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### N Number and Quantity

- 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.

- 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.

- 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.3c Use the properties of exponents to transform expressions for exponential functions.

- 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.CED Creating Equations
- Create equations that describe numbers or relationships.
- A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
- A.CED.1a Focus on applying linear and simple exponential expressions.

- A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- A.CED.2a Focus on applying linear and simple exponential expressions.

- 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.
- A.CED.4b Focus on formulas in which the variable of interest is linear.

- A.CED.1 Create equations and inequalities in one variable and use them to solve problems.

- 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.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

- Solve systems of equations.
- A.REI.5 Verify 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.
- A.REI.6 Solve systems of linear equations algebraically and graphically.
- A.REI.6a Limit to pairs of linear equations in two variables.

- Represent and solve equations and inequalities graphically.
- 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, often forming a curve (which could be a line).
- A.REI.11 Explain why the
*x*-coordinates of the points where the graphs of the equation*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, making tables of values, or finding successive approximations. - 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.

- 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 that sequences are functions, sometimes defined recursively, 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
- 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 graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
- F.IF.4a Focus on linear and exponential functions.

- F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
- F.IF.5a Focus on linear and exponential functions.

- F.IF.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.
- Analyze functions using different representations.
- F.IF.7 Graph functions expressed symbolically and indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.
- F.IF.7a Graph linear functions and indicate intercepts.
- F.IF.7e Graph simple exponential functions, indicating intercepts and end behavior.

- F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- F.IF.9a Focus on linear and exponential functions.

- F.IF.7 Graph functions expressed symbolically and indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.

- 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 Write a function that describes a relationship between two quantities.
- F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from context.
*Focus on linear and exponential functions.*

- F.BF.1a Determine an explicit expression, a recursive process, or steps for calculation from context.
- F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

- F.BF.1 Write a function that describes a relationship between two quantities.
- Build new functions from existing functions.
- F.BF.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. - F.BF.4 Find inverse functions.
- F.BF.4a Informally determine the input of a function when the output is known.

- F.BF.3 Identify the effect on the graph of replacing

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

- F.LE.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).

- 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.
- F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

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

### G Geometry

- G.CO Congruence
- Experiment with transformations in the plane.
- G.CO.1 Know precise definitions of ray, angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and arc length.
- G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not, e.g., translation versus horizontal stretch.
- G.CO.3 Identify the symmetries of a figure, which are the rotations and reflections that carry it onto itself.
- G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
- G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using items such as graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

- Understand congruence in terms of rigid motions.
- G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
- G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
- G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

- Prove geometric theorems both formally and informally using a variety of methods.
- G.CO.9 Prove and apply theorems about lines and angles.
- G.CO.10 Prove and apply theorems about triangles.
- G.CO.11 Prove and apply theorems about parallelograms.

- Make geometric constructions.
- G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
- G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

- Classify and analyze geometric figures.
- G.CO.14 Classify two-dimensional figures in a hierarchy based on properties.

- Experiment with transformations in the plane.
- G.C Circles
- Understand and apply theorems about circles.
- G.C.2 Identify and describe relationships among angles, radii, chords, tangents, and arcs and use them to solve problems.
- G.C.3 Construct the inscribed and circumscribed circles of a triangle; prove and apply the property that opposite angles are supplementary for a quadrilateral inscribed in a circle.
- G.C.4 Construct a tangent line from a point outside a given circle to the circle.

- Understand and apply theorems about circles.
- G.GPE Expressing Geometric Properties with Equations
- Use coordinates to prove simple geometric theorems algebraically and to verify specific geometric statements.
- G.GPE.5 Justify the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems, e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point.
- G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

- Use coordinates to prove simple geometric theorems algebraically and to verify specific geometric statements.

### 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 Represent data with plots on the real number line (dot plots, histograms, and box plots) in the context of real-world applications using the GAISE model.
- S.ID.2 In the context of real-world applications by using the GAISE model, use statistics appropriate to the shape of the data distribution to compare center (median and mean) and spread (mean absolute deviation, interquartile range, and standard deviation) of two or more different data sets.
- S.ID.3 In the context of real-world applications by using the GAISE model, interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

- Summarize, represent, and interpret data on two categorical and quantitative variables.
- 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.
- S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
- S.ID.6c Fit a linear function for a scatterplot that suggests a linear association.

- Interpret linear models.
- S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit

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