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### N Number and Quantity

- N.RN The Real Number System
- Use properties of rational numbers and irrational numbers.
- N.RN.1 Know and apply the properties of integer exponents to generate equivalent numerical and algebraic expressions.

- Use properties of rational numbers and irrational numbers.
- N.Q Quantities
- Reason quantitatively and use units to solve problems.
- N.Q.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.
- N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
- N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
- Checkpoint opportunity

- Reason quantitatively and use units to solve problems.

### A Algebra

- A.SSE Seeing Structure in Expressions
- 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. For example, interpret
*P*(1 +*r*)^{n}as the product of P and (1 +*r*)^{n}.

- A.SSE.2 Use the structure of an expression to identify ways to rewrite it.

- A.SSE.1 Interpret expressions that represent a quantity in terms of its context.
- 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.

- Checkpoint opportunity

- 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.
- A.APR Arithmetic with Polynomials and Rational Expressions
- Perform arithmetic operations on polynomials.
- A.APR.1 Add, subtract, and multiply polynomials.
- Checkpoint opportunity

- Use polynomial identities to solve problems.
- A.APR.4 Generate polynomial identities from a pattern.

- Perform arithmetic operations on polynomials.
- A.CED Creating Equations
- Create equations that describe numbers or relationships.
- A.CED.1 Apply and extend previous understanding to create equations and inequalities in one variable and use them to solve problems.
- A.CED.2 Apply and extend previous understanding to create equations in two or more 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.
- Checkpoint opportunity

- Create equations that describe numbers or relationships.
- A.REI Reasoning with Equations and Inequalities
- 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.

- Solve equations and inequalities in one variable.
- A.REI.2 Apply and extend previous understanding to solve equations, inequalities, and compound inequalities in one variable, including literal equations and inequalities.
- A.REI.3 Solve equations in one variable and give examples showing how extraneous solutions may arise.
- A.REI.3a Solve rational, absolute value and square root equations.

- A.REI.5 Solve quadratic equations and inequalities.
- A.REI.5a Solve quadratic equations by inspection (e.g., for
*x*² = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives no real solutions.

- A.REI.5a Solve quadratic equations by inspection (e.g., for
- Checkpoint opportunity

- Solve systems of equations.
- A.REI.6 Analyze and solve pairs of simultaneous linear equations.
- A.REI.6a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
- A.REI.6b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
- A.REI.6c Solve real-world and mathematical problems leading to two linear equations in two variables.

- A.REI.6 Analyze and solve pairs of simultaneous linear equations.
- Represent and solve equations and inequalities graphically.
- A.REI.8 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.9 Solve an equation
*f*(*x*) =*g*(*x*) by graphing*y*=*f*(*x*) and*y*=*g*(*x*) and finding the*x*-value of the intersection point. Include cases where*f*(*x*) and/or*g*(*x*) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. - A.REI.10 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.

### F Functions

- F.IF Interpreting Functions
- 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.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
- F.IF.3 Recognize patterns in order to write functions whose domain is a subset of the integers.

- 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
- 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 expressions, graphs and tables in terms of the quantities, and sketch graphs showing key features given a description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
- 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.
- Checkpoint opportunity

- 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 linear, quadratic and absolute value functions and show intercepts, maxima, minima and end behavior.

- F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.
- F.IF.8a Use different forms of linear functions, such as slope-intercept, standard, and point-slope form to show rate of change and intercepts.

- F.IF.9 Compare properties of two functions using a variety of representations (algebraically, graphically, numerically in tables, or by verbal descriptions).
- Checkpoint opportunity

- 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.

- Understand the concept of a function and use function notation.
- F.BF Building Functions
- Build a function that models a relationship between two quantities.
- F.BF.1 Use functions to model real-world relationships.
- F.BF.1a Combine multiple functions to model complex relationships.

- F.BF.1 Use functions to model real-world relationships.
- Build new functions from existing functions.
- F.BF.3 Transform parent functions (
*f*(*x*)) by replacing*f*(*x*) with*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. - Checkpoint opportunity

- F.BF.3 Transform parent functions (

- Build a function that models a relationship between two quantities.

### S Statistics and Probability

- S.ID Interpreting Categorical and Quantitative Data
- Summarize, represent, and interpret data on a single count or measurement variable.
- S.ID.1 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.2 Interpret differences in shape, center, and spread in the context of the data sets using dot plots, histograms, and box plots, accounting for possible effects of extreme data points (outliers).
- Checkpoint opportunity

- Summarize, represent, and interpret data on two categorical and quantitative variables.
- S.ID.4 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.5 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S.ID.5a Use a given linear function to solve problems in the context of data.
- S.ID.5b Fit a linear function to data and use it to solve problems in the context of the data.

- Checkpoint opportunity

- Interpret linear models.
- S.ID.6 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- Checkpoint opportunity

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