.
- A1.IF.C.8 Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context.
- A1.IF.C.9 Compare the properties of two functions given different representations.
- Checkpoint opportunity

### A1.BF Building Functions

- A1.BF.A Build new functions from existing functions (limited to linear, quadratic and exponential).
- A1.BF.A.1 Analyze the effect of translations and scale changes on functions.
- Checkpoint opportunity

### A1.LQE Linear, Quadratic and Exponential Models

- A1.LQE.A Construct and compare linear, quadratic and exponential models and solve problems.
- A1.LQE.A.1 Distinguish between situations that can be modeled with linear or exponential functions.
- A1.LQE.A.1.a Determine that linear functions change by equal differences over equal intervals.
- A1.LQE.A.1.b Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.

- A1.LQE.A.2 Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.
- A1.LQE.A.3 Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.
- Checkpoint opportunity

- A1.LQE.A.1 Distinguish between situations that can be modeled with linear or exponential functions.
- A1.LQE.B Use arithmetic and geometric sequences.
- A1.LQE.B.4 Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.
- A1.LQE.B.5 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers.
- A1.LQE.B.6 Find the terms of sequences given an explicit or recursive formula.
- Checkpoint opportunity

### A1.DS Data and Statistical Analysis

- A1.DS.A Summarize, represent and interpret data.
- A1.DS.A.1 Analyze and interpret graphical displays of data.
- A1.DS.A.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
- A1.DS.A.3 Interpret differences in shape, center and spreads in the context of the data sets, accounting for possible effects of outliers.
- A1.DS.A.4 Summarize data in two-way frequency tables.
- A1.DS.A.4.a Interpret relative frequencies in the context of the data.
- A1.DS.A.4.b Recognize possible associations and trends in the data.

- A1.DS.A.5 Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.
- A1.DS.A.5.a Construct a linear function to model bivariate data represented on a scatter plot that minimizes residuals.
- A1.DS.A.5.b Construct an exponential function to model bivariate data represented on a scatter plot that minimizes residuals.

- A1.DS.A.6 Interpret the slope (rate of change) and the y-intercept (constant term) of a linear model in the context of the data.
- A1.DS.A.7 Determine and interpret the correlation coefficient for a linear association.
- A1.DS.A.8 Distinguish between correlation and causation.
- Checkpoint opportunity